Abstract:Geometry and orientation plays an important role in natural convection heat transfer. For
horizontal rectangular fin array a chimney flow pattern is developed due to density difference. This flow
pattern creates a stagnant zone near central bottom region. That portion does not contribute much towards
heat dissipation. This area is removed from fins and they became inverted notched fins. This modified geometry
reduces material cost, material weight without hampering heat transfer rate. Numerical models are prepaid to
investigate heat transfer characteristics in plane fins and inverted notched fins. This investigation is also
extended over different types of notches and their effectiveness comparison. Fin spacing, fin height, fin length,
heater input, percentage of area removed in the form of inverted notch are the parameters under
consideration. This analysis is done numerically using CFD package (Fluent). It is found that the heat transfer
coefficient of inverted notch fin array is 25% to 35% higher as compared with normal fin array. Also we found
that the triangular shape notch gives better result than trapezoidal and rectangular shape notch.
Key words: Inverted Notched Fin, Chimney Flow, Natural Convection, Heat transfer coefficient enhancement
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
Analysis of Coiled-Tube Heat Exchangers to Improve Heat Transfer Rate With Sp...IJMER
Steady heat transfer enhancement has been studied in helically coiled-tube heat exchangers. The outer side of the wall of the heat exchanger contains a helical corrugation which makes a helical rib on the inner side of the tube wall to induce additional swirling motion of fluid particles. Numerical calculations have been carried out to examine different geometrical parameters and the impact of flow and thermal boundary conditions for the heat transfer rate in laminar and transitional flow regimes. Calculated results have been compared to existing empirical formula and experimental tests to investigate the validity of the numerical results in case of common helical tube heat exchanger and additionally results of the numerical computation of corrugated straight tubes for laminar and transition flow have been validated with experimental tests available in the literature. Comparison of the flow and temperature fields in case of common helical tube and the coil with spirally corrugated wall configuration are discussed. Heat exchanger coils with helically corrugated wall configuration show 80–100% increase for the inner side heat transfer rate due to the additionally developed swirling motion while the relative pressure drop is 10–600% larger compared to the common helically coiled heat exchangers. New empirical Co-relation has been proposed for the fully developed inner side heat transfer prediction in case of helically corrugated wall configuration.
Heat transfer augmentation in different geometries of dimpled surface under n...eSAT Journals
Abstract The prime objective of present work is to study experimentally the heat transfer augmentation through various geometries of dimpled surfaces in longitudinal and lateral directions. In this paper horizontal rectangular plates of copper and aluminum with different dimpled geometries (like square, circular and triangular) for in-line arrangements were studied in natural convection with steady laminar external flow condition. The various parameters considered for study are Nusselt number, heat transfer coefficient and heat transfer rate for a constant Prandtl number (0.7) and Grashof number (104-107).It has been found that the heat transfer coefficient and heat transfer rate increases for various dimpled surfaces as compared to plane surface. It has been also found that the heat transfer coefficient and heat transfer rate increases along longitudinal direction as compared to lateral direction. And it is seen that heat transfer rate is maximum for triangular shape dimple when the apex of triangle is faced towards inlet of air flow Finally it is concluded that heat transfer enhancement takes place along the dimpled surface
Heat transfer augmentation in different geometries of dimpled surface under n...eSAT Publishing House
The document experimentally studies heat transfer augmentation through various dimpled surface geometries under natural convection. It tests aluminum and copper plates with square, circular, and triangular dimple shapes. It finds that heat transfer rate, coefficient, and Nusselt number all increase for dimpled surfaces compared to plain surfaces, and are highest for triangular dimples with the apex facing inlet air flow. Heat transfer generally increases more for aluminum with square and triangular base dimples, while copper performs better with circular and triangular apex dimples. The study concludes dimples enhance heat transfer under natural convection compared to plain surfaces.
Experimental Investigation of Heat Transfer through Rectangular and Trapezoid...IRJET Journal
The document describes an experimental investigation of heat transfer through rectangular and trapezoidal fins made of aluminum 6063 alloy. Rectangular and trapezoidal fins were fabricated from the alloy and experiments were conducted under steady state conditions. Local temperature, heat flux, heat transfer coefficients, and Reynolds numbers were estimated. The findings showed that forced convection was more effective than free convection, and the trapezoidal fin enhanced heat transfer by up to 48% compared to the rectangular fin under different heat supply conditions. The document provides details on the experimental setup, material properties of the aluminum 6063 alloy, and methodology for collecting temperature readings along the fins.
IRJET- Thermal Analysis on Solar Air Heater DuctIRJET Journal
This document summarizes a numerical study on the effects of transverse rectangular ribs on heat transfer properties in a solar air heater duct. Computational fluid dynamics (CFD) simulations were performed to analyze thin and square ribs arranged in single, staggered, and inline patterns. The simulations found that introducing ribs significantly increased heat transfer compared to a smooth duct. Thin ribs performed better than square ribs. Inline thin ribs produced a 1.83 times higher heat transfer coefficient than the smooth duct. Reynolds number increases led to higher Nusselt numbers for all cases. Staggered ribs had lower heat transfer than inline ribs. The study provides conclusions on rib effects and turbulence model selection for predicting solar air heater performance.
This document describes mathematical models for simulating the temperature fields of gas turbine blades during convective cooling. It presents boundary integral equation methods (BIEM) and finite difference methods (FDM) for calculating the stationary and quasi-stationary temperature distribution on a blade profile with radial cooling channels. The BIEM approach formulates the problem as a system of boundary integral equations involving temperature values and heat transfer coefficients on the blade surface and cooling channel boundaries. Numerical methods are developed to solve these equations, including discrete logarithmic potential operators and non-uniform surface discretizations. The reliability of the proposed methods is confirmed through computational and experimental analysis of heat transfer for a gas turbine nozzle blade.
Enhancement of Heat Transfer and Thermo-Hydraulic Performance Using Triangula...IJERA Editor
Solar heat has been thrust area of research to explore renewable energy utilisation for the past few decades. In
solar air heaters artificial roughness is tried on the surface of the absorber plate by adding small roughness
elements to enhance the heat transfer rate. In the present work triangular protrusion are provided to act as
roughness elements over the surface of the aluminum absorber plate. The experimental study is carried out on
the effect of change in apex angle of protrusions on the heat transfer rate by keeping the other design parameters
unchanged. Maximum heat transfer rate and thermo-hydraulic performance between the range of apex angle 300
and 600 is studied. The Nusselt number is between 50 and 110, friction factor 4.5-6.7x10-3, Stanton number is 6-
14x10-3. The heat transfer rate and thermo-hydraulic performance are observed to be maximum for 450 apex
angle and least for the 600 plate.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
Analysis of Coiled-Tube Heat Exchangers to Improve Heat Transfer Rate With Sp...IJMER
Steady heat transfer enhancement has been studied in helically coiled-tube heat exchangers. The outer side of the wall of the heat exchanger contains a helical corrugation which makes a helical rib on the inner side of the tube wall to induce additional swirling motion of fluid particles. Numerical calculations have been carried out to examine different geometrical parameters and the impact of flow and thermal boundary conditions for the heat transfer rate in laminar and transitional flow regimes. Calculated results have been compared to existing empirical formula and experimental tests to investigate the validity of the numerical results in case of common helical tube heat exchanger and additionally results of the numerical computation of corrugated straight tubes for laminar and transition flow have been validated with experimental tests available in the literature. Comparison of the flow and temperature fields in case of common helical tube and the coil with spirally corrugated wall configuration are discussed. Heat exchanger coils with helically corrugated wall configuration show 80–100% increase for the inner side heat transfer rate due to the additionally developed swirling motion while the relative pressure drop is 10–600% larger compared to the common helically coiled heat exchangers. New empirical Co-relation has been proposed for the fully developed inner side heat transfer prediction in case of helically corrugated wall configuration.
Heat transfer augmentation in different geometries of dimpled surface under n...eSAT Journals
Abstract The prime objective of present work is to study experimentally the heat transfer augmentation through various geometries of dimpled surfaces in longitudinal and lateral directions. In this paper horizontal rectangular plates of copper and aluminum with different dimpled geometries (like square, circular and triangular) for in-line arrangements were studied in natural convection with steady laminar external flow condition. The various parameters considered for study are Nusselt number, heat transfer coefficient and heat transfer rate for a constant Prandtl number (0.7) and Grashof number (104-107).It has been found that the heat transfer coefficient and heat transfer rate increases for various dimpled surfaces as compared to plane surface. It has been also found that the heat transfer coefficient and heat transfer rate increases along longitudinal direction as compared to lateral direction. And it is seen that heat transfer rate is maximum for triangular shape dimple when the apex of triangle is faced towards inlet of air flow Finally it is concluded that heat transfer enhancement takes place along the dimpled surface
Heat transfer augmentation in different geometries of dimpled surface under n...eSAT Publishing House
The document experimentally studies heat transfer augmentation through various dimpled surface geometries under natural convection. It tests aluminum and copper plates with square, circular, and triangular dimple shapes. It finds that heat transfer rate, coefficient, and Nusselt number all increase for dimpled surfaces compared to plain surfaces, and are highest for triangular dimples with the apex facing inlet air flow. Heat transfer generally increases more for aluminum with square and triangular base dimples, while copper performs better with circular and triangular apex dimples. The study concludes dimples enhance heat transfer under natural convection compared to plain surfaces.
Experimental Investigation of Heat Transfer through Rectangular and Trapezoid...IRJET Journal
The document describes an experimental investigation of heat transfer through rectangular and trapezoidal fins made of aluminum 6063 alloy. Rectangular and trapezoidal fins were fabricated from the alloy and experiments were conducted under steady state conditions. Local temperature, heat flux, heat transfer coefficients, and Reynolds numbers were estimated. The findings showed that forced convection was more effective than free convection, and the trapezoidal fin enhanced heat transfer by up to 48% compared to the rectangular fin under different heat supply conditions. The document provides details on the experimental setup, material properties of the aluminum 6063 alloy, and methodology for collecting temperature readings along the fins.
IRJET- Thermal Analysis on Solar Air Heater DuctIRJET Journal
This document summarizes a numerical study on the effects of transverse rectangular ribs on heat transfer properties in a solar air heater duct. Computational fluid dynamics (CFD) simulations were performed to analyze thin and square ribs arranged in single, staggered, and inline patterns. The simulations found that introducing ribs significantly increased heat transfer compared to a smooth duct. Thin ribs performed better than square ribs. Inline thin ribs produced a 1.83 times higher heat transfer coefficient than the smooth duct. Reynolds number increases led to higher Nusselt numbers for all cases. Staggered ribs had lower heat transfer than inline ribs. The study provides conclusions on rib effects and turbulence model selection for predicting solar air heater performance.
This document describes mathematical models for simulating the temperature fields of gas turbine blades during convective cooling. It presents boundary integral equation methods (BIEM) and finite difference methods (FDM) for calculating the stationary and quasi-stationary temperature distribution on a blade profile with radial cooling channels. The BIEM approach formulates the problem as a system of boundary integral equations involving temperature values and heat transfer coefficients on the blade surface and cooling channel boundaries. Numerical methods are developed to solve these equations, including discrete logarithmic potential operators and non-uniform surface discretizations. The reliability of the proposed methods is confirmed through computational and experimental analysis of heat transfer for a gas turbine nozzle blade.
Enhancement of Heat Transfer and Thermo-Hydraulic Performance Using Triangula...IJERA Editor
Solar heat has been thrust area of research to explore renewable energy utilisation for the past few decades. In
solar air heaters artificial roughness is tried on the surface of the absorber plate by adding small roughness
elements to enhance the heat transfer rate. In the present work triangular protrusion are provided to act as
roughness elements over the surface of the aluminum absorber plate. The experimental study is carried out on
the effect of change in apex angle of protrusions on the heat transfer rate by keeping the other design parameters
unchanged. Maximum heat transfer rate and thermo-hydraulic performance between the range of apex angle 300
and 600 is studied. The Nusselt number is between 50 and 110, friction factor 4.5-6.7x10-3, Stanton number is 6-
14x10-3. The heat transfer rate and thermo-hydraulic performance are observed to be maximum for 450 apex
angle and least for the 600 plate.
Numerical simulation of gas turbine blade cooling for enhancement of heat tra...eSAT Publishing House
This document summarizes a numerical simulation study of gas turbine blade tip cooling. The study models a two-pass serpentine cooling channel inside the blade with and without pin fins on the tip surface. It was found that providing pin fins at the tip surface can increase heat transfer by up to 1.3 times compared to a smooth surface, with pressure drop increasing by less than 6%. Proper placement and number of pin fins is recommended for enhancing heat transfer and cooling of the turbine blade tip.
IRJET- Optimization of Annular Fins by Modifying its Geometry with and Withou...IRJET Journal
This document reviews optimization of annular fins by modifying their geometry with and without perforations. It begins with an abstract discussing how fins dissipate heat and how their efficiency can be improved by increasing length, changing geometry, or adding more fins. It then discusses types of fins and their applications. The main body discusses how heat transfer occurs in fins and classifications of fins. It reviews literature on optimizing annular fin performance by varying materials, geometry, perforations, and other factors. The conclusion is that further optimization of annular fins is still possible in these and other ways. The future scope discusses analyzing perforated fins of different shapes and materials to further optimize efficiency and effectiveness.
STUDY OF HEAT TRANSFER ON BROKEN ARC ROUGHNESS ELEMENTS ON THE ABSORBER PLATE...IAEME Publication
Performance of solar air heater can be enhanced by adding roughness to the inner periphery. The present study on the effect of various shape parameters for broken arc roughness elements of heat transfer and friction factor characteristics of rectangular duct. The duct has Reynolds number (Re) range of 3000-22300, respective roughness height (e/D) values is 0.045, arc angle (α) is 60˚ and roughness width (W/w) is 5 and relatively roughness pitch is 8.
This document summarizes the numerical analysis of different parallel plate heat sink designs for electronic cooling applications. It discusses:
1) The simulation of a baseline heat sink case and a shielded heat sink within a chimney structure to compare heat transfer performance. The shielded case showed a 50% improvement in heat transfer.
2) The addition of a cross-cut modification to the heat sink, which was modeled using two turbulence models. This cross-cut design showed an average 17% increase in heat transfer compared to the shielded straight fin case.
3) The modeling of the cross-cut heat sink within a pumping system to induce forced convection. A pressure difference between the cross-cut and outlet was
This document summarizes a research project that aims to thermally enhance a plate-fin heat exchanger using secondary structures called cross-cuts. Cross-cuts are sections removed from fins perpendicular to airflow to disrupt boundary layer development. The project will test various cross-cut configurations and validate correlations from a previous study. A plate-fin heat sink will be compared to designs with one and two cross-cuts. The goal is to validate that a single cross-cut provides the best thermal performance improvement of 4-13% over the base design within a pumping power range of 0.01-1W.
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology
This document discusses a study that uses computational fluid dynamics (CFD) simulation to analyze the fluid flow and heat transfer characteristics of rectangular fin arrays equipped with circular perforations on a horizontal surface, and compares it to a solid fin array. The simulation is performed using ANSYS software. It validates the simulation results with experimental data. The study varies parameters like diameter and number of perforations as well as heat input. It finds that perforations enhance heat dissipation by increasing fluid flow and movement around the fins compared to a solid fin array.
Comparative Study of Heat Transfer Enhancement in Rectangular And Interruped ...IJERDJOURNAL
Abstract: To increase the heat transfer rate of heat exchanger through fins in compact regionthe louvered interrupted plate fins has designed for increasing fins surface area. FLUENT and Multi-physics software are used in order to develop a 3-D numerical model for investigation ofinterrupted louvered fins. ILF analyzed by CFD tool, on the basis of geometrical parameters the compact relationship for Nusselt Number exhibits enhancement of thermal performance. Fin-plate weight reduces while surface area increases. Air is taken as the working fluid andThe flow regime is assumed to be turbulence, and the mean velocity is such that the Reynolds numbers of interest are above the critical Reynolds number. This study gives a performance data for a rectangular fin in simple and ILF in a plate-fin heat exchanger. In order to evaluate the performance, bulk temperature and combined span wise average Nusselt number (Nusa) are calculated. The heat transferenhancement is observed with the use of different interruption angles of 300 , 400 and 50
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Analysis of Natural Convention Heat Transfer Enhancement in Finned Tube Heat ...journal ijrtem
ABSTRACT: Most of the engineering problems require high performance heat transfer components with progressively less weight, volumes, accommodating shapes and costs. Air cooled heat exchangers are subjected to air on outer side of heat exchanger surface on in heat recovery systems like economizers gases are subjected on one side of tube surface. On air or gas side heat transfer coefficient is less. Extended surface (fins) are one of the next exchanging devices that are employed extensively to increase heat transfer rates from tubular heat exchangers. The rate of heat transfer depends on the surface area of fin available for exchanging the heat transfer rate from the primary surface of cylindrical shape. Present study focuses on enhancement of heat transfer by using both circular and elliptical type of fins. The present paper attempts to examine trend of heat transfer coefficient experimentally and by using CFD software for various types of elliptical fins with i) varying elliptical ratio, ii) changing orientation of mounting of heat exchanger tube with elliptical fins, iii) varying spacing or fin density. KEY WORDS: Natural convection, Heat transfer enhancements, Elliptical fin, Fin orientation, Fin density.
This document discusses a numerical study examining the effects of tip clearance and casing recess on heat transfer and stage efficiency in axial turbines. Calculations were performed considering passage geometries with and without casing recess, and tip clearances of 0%, 1%, 1.5%, and 3% of the passage height. The results showed an increase in thermal load on heat transfer surfaces with increased tip clearance. Casing recess reduced heat transfer on the pressure side but effects on the suction side were more complex. Casing recess significantly reduced heat load and peak values on the blade tip. A small reduction in heat transfer on the casing was also observed. Efficiency was found to linearly decrease with increased tip clearance, and casing recess had a small positive
IRJET-Enhancing the Performance of Hybrid Microgrid using non Isolated Single...IRJET Journal
This document analyzes heat transfer in a light passenger car radiator with various geometrical configurations using computational fluid dynamics (CFD). It studies a staggered fin-and-tube radiator with circular and oval tubes. The radiator is modeled and analyzed in FLUENT to obtain velocity, temperature, and pressure contours. Oval tubes are found to improve heat transfer compared to circular tubes. Specifically, oval tube configurations reduce temperature differences between the tubes and air, indicating more efficient heat absorption. While circular tubes show higher temperatures, oval tube designs enhance convection and lower outlet temperatures. In conclusion, varying the tube shape geometrically through oval designs improves the radiator's thermal performance.
This document discusses a numerical analysis of natural convection cooling of electronic components mounted on an aluminum plate within the walls of a train. The study examines the effect of a discontinuous heat flux distribution from the components on heat transfer. The results show that the heat flux distribution significantly influences cooling efficiency. Optimizing the placement and sizing of components can maximize heat transfer and minimize temperatures for improved cooling of power converters inside trains.
The document compares the thermal performance of flat plate fins and inline strip fins heat sinks. It presents Nusselt number correlations from literature to model the convective heat transfer from the fins. The correlations consider heat transfer from the fins but not the bare heat sink base. The study includes an estimate of heat transfer from the base, providing a more realistic thermal resistance calculation. Results show inline strip fins have higher heat transfer coefficients that compensate for their reduced area, yielding lower thermal resistances than plate fins. Considering heat transfer from the base provides an even lower thermal resistance for both heat sink designs.
Natural convection heat transfer in inclined open annulus passege heated from...IAEME Publication
This document summarizes an experimental study on natural convection heat transfer in an open cylindrical annulus heated from both the inner and outer sides. The study examines the effects of inclination angle (0°, 30°, 60°, 90°) and heat flux (70-600 W/m2) on the local and average Nusselt number. The results show that the Nusselt number increases with both increasing heat flux and inclination angle from horizontal to vertical. Empirical correlations between the average Nusselt number and Rayleigh number are developed from the results.
This document summarizes a study on improving the cooling efficiency of fins in a two-stage reciprocating compressor through finite element analysis and dimensional modification. The existing annular fins are made of aluminum alloy. A finite element model of the fins is created in ANSYS to analyze temperature distribution over time under natural convection conditions. The results show the fins reach room temperature in 30 minutes. The fins are then modified by increasing the number of fins from 11 to 13. Finite element analysis of the modified fins shows cooling time is reduced to 22 minutes. In conclusion, modifying the fin geometry through additional fins improves the cooling rate of the reciprocating compressor.
Natural convection heat transfer inside inclined open cylinderIAEME Publication
This document summarizes an experimental study on natural convection heat transfer inside an inclined open cylinder. The study investigated the effects of inclination angle (0°, 30°, 60°, 90°) and heat flux (70-600 W/m2) on the heat transfer. Empirical correlations were developed relating the average Nusselt number to the Rayleigh number. Results showed that heat transfer, as measured by the local and average Nusselt number, increased with increasing heat flux and inclination angle from horizontal to vertical.
This document summarizes a numerical study that examines the effects of fin spacing, fin material, and jet velocity on the heat transfer performance of plate fin heat sinks cooled by impinging air jets. The study considers fin spacings of 2mm, 3mm, and 4mm, and fin materials of aluminum, copper, and steel. Jet velocities of 5m/s, 10m/s, and 15m/s are examined. The results show that heat transfer rate increases with decreasing fin spacing, higher thermal conductivity fin materials like copper, and increasing jet velocity. Copper fins achieved the highest heat transfer rates but are heavier and more expensive than aluminum. A fin spacing of 2mm with aluminum fins and a jet velocity of 15
This document summarizes research on using finite element analysis and crash test dummies to assess driver side knee injuries and the performance of knee airbags. It describes how a finite element model of a knee airbag was developed and simulated a frontal crash impact scenario with and without the airbag. The results showed that the knee airbag reduced peak knee forces by 68.5% compared to the case without an airbag, demonstrating the effectiveness of knee airbags in mitigating knee injuries during frontal collisions.
This document discusses determining the optimal location for wind turbines on the roofs of two different buildings using wind tunnel testing. Models of both buildings were constructed at a 1:100 scale and tested in a wind tunnel. For Building A, the most stable locations for wind turbines were found to be above 2.5 meters on the west-facing wall and above 10 meters in the center of the roof. Turbulence was highest near the center and downwind side of the roof. An automatic weather station installed on Building A's roof measured turbulence intensity values consistent with the wind tunnel results.
This document proposes a dynamic seat allocation system for Indian Railways using QR codes and a mobile application. The key points are:
1. The system uses QR codes embedded with passenger-specific URLs to identify passengers and dynamically allocate vacant seats. Passengers scan the QR code when boarding to check-in.
2. If seats remain vacant, the system reflects them as available for other passengers like waitlisted travelers to book instantly. This increases revenue and transparency.
3. Traveling ticket examiners use a mobile app to verify passenger details by scanning QR codes, making the checking process faster and more efficient.
This document evaluates the implementation of total quality management (TQM) as an engineering practice in Jordanian construction projects. It analyzes TQM implementation based on two main factors - continuous improvement and customer satisfaction. Data was collected through a questionnaire survey of 177 engineers. The study found that TQM implementation was at a moderate level across all construction project phases in Jordan. TQM is considered an important modern management system that can help address quality problems in the Jordanian construction sector if fully adopted.
Numerical simulation of gas turbine blade cooling for enhancement of heat tra...eSAT Publishing House
This document summarizes a numerical simulation study of gas turbine blade tip cooling. The study models a two-pass serpentine cooling channel inside the blade with and without pin fins on the tip surface. It was found that providing pin fins at the tip surface can increase heat transfer by up to 1.3 times compared to a smooth surface, with pressure drop increasing by less than 6%. Proper placement and number of pin fins is recommended for enhancing heat transfer and cooling of the turbine blade tip.
IRJET- Optimization of Annular Fins by Modifying its Geometry with and Withou...IRJET Journal
This document reviews optimization of annular fins by modifying their geometry with and without perforations. It begins with an abstract discussing how fins dissipate heat and how their efficiency can be improved by increasing length, changing geometry, or adding more fins. It then discusses types of fins and their applications. The main body discusses how heat transfer occurs in fins and classifications of fins. It reviews literature on optimizing annular fin performance by varying materials, geometry, perforations, and other factors. The conclusion is that further optimization of annular fins is still possible in these and other ways. The future scope discusses analyzing perforated fins of different shapes and materials to further optimize efficiency and effectiveness.
STUDY OF HEAT TRANSFER ON BROKEN ARC ROUGHNESS ELEMENTS ON THE ABSORBER PLATE...IAEME Publication
Performance of solar air heater can be enhanced by adding roughness to the inner periphery. The present study on the effect of various shape parameters for broken arc roughness elements of heat transfer and friction factor characteristics of rectangular duct. The duct has Reynolds number (Re) range of 3000-22300, respective roughness height (e/D) values is 0.045, arc angle (α) is 60˚ and roughness width (W/w) is 5 and relatively roughness pitch is 8.
This document summarizes the numerical analysis of different parallel plate heat sink designs for electronic cooling applications. It discusses:
1) The simulation of a baseline heat sink case and a shielded heat sink within a chimney structure to compare heat transfer performance. The shielded case showed a 50% improvement in heat transfer.
2) The addition of a cross-cut modification to the heat sink, which was modeled using two turbulence models. This cross-cut design showed an average 17% increase in heat transfer compared to the shielded straight fin case.
3) The modeling of the cross-cut heat sink within a pumping system to induce forced convection. A pressure difference between the cross-cut and outlet was
This document summarizes a research project that aims to thermally enhance a plate-fin heat exchanger using secondary structures called cross-cuts. Cross-cuts are sections removed from fins perpendicular to airflow to disrupt boundary layer development. The project will test various cross-cut configurations and validate correlations from a previous study. A plate-fin heat sink will be compared to designs with one and two cross-cuts. The goal is to validate that a single cross-cut provides the best thermal performance improvement of 4-13% over the base design within a pumping power range of 0.01-1W.
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology
This document discusses a study that uses computational fluid dynamics (CFD) simulation to analyze the fluid flow and heat transfer characteristics of rectangular fin arrays equipped with circular perforations on a horizontal surface, and compares it to a solid fin array. The simulation is performed using ANSYS software. It validates the simulation results with experimental data. The study varies parameters like diameter and number of perforations as well as heat input. It finds that perforations enhance heat dissipation by increasing fluid flow and movement around the fins compared to a solid fin array.
Comparative Study of Heat Transfer Enhancement in Rectangular And Interruped ...IJERDJOURNAL
Abstract: To increase the heat transfer rate of heat exchanger through fins in compact regionthe louvered interrupted plate fins has designed for increasing fins surface area. FLUENT and Multi-physics software are used in order to develop a 3-D numerical model for investigation ofinterrupted louvered fins. ILF analyzed by CFD tool, on the basis of geometrical parameters the compact relationship for Nusselt Number exhibits enhancement of thermal performance. Fin-plate weight reduces while surface area increases. Air is taken as the working fluid andThe flow regime is assumed to be turbulence, and the mean velocity is such that the Reynolds numbers of interest are above the critical Reynolds number. This study gives a performance data for a rectangular fin in simple and ILF in a plate-fin heat exchanger. In order to evaluate the performance, bulk temperature and combined span wise average Nusselt number (Nusa) are calculated. The heat transferenhancement is observed with the use of different interruption angles of 300 , 400 and 50
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Analysis of Natural Convention Heat Transfer Enhancement in Finned Tube Heat ...journal ijrtem
ABSTRACT: Most of the engineering problems require high performance heat transfer components with progressively less weight, volumes, accommodating shapes and costs. Air cooled heat exchangers are subjected to air on outer side of heat exchanger surface on in heat recovery systems like economizers gases are subjected on one side of tube surface. On air or gas side heat transfer coefficient is less. Extended surface (fins) are one of the next exchanging devices that are employed extensively to increase heat transfer rates from tubular heat exchangers. The rate of heat transfer depends on the surface area of fin available for exchanging the heat transfer rate from the primary surface of cylindrical shape. Present study focuses on enhancement of heat transfer by using both circular and elliptical type of fins. The present paper attempts to examine trend of heat transfer coefficient experimentally and by using CFD software for various types of elliptical fins with i) varying elliptical ratio, ii) changing orientation of mounting of heat exchanger tube with elliptical fins, iii) varying spacing or fin density. KEY WORDS: Natural convection, Heat transfer enhancements, Elliptical fin, Fin orientation, Fin density.
This document discusses a numerical study examining the effects of tip clearance and casing recess on heat transfer and stage efficiency in axial turbines. Calculations were performed considering passage geometries with and without casing recess, and tip clearances of 0%, 1%, 1.5%, and 3% of the passage height. The results showed an increase in thermal load on heat transfer surfaces with increased tip clearance. Casing recess reduced heat transfer on the pressure side but effects on the suction side were more complex. Casing recess significantly reduced heat load and peak values on the blade tip. A small reduction in heat transfer on the casing was also observed. Efficiency was found to linearly decrease with increased tip clearance, and casing recess had a small positive
IRJET-Enhancing the Performance of Hybrid Microgrid using non Isolated Single...IRJET Journal
This document analyzes heat transfer in a light passenger car radiator with various geometrical configurations using computational fluid dynamics (CFD). It studies a staggered fin-and-tube radiator with circular and oval tubes. The radiator is modeled and analyzed in FLUENT to obtain velocity, temperature, and pressure contours. Oval tubes are found to improve heat transfer compared to circular tubes. Specifically, oval tube configurations reduce temperature differences between the tubes and air, indicating more efficient heat absorption. While circular tubes show higher temperatures, oval tube designs enhance convection and lower outlet temperatures. In conclusion, varying the tube shape geometrically through oval designs improves the radiator's thermal performance.
This document discusses a numerical analysis of natural convection cooling of electronic components mounted on an aluminum plate within the walls of a train. The study examines the effect of a discontinuous heat flux distribution from the components on heat transfer. The results show that the heat flux distribution significantly influences cooling efficiency. Optimizing the placement and sizing of components can maximize heat transfer and minimize temperatures for improved cooling of power converters inside trains.
The document compares the thermal performance of flat plate fins and inline strip fins heat sinks. It presents Nusselt number correlations from literature to model the convective heat transfer from the fins. The correlations consider heat transfer from the fins but not the bare heat sink base. The study includes an estimate of heat transfer from the base, providing a more realistic thermal resistance calculation. Results show inline strip fins have higher heat transfer coefficients that compensate for their reduced area, yielding lower thermal resistances than plate fins. Considering heat transfer from the base provides an even lower thermal resistance for both heat sink designs.
Natural convection heat transfer in inclined open annulus passege heated from...IAEME Publication
This document summarizes an experimental study on natural convection heat transfer in an open cylindrical annulus heated from both the inner and outer sides. The study examines the effects of inclination angle (0°, 30°, 60°, 90°) and heat flux (70-600 W/m2) on the local and average Nusselt number. The results show that the Nusselt number increases with both increasing heat flux and inclination angle from horizontal to vertical. Empirical correlations between the average Nusselt number and Rayleigh number are developed from the results.
This document summarizes a study on improving the cooling efficiency of fins in a two-stage reciprocating compressor through finite element analysis and dimensional modification. The existing annular fins are made of aluminum alloy. A finite element model of the fins is created in ANSYS to analyze temperature distribution over time under natural convection conditions. The results show the fins reach room temperature in 30 minutes. The fins are then modified by increasing the number of fins from 11 to 13. Finite element analysis of the modified fins shows cooling time is reduced to 22 minutes. In conclusion, modifying the fin geometry through additional fins improves the cooling rate of the reciprocating compressor.
Natural convection heat transfer inside inclined open cylinderIAEME Publication
This document summarizes an experimental study on natural convection heat transfer inside an inclined open cylinder. The study investigated the effects of inclination angle (0°, 30°, 60°, 90°) and heat flux (70-600 W/m2) on the heat transfer. Empirical correlations were developed relating the average Nusselt number to the Rayleigh number. Results showed that heat transfer, as measured by the local and average Nusselt number, increased with increasing heat flux and inclination angle from horizontal to vertical.
This document summarizes a numerical study that examines the effects of fin spacing, fin material, and jet velocity on the heat transfer performance of plate fin heat sinks cooled by impinging air jets. The study considers fin spacings of 2mm, 3mm, and 4mm, and fin materials of aluminum, copper, and steel. Jet velocities of 5m/s, 10m/s, and 15m/s are examined. The results show that heat transfer rate increases with decreasing fin spacing, higher thermal conductivity fin materials like copper, and increasing jet velocity. Copper fins achieved the highest heat transfer rates but are heavier and more expensive than aluminum. A fin spacing of 2mm with aluminum fins and a jet velocity of 15
This document summarizes research on using finite element analysis and crash test dummies to assess driver side knee injuries and the performance of knee airbags. It describes how a finite element model of a knee airbag was developed and simulated a frontal crash impact scenario with and without the airbag. The results showed that the knee airbag reduced peak knee forces by 68.5% compared to the case without an airbag, demonstrating the effectiveness of knee airbags in mitigating knee injuries during frontal collisions.
This document discusses determining the optimal location for wind turbines on the roofs of two different buildings using wind tunnel testing. Models of both buildings were constructed at a 1:100 scale and tested in a wind tunnel. For Building A, the most stable locations for wind turbines were found to be above 2.5 meters on the west-facing wall and above 10 meters in the center of the roof. Turbulence was highest near the center and downwind side of the roof. An automatic weather station installed on Building A's roof measured turbulence intensity values consistent with the wind tunnel results.
This document proposes a dynamic seat allocation system for Indian Railways using QR codes and a mobile application. The key points are:
1. The system uses QR codes embedded with passenger-specific URLs to identify passengers and dynamically allocate vacant seats. Passengers scan the QR code when boarding to check-in.
2. If seats remain vacant, the system reflects them as available for other passengers like waitlisted travelers to book instantly. This increases revenue and transparency.
3. Traveling ticket examiners use a mobile app to verify passenger details by scanning QR codes, making the checking process faster and more efficient.
This document evaluates the implementation of total quality management (TQM) as an engineering practice in Jordanian construction projects. It analyzes TQM implementation based on two main factors - continuous improvement and customer satisfaction. Data was collected through a questionnaire survey of 177 engineers. The study found that TQM implementation was at a moderate level across all construction project phases in Jordan. TQM is considered an important modern management system that can help address quality problems in the Jordanian construction sector if fully adopted.
This document discusses using a genetic algorithm for global optimization of a portal steel frame with tapered I-section members. It describes modeling a 3D frame in ANSYS, performing a linear buckling analysis considering local, lateral and frame stability. Parametric studies were conducted to investigate influential design parameters. The optimized geometry from the genetic algorithm was compared to a reference frame, showing advantages of the proposed model over traditional member checks.
This document summarizes an electrical energy audit conducted at the Nandi Institute of Technology and Management Sciences (NIT&MS) campus in Bangalore, India. The audit found that the total average monthly electrical energy consumption across the campus was 3,842.842 kWh. Personal computers in labs, offices, and libraries accounted for the highest consumption at 39.14% of total usage. Fans were the second highest usage at 21.53%. Recommendations to improve energy efficiency included replacing conventional ballasts with electronic ones, installing motion sensors, replacing CRT monitors with LCDs, and switching to LED lights. Implementing all recommendations could save an estimated 10,435.84 kWh per year and reduce electricity costs by
This document summarizes a research paper that proposes an opinion mining methodology using ontologies and natural language processing techniques to perform feature-based sentiment analysis of customer reviews. It begins by collecting customer reviews from websites. The reviews are preprocessed by removing URLs, usernames, etc. and part-of-speech tagging is used to extract product features. An ontology is constructed to organize the features and their relationships. Term frequencies are calculated to determine feature importance. Sentiment analysis is performed using SentiWordNet to assign semantic scores and polarities (positive, negative, neutral) to each feature. N-gram analysis is also used to identify opinion words related to features. The methodology is evaluated using precision, recall and F-measure. The results
This document summarizes a study on the use of fly ash mixtures as landfill liner materials. It begins with an abstract that describes investigating the hydraulic and compressibility behavior of fly ash-bentonite mixtures under different compaction conditions. The introduction provides background on landfill liners and the need to find alternative, locally available materials when natural soils are unsuitable. The literature review covers criteria for landfill liner design and previous research on fly ash, fly ash cement mixtures, and their permeability and strength properties. The purpose is to evaluate fly ash as a liner material and identify mixtures that meet hydraulic conductivity criteria for landfill liners.
Geostatistical approach to the estimation of the uncertainty and spatial vari...IOSR Journals
Abstract. This article presents a case of application of geostatistical methods in geotechnical engineering:
There is a railway platform, going to be built on compressible soils which presents important settlement.
Geotechnical data were analyzed by a geostatistical approach using GIS software to characterize the spatial
variability of the thickness of the compressible soils and their deformation Module.
Then these data were crossed with settlement calculations by oedometer method to estimate the distribution of
soil compaction on the entire site.
Key words: Morocco, Kenitra, geotechnical studies, settlement, geostatistics, kriging.
CFD Simulation of Swirling Effect in S-Shaped Diffusing Duct by Swirl Angle o...IOSR Journals
This document describes a computational fluid dynamics (CFD) simulation of swirling flow through an S-shaped diffusing duct with a 10 degree swirl angle. The study models airflow through a duct with an area ratio of 1.9, length of 300mm, and turning angle of 22.5 degrees. Simulations were conducted for uniform inlet flow and swirling inlet flow clockwise and counter-clockwise. Results show that swirling flow improves static pressure recovery over uniform flow. Clockwise swirling flow provided the highest pressure recovery and most uniform exit flow. Turbulence intensity and secondary flows increased through the duct but did not exceed 15% of inlet velocity.
This document proposes applying an image restoration algorithm called CLRS to improve the reliability of block quantum cellular automata (QCA) gates. QCA gates are sensitive to errors from manufacturing imperfections at the nanoscale. The CLRS algorithm uses neural networks and Markov random fields to iteratively minimize an energy function and restore images corrupted by noise. The author develops a mathematical model for applying CLRS to block QCA gates by representing the gate as a grid of cells and modeling the cell charges and discontinuities as Markov random fields. The algorithm aims to correct errors in cell placement and charges to find the lowest energy, most reliable configuration of the block QCA gate. Simulation results will analyze the effectiveness of CLRS at compensating for
Thermal conductivity Characterization of Bamboo fiber reinforced in Epoxy ResinIOSR Journals
Over a past few decades composites, plastics, ceramics have been the dominant engineering material. The areas of applications of composites materials have grown rapidly and have even found new markets. The current challenge is to make the durable in tough conditions to replace other materials and also to make them cost effective .This has resulted in development of many new techniques currently being used in the industry. While the use of composites it is clear choice in many applications but the selection of material will depend on the factor such as working life, lifetime requirement, complexity of product shape produced, saving the term cost. The availability of natural fiber is abundances and also they are very inexpensive when compared to other advanced manmade fibers. The primary advantage of natural fibers are low density, low cost, biodegradability, acceptable specific properties, less wear during extracting as well as manufacturing composites and wide varieties of natural fibers are locally available. The main focus of this investigation is to determine the thermal conductivity of bamboo fiber reinforced in epoxy resin composites. The test samples were prepared as per ASTM standards using simple hand-layup technique at different fiber weight fractions (10%, 20%30%, 40%50%, 60%). Thermal conductivity (K) of the composites material were determined experimentally and is validated by the results obtained by rule of mixture, E-S model and also by finite element modeling
This document presents an analysis of orthotropic reinforced concrete slabs with long side openings using the affine theorem and yield line method. Ten possible yield line failure patterns are considered for slabs with continuous, simply supported, two long sides continuous, and two short sides continuous edge conditions. Virtual work equations are formulated for each failure pattern. Numerical examples are provided to illustrate the governing failure patterns for different slab geometries and support conditions. The affine theorem is used to transform orthotropic slab properties into equivalent isotropic properties to simplify the analysis.
This document reviews the effect of adding Al2O3 nano-particles on the mechanical properties of aluminium-based alloys. It discusses how aluminium/Al2O3 nano-metal matrix composites can be produced using stir casting and powder metallurgy techniques. The mechanical properties like hardness, tensile strength and compressive strength of the composites increase with the addition of Al2O3 nano-particles up to 3-4% due to uniform dispersion and load transfer. However, agglomeration of particles occurs at higher loadings reducing the mechanical properties. The document concludes that addition of Al2O3 nano-particles up to 3% improves the mechanical properties of aluminium alloys.
A proposed model develops a low-cost PLC-based GSM control module that integrates mobile applications and home/industrial automation technologies. The model uses a programmable logic controller connected to a microcontroller to control devices via SMS messages sent over the GSM network from a mobile phone. The microcontroller encodes and decodes SMS messages using AT commands to interface with the PLC and control connected devices remotely.
This document summarizes an investigation into flank wear on minimal cutting fluid application during turning of OHNS steel. Seven input parameters were varied at three levels in a 27-run Taguchi experiment. Analysis found that feed rate had the greatest influence on flank wear, cutting temperature, and chip thickness based on ANOVA. Optimal cutting and fluid application parameters were determined to be a cutting speed of 168.23 m/min, feed of 0.04 mm/rev, depth of cut of 1 mm, pressure of 100 bar, frequency of 900 pulses/min, application rate of 3 ml/min, and fluid composition of 20%. The study provides optimized parameters for improved tool performance during turning of OHNS steel with minimal cutting fluid application.
This document summarizes research on improving the performance of WiMAX systems using FEC zigzag coding and MIMO techniques. It first provides background on WiMAX and discusses how OFDM, MIMO, and various channel coding schemes like zigzag codes work. It then evaluates the bit-error rate performance of WiMAX systems using zigzag-coded modulation with different code rates and lengths. The results show zigzag coding presents stronger error correction than Reed-Solomon with Convolutional coding. Encoding and decoding of zigzag codes is explained, along with how concatenated zigzag codes provide even stronger error correction through interleaving and turbo processing.
1. Seismic refraction methods were used to measure the velocity gradients of underground layers in Unwana, Nigeria. Forward and reverse shootings were conducted along a profile line using a seismograph.
2. Velocities of 315m/s and 300m/s were found for the first layer, and 608m/s and 600m/s for the second layer from forward and reverse shootings. Thicknesses of 2.1m and 2.0m for the first layer, and 7.3m and 4.7m for the second layer were measured.
3. Velocity gradients of 149s-1 and 150s-1 for the first layer indicated horizontally homogeneous materials.
There are three main points summarized from the document:
1) Taraba State in Nigeria faces significant challenges in providing reliable water infrastructure and sanitation services to its population. Only 2 of 14 water treatment plants are fully operational, and over half of the population lacks access to basic sanitation.
2) Broken or aging water distribution systems allow contamination to enter drinking water supplies. Leaking pipes waste water and money. Many residents receive intermittent, low quality water services.
3) Building the capacity of water treatment plant staff and increasing community education on hygiene and sanitation practices could help address water quality issues. However, more investment is needed to repair and maintain water infrastructure across Taraba State.
1) The document describes the design and implementation of a private area network for a university campus that provides secure and smooth computing.
2) It proposes using Cisco EIGRP for routing, access control lists for security, and implementing a modified campus area network with network security concepts.
3) The private area network would allow higher university authorities to directly contact any department securely and without relying on external communication tools, improving privacy and security control for the university.
This document describes a computational fluid dynamics (CFD) analysis of natural convection flow through a square cavity using ANSYS software. The study investigates laminar natural convection heat transfer in two-dimensional vertical air cavities for a range of Rayleigh numbers from 103 to 106 and an aspect ratio of 1. The geometry of the square cavity is created and meshed in ANSYS. Steady-state simulations are performed using the finite volume method. Boundary conditions of isothermal side walls and adiabatic top and bottom walls are applied. Contour plots and streamlines of velocity and temperature are analyzed to understand heat transfer trends. Nusselt number correlations as a function of Rayleigh number are proposed based
A Thesis on Design Optimization of Heat Sink in Power ElectronicsIJERA Editor
The heat sinks are used in electronic systems to remove heat from the chip and effectively transfer it to the ambient. The heat sink geometry is designed by the mechanical engineers with the primary aim of reducing the thermal resistance of the heat sink for better cooling in the electronic systems. Due to the proximity of the heat sink with the ICs, the RF fields created by RF currents in the ICs/PCBs gets coupled to heat sinks. Hence, the coupled RF current can cause radiated emission. This radiated noise from the device can couple and disturb the functioning of the nearby electronic systems. Also this radiated emission from the device poses a problem to the system compliance with respect to EMI/EMC regulations. The international EMI/EMC standards require the radiated emission from the electronic devices to be kept below the specified limits. As a result the design of Heat Sink is very important factor for the efficient operation of the electronic equipment. In this project design optimization of a Heat sink in a Power amplifier is performed to reduce the weight and size .Power amplifier is electronic equipment mounted in an army vehicle. The power modules inside the amplifier generates a heat of 1440 Watts and a temperature of 140 0c.Two Heat sinks are used to dissipate the heat generated inside the equipment and maintain a temperature of less than 850c. The existing heat sink which is being used is weighing around 10.3kgs and height of 51mm; as a result the unit is very robust. The objective of my project is To design & optimize the heat sink to reduce the weight and size. The optimized heat sink should also dissipate heat generated by power modules and maintain a temperature of less than 850c inside. To achieve the design a steady state thermal analysis will be performed on the heat sink and plot the Temperature distribution on the fins. Based on the above analysis results we will increase/decrease the number of fins, thickness of fins, and height of fins to reduce the weight of the heat sink. We will perform CFD analysis of the power amplifier by mounting the optimized heat sink and plot temperature, pressure and velocity distribution in the power amplifier enclosure. Efforts are made to optimize temperature, pressure and velocity distribution in the power amplifier enclosure by reorienting the power modules in the enclosure. UNIGRAPHICS software is used for 3D modeling SOLID WORKS FLOW SIMULATION software is used for thermal and CFD analysis.
Experimental Investigation of Flow Pattern on Rectangular Fin Arrays under Na...IJMER
Abstract: In Natural convection heat transfer with the help of fin arrays, parameter are fin length to height ratio, spacing
and orientation of geometry. In the longitudinally short fin array, where single chimney flow pattern is present hence heat
transfer coefficient is high. In long rectangular fin arrays, air is stagnant at central zone hence it is not so much contributed
in heat dissipation. In present study experimental setup is developed to studying the effect of natural convection over
rectangular fin array. Fin spacing, height and heater input are the parameter study during experimentation. Lampblack
coating is used to black fin surface. Flow patterns of various spacing’s are investigated using smoke flow visualization
techniques.
Keyword: Fin Arrays, Flow Visualization, Flow Pattern, Heat Transfer Coefficient, Natural convection.
This document summarizes an experimental study on heat transfer enhancement from surface roughness at laminar flow. Specifically, it examines using circular and oval dimples on an aluminum plate to increase heat transfer from the plate to air flowing over it at Reynolds numbers from 600 to 2000. The study finds that both circular and oval dimples enhance heat transfer compared to a flat plate, while maintaining equivalent or lower pressure drops. The experimental results are validated by comparing the measured Nusselt numbers to theoretical values for a plain vertical plate under laminar flow conditions. In general, the dimpled surfaces increase thermal performance without significantly increasing pressure drops compared to a smooth surface.
Cfd analysis of turbulence in a gas turbine combustor with reference to the c...IAEME Publication
This document discusses computational fluid dynamics (CFD) analysis of turbulence in a gas turbine combustor with reference to exit phenomena. It summarizes several studies that have used experimental and computational methods to model combustor exit profiles and their effects on secondary flows in turbine vanes. The document outlines CFD models of different combustor configurations, including variations in cooling schemes, dilution jets, and exit slots. Results show that dilution jets and exit slots can create non-uniformities in temperature, pressure and velocity at the combustor exit which influence the development of secondary flows in downstream vanes. Understanding these interactions is important for improving turbine performance and cooling effectiveness.
Cfd analysis of turbulence in a gas turbine combustor with reference to the c...IAEME Publication
This document discusses computational fluid dynamics (CFD) analysis of turbulence in a gas turbine combustor with reference to exit phenomena. It analyzes the interaction between the combustor and turbine regarding increased temperatures and heat transfer. The objective is to better understand non-uniformities in the flow field at the combustor exit in terms of temperature, pressure and velocity in the spanwise and pitchwise directions. The analysis uses CFD to model different combustor configurations and evaluate the effects on the exit flow field and downstream turbine vane.
This document summarizes a numerical study of two-dimensional natural convection in a square enclosure with differentially heated walls. The study evaluates the effects of variable properties of air, including density, thermal conductivity, and viscosity, on heat transfer rates and flow patterns using a finite volume method. Key findings include:
1) Heat transfer rates decrease when accounting for decreasing thermal conductivity with increasing temperature but are unaffected by variable viscosity.
2) Variable density has a significant impact on results and invalidates the constant density assumption for some cases.
3) Constant property assumptions are better for higher Rayleigh numbers.
4) Heat transfer increases with the addition of slip boundary conditions, especially at higher Rayleigh numbers.
Review of Convective Heat Transfer from Plate Fins Under Natural and Mixed Co...IRJET Journal
This document reviews research on convective heat transfer from plate fins under natural and mixed convection conditions. It summarizes several previous studies that investigated the effects of fin geometry (such as fin length, height, width, spacing, thickness) and operating parameters (such as heat supplied, temperature difference) on heat transfer. The studies found that convective heat transfer increases with fin spacing until an optimal spacing is reached, beyond which further increases in spacing decrease heat transfer. Inclination angle and mixed convection were also found to impact heat transfer. The document provides background on using fins to dissipate heat from electronic devices and explores parameters that most affect natural convective heat transfer within constrained heat sink dimensions.
Analysis of Double Pipe Heat Exchanger With Helical FinsIRJET Journal
This document analyzes a double pipe heat exchanger with helical fins through computational fluid dynamics (CFD). It aims to study the flow and temperature fields inside the tubes for different helical fin angles. The geometry of the double pipe heat exchanger is modeled in CATIA V5 and meshed in Hypermesh. CFD simulations are performed in ANSYS Fluent to analyze the flow and temperature distributions for fin angles of 0, 5, 10, 15, 20, and 25 degrees. The results determine that heat transfer rate and overall heat transfer coefficient increase with helical fins compared to a smooth tube, with fins providing additional surface area to enhance heat transfer.
HEAT TRANSFER CO EFFICIENT VS HEAT FLOW RATE BY FORCED CONVECTIONTajammul Kamal
This document is a project report submitted by a student for their diploma in petrochemical engineering. It investigates heat transfer coefficients and heat flow rates through forced convection. Specifically, it looks at optimizing the design of heat sinks by considering factors like fin shape, thickness, spacing, and their effects on thermal resistance and heat dissipation. It provides background on previous related studies and the importance of heat transfer in applications like electronics cooling. The goal is to develop equations to determine the optimum specifications of fins in a heat sink based on parameters like the Biot number, heat transfer coefficient, and fin shape.
IRJET - Experimental Investigation of Heat Transfer through Rectangular and ...IRJET Journal
1. The document experimentally investigates heat transfer through rectangular and trapezoidal fins made of aluminum 6063 alloy with variable cross-sections. Rectangular fins measuring 110x50x10mm and trapezoidal fins measuring 110x30x10mm were fabricated and their heat transfer coefficients were measured under different heat input conditions.
2. Several studies on heat transfer through different fin geometries are reviewed. One study found that sideward vertically oriented trapezoidal fins performed best for natural convection cooling. Another study computationally analyzed heat transfer from vertical trapezoidal and rectangular fins and found trapezoidal fins performed better.
3. The document aims to compare heat transfer through rectangular, trapezoidal and parabolic
This document summarizes a study on cooling power converters on trains through natural convection. It presents a numerical analysis of heat transfer from an aluminum plate representing the train wall with a discontinuous heat flux from 12 resistors simulating electronic components. The results show that the heat flux distribution significantly influences heat transfer. Experiments were also conducted with an apparatus modeling the system, varying heat flux levels from 1600 to 3200 W/m^2 applied uniformly to the resistors.
Cooling Of Power Converters by Natural ConvectionIJERA Editor
This document summarizes a study on cooling power converters on trains through natural convection. It discusses a numerical analysis of the effect of discrete heat flux distributions on a vertical aluminum plate representing the train wall. The plate contains 12 resistors in 3 rows and 4 columns representing electronic components. Simulations were run to determine the influence of heat flux distribution and channel dimensions on maximum temperature. Experimental work was also conducted to validate the numerical model. In conclusion, the heat flux distribution significantly impacts heat transfer, with distributed fluxes allowing better cooling than uniform fluxes.
Experimental Investigation of Natural Convection Heat Transfer Enhancement fr...IRJET Journal
This document describes an experimental investigation of natural convection heat transfer from rectangular fin arrays with combinations of V-notches and perforations. Four fin array configurations were tested: one without notches or perforations (un-notched), and three with different combinations of V-notches and perforations removing different percentages of the fin area. The fin arrays were heated to different temperatures and the resulting heat transfer coefficients were measured and compared. The results showed that the combination of V-notches and perforations both increased the surface area and the turbulence near the fins, allowing more air contact and higher heat transfer coefficients compared to the un-notched fins. Among the configurations tested, the fin array with 20% of its area removed
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
IRJET- A Reviw on Different Geometrical Fins and their Effect on Heat Tra...IRJET Journal
This document summarizes research on different geometric fin designs and their effect on heat transfer rates. It discusses how fins are used to increase surface area and improve heat transfer. Various fin geometries are described including longitudinal, radial, and pin fins. The performance of fins is evaluated using metrics like fin effectiveness and efficiency. Higher thermal conductivity materials, thinner fins with closer spacing, and conditions with lower heat transfer coefficients can improve fin performance. The document reviews several studies on topics like annular fins, dimpled pin fins, and modeling transient heat transfer in piston bore fins.
This document summarizes a study that uses computational fluid dynamics (CFD) to analyze the flow and heat transfer characteristics of different elliptical pin fin heat sink configurations. The study aims to examine the effects of elliptical pin fin design parameters on heat sink performance. CFD simulations are conducted using ANSYS Fluent software to compute the thermal resistance, heat transfer coefficient, and surface Nusselt number of plate fin and elliptical pin fin heat sinks. Results show that the elliptical pin fin heat sink has better heat transfer performance than the plate fin heat sink. Simulation results for thermal resistance and pressure drop are validated against experimental data from previous studies.
IRJET- Numerical Investigation of Heat Transfer Enhancement in Circular Pipe ...IRJET Journal
1. The document numerically investigates heat transfer enhancement in a circular pipe with various rib geometries, including flat, conical, and right angle ribs.
2. It uses computational fluid dynamics to model water flow through the pipe with Reynolds numbers from 5000 to 60000 and a constant heat flux of 50 W/cm2 applied to the pipe surface.
3. The results show that ribs on the inside of the pipe enhance turbulence in the flow and produce recirculation, disturbing the thermal boundary layer and increasing the rate of heat transfer through the pipe.
1) The document analyzes heat transfer in a double pipe heat exchanger with helical tape inserts in the annulus of the inner pipe using computational fluid dynamics (CFD).
2) A 3D model is developed and simulations are run using the SST k-ω turbulent model to analyze how helical tape inserts influence heat transfer and pressure drop at different pitch lengths and Reynolds numbers.
3) The results show that helical tape inserts increase the heat transfer rate but also increase pressure drop due to flow disruption. Nusselt number and friction factor are found to correlate well with Reynolds number for enhancing heat transfer.
Thermal analysis of various duct cross sections using altair hyperworks softwaresushil Choudhary
In this work thermal analysis and comparison of various duct cross sections is done computationally using Altair
Hyperworks Software. Simple Analytical results were obtained for conduction and convection through the ducts
which can be used to build up thermal circuit. The inner surface of all ducts is maintained at constant
temperature and ambient air is at certain temperature that is less than inner surface temperature of pipe. Due to
temperature difference heat will flow from higher temperature to lower temperature. Due to temperature
difference heat will flow from higher temperature to lower temperature. The material of pipe provides
conductive resistance and air provides convective resistance. Hence this is a mix mode of heat transfer. The heat
transfer takes place in one dimension only and properties are considered to be isotropic. The ducts are assumed
to be made of aluminium having known thermal conductivity and density. The surroundings of ducts have
known convective heat transfer coefficient and temperature. The results are obtained on hyperview which are for
heat flux, temperature gradient and grid temperature. The different characteristics can be obtained by varying the
material of the ducts.
Similar to Numerical Analysis of Inverted Notched Fin Array Using Natural Convection (20)
This document provides a technical review of secure banking using RSA and AES encryption methodologies. It discusses how RSA and AES are commonly used encryption standards for secure data transmission between ATMs and bank servers. The document first provides background on ATM security measures and risks of attacks. It then reviews related work analyzing encryption techniques. The document proposes using a one-time password in addition to a PIN for ATM authentication. It concludes that implementing encryption standards like RSA and AES can make transactions more secure and build trust in online banking.
This document analyzes the performance of various modulation schemes for achieving energy efficient communication over fading channels in wireless sensor networks. It finds that for long transmission distances, low-order modulations like BPSK are optimal due to their lower SNR requirements. However, as transmission distance decreases, higher-order modulations like 16-QAM and 64-QAM become more optimal since they can transmit more bits per symbol, outweighing their higher SNR needs. Simulations show lifetime extensions up to 550% are possible in short-range networks by using higher-order modulations instead of just BPSK. The optimal modulation depends on transmission distance and balancing the energy used by electronic components versus power amplifiers.
This document provides a review of mobility management techniques in vehicular ad hoc networks (VANETs). It discusses three modes of communication in VANETs: vehicle-to-infrastructure (V2I), vehicle-to-vehicle (V2V), and hybrid vehicle (HV) communication. For each communication mode, different mobility management schemes are required due to their unique characteristics. The document also discusses mobility management challenges in VANETs and outlines some open research issues in improving mobility management for seamless communication in these dynamic networks.
This document provides a review of different techniques for segmenting brain MRI images to detect tumors. It compares the K-means and Fuzzy C-means clustering algorithms. K-means is an exclusive clustering algorithm that groups data points into distinct clusters, while Fuzzy C-means is an overlapping clustering algorithm that allows data points to belong to multiple clusters. The document finds that Fuzzy C-means requires more time for brain tumor detection compared to other methods like hierarchical clustering or K-means. It also reviews related work applying these clustering algorithms to segment brain MRI images.
1) The document simulates and compares the performance of AODV and DSDV routing protocols in a mobile ad hoc network under three conditions: when users are fixed, when users move towards the base station, and when users move away from the base station.
2) The results show that both protocols have higher packet delivery and lower packet loss when users are either fixed or moving towards the base station, since signal strength is better in those scenarios. Performance degrades when users move away from the base station due to weaker signals.
3) AODV generally has better performance than DSDV, with higher throughput and packet delivery rates observed across the different user mobility conditions.
This document describes the design and implementation of 4-bit QPSK and 256-bit QAM modulation techniques using MATLAB. It compares the two techniques based on SNR, BER, and efficiency. The key steps of implementing each technique in MATLAB are outlined, including generating random bits, modulation, adding noise, and measuring BER. Simulation results show scatter plots and eye diagrams of the modulated signals. A table compares the results, showing that 256-bit QAM provides better performance than 4-bit QPSK. The document concludes that QAM modulation is more effective for digital transmission systems.
The document proposes a hybrid technique using Anisotropic Scale Invariant Feature Transform (A-SIFT) and Robust Ensemble Support Vector Machine (RESVM) to accurately identify faces in images. A-SIFT improves upon traditional SIFT by applying anisotropic scaling to extract richer directional keypoints. Keypoints are processed with RESVM and hypothesis testing to increase accuracy above 95% by repeatedly reprocessing images until the threshold is met. The technique was tested on similar and different facial images and achieved better results than SIFT in retrieval time and reduced keypoints.
This document studies the effects of dielectric superstrate thickness on microstrip patch antenna parameters. Three types of probes-fed patch antennas (rectangular, circular, and square) were designed to operate at 2.4 GHz using Arlondiclad 880 substrate. The antennas were tested with and without an Arlondiclad 880 superstrate of varying thicknesses. It was found that adding a superstrate slightly degraded performance by lowering the resonant frequency and increasing return loss and VSWR, while decreasing bandwidth and gain. Specifically, increasing the superstrate thickness or dielectric constant resulted in greater changes to the antenna parameters.
This document describes a wireless environment monitoring system that utilizes soil energy as a sustainable power source for wireless sensors. The system uses a microbial fuel cell to generate electricity from the microbial activity in soil. Two microbial fuel cells were created using different soil types and various additives to produce different current and voltage outputs. An electronic circuit was designed on a printed circuit board with components like a microcontroller and ZigBee transceiver. Sensors for temperature and humidity were connected to the circuit to monitor the environment wirelessly. The system provides a low-cost way to power remote sensors without needing battery replacement and avoids the high costs of wiring a power source.
1) The document proposes a model for a frequency tunable inverted-F antenna that uses ferrite material.
2) The resonant frequency of the antenna can be significantly shifted from 2.41GHz to 3.15GHz, a 31% shift, by increasing the static magnetic field placed on the ferrite material.
3) Altering the permeability of the ferrite allows tuning of the antenna's resonant frequency without changing the physical dimensions, providing flexibility to operate over a wide frequency range.
This document summarizes a research paper that presents a speech enhancement method using stationary wavelet transform. The method first classifies speech into voiced, unvoiced, and silence regions based on short-time energy. It then applies different thresholding techniques to the wavelet coefficients of each region - modified hard thresholding for voiced speech, semi-soft thresholding for unvoiced speech, and setting coefficients to zero for silence. Experimental results using speech from the TIMIT database corrupted with white Gaussian noise at various SNR levels show improved performance over other popular denoising methods.
This document reviews the design of an energy-optimized wireless sensor node that encrypts data for transmission. It discusses how sensing schemes that group nodes into clusters and transmit aggregated data can reduce energy consumption compared to individual node transmissions. The proposed node design calculates the minimum transmission power needed based on received signal strength and uses a periodic sleep/wake cycle to optimize energy when not sensing or transmitting. It aims to encrypt data at both the node and network level to further optimize energy usage for wireless communication.
This document discusses group consumption modes. It analyzes factors that impact group consumption, including external environmental factors like technological developments enabling new forms of online and offline interactions, as well as internal motivational factors at both the group and individual level. The document then proposes that group consumption modes can be divided into four types based on two dimensions: vertical (group relationship intensity) and horizontal (consumption action period). These four types are instrument-oriented, information-oriented, enjoyment-oriented, and relationship-oriented consumption modes. Finally, the document notes that consumption modes are dynamic and can evolve over time.
The document summarizes a study of different microstrip patch antenna configurations with slotted ground planes. Three antenna designs were proposed and their performance evaluated through simulation: a conventional square patch, an elliptical patch, and a star-shaped patch. All antennas were mounted on an FR4 substrate. The effects of adding different slot patterns to the ground plane on resonance frequency, bandwidth, gain and efficiency were analyzed parametrically. Key findings were that reshaping the patch and adding slots increased bandwidth and shifted resonance frequency. The elliptical and star patches in particular performed better than the conventional design. Three antenna configurations were selected for fabrication and measurement based on the simulations: a conventional patch with a slot under the patch, an elliptical patch with slots
1) The document describes a study conducted to improve call drop rates in a GSM network through RF optimization.
2) Drive testing was performed before and after optimization using TEMS software to record network parameters like RxLevel, RxQuality, and events.
3) Analysis found call drops were occurring due to issues like handover failures between sectors, interference from adjacent channels, and overshooting due to antenna tilt.
4) Corrective actions taken included defining neighbors between sectors, adjusting frequencies to reduce interference, and lowering the mechanical tilt of an antenna.
5) Post-optimization drive testing showed improvements in RxLevel, RxQuality, and a reduction in dropped calls.
This document describes the design of an intelligent autonomous wheeled robot that uses RF transmission for communication. The robot has two modes - automatic mode where it can make its own decisions, and user control mode where a user can control it remotely. It is designed using a microcontroller and can perform tasks like object recognition using computer vision and color detection in MATLAB, as well as wall painting using pneumatic systems. The robot's movement is controlled by DC motors and it uses sensors like ultrasonic sensors and gas sensors to navigate autonomously. RF transmission allows communication between the robot and a remote control unit. The overall aim is to develop a low-cost robotic system for industrial applications like material handling.
This document reviews cryptography techniques to secure the Ad-hoc On-Demand Distance Vector (AODV) routing protocol in mobile ad-hoc networks. It discusses various types of attacks on AODV like impersonation, denial of service, eavesdropping, black hole attacks, wormhole attacks, and Sybil attacks. It then proposes using the RC6 cryptography algorithm to secure AODV by encrypting data packets and detecting and removing malicious nodes launching black hole attacks. Simulation results show that after applying RC6, the packet delivery ratio and throughput of AODV increase while delay decreases, improving the security and performance of the network under attack.
The document describes a proposed modification to the conventional Booth multiplier that aims to increase its speed by applying concepts from Vedic mathematics. Specifically, it utilizes the Urdhva Tiryakbhyam formula to generate all partial products concurrently rather than sequentially. The proposed 8x8 bit multiplier was coded in VHDL, simulated, and found to have a path delay 44.35% lower than a conventional Booth multiplier, demonstrating its potential for higher speed.
This document discusses image deblurring techniques. It begins by introducing image restoration and focusing on image deblurring. It then discusses challenges with image deblurring being an ill-posed problem. It reviews existing approaches to screen image deconvolution including estimating point spread functions and iteratively estimating blur kernels and sharp images. The document also discusses handling spatially variant blur and summarizes the relationship between the proposed method and previous work for different blur types. It proposes using color filters in the aperture to exploit parallax cues for segmentation and blur estimation. Finally, it proposes moving the image sensor circularly during exposure to prevent high frequency attenuation from motion blur.
This document describes modeling an adaptive controller for an aircraft roll control system using PID, fuzzy-PID, and genetic algorithm. It begins by introducing the aircraft roll control system and motivation for developing an adaptive controller to minimize errors from noisy analog sensor signals. It then provides the mathematical model of aircraft roll dynamics and describes modeling the real-time flight control system in MATLAB/Simulink. The document evaluates PID, fuzzy-PID, and PID-GA (genetic algorithm) controllers for aircraft roll control and finds that the PID-GA controller delivers the best performance.
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...IJECEIAES
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
Low power architecture of logic gates using adiabatic techniquesnooriasukmaningtyas
The growing significance of portable systems to limit power consumption in ultra-large-scale-integration chips of very high density, has recently led to rapid and inventive progresses in low-power design. The most effective technique is adiabatic logic circuit design in energy-efficient hardware. This paper presents two adiabatic approaches for the design of low power circuits, modified positive feedback adiabatic logic (modified PFAL) and the other is direct current diode based positive feedback adiabatic logic (DC-DB PFAL). Logic gates are the preliminary components in any digital circuit design. By improving the performance of basic gates, one can improvise the whole system performance. In this paper proposed circuit design of the low power architecture of OR/NOR, AND/NAND, and XOR/XNOR gates are presented using the said approaches and their results are analyzed for powerdissipation, delay, power-delay-product and rise time and compared with the other adiabatic techniques along with the conventional complementary metal oxide semiconductor (CMOS) designs reported in the literature. It has been found that the designs with DC-DB PFAL technique outperform with the percentage improvement of 65% for NOR gate and 7% for NAND gate and 34% for XNOR gate over the modified PFAL techniques at 10 MHz respectively.
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
5214-1693458878915-Unit 6 2023 to 2024 academic year assignment (AutoRecovere...
Numerical Analysis of Inverted Notched Fin Array Using Natural Convection
1. IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE)
e-ISSN: 2278-1684,p-ISSN: 2320-334X, Volume 6, Issue 4 (May. - Jun. 2013), PP 47-56
www.iosrjournals.org
www.iosrjournals.org 47 | Page
Numerical Analysis of Inverted Notched Fin Array Using
Natural Convection
Salila Ranjan Dixit1
, DrTarinicharana Panda2
1
(Mechanical engineering department, CMJ University, Meghalaya, India)
2
(Principal, OEC, BBSR, Orissa, India)
Abstract:Geometry and orientation plays an important role in natural convection heat transfer. For
horizontal rectangular fin array a chimney flow pattern is developed due to density difference. This flow
pattern creates a stagnant zone near central bottom region. That portion does not contribute much towards
heat dissipation. This area is removed from fins and they became inverted notched fins. This modified geometry
reduces material cost, material weight without hampering heat transfer rate. Numerical models are prepaid to
investigate heat transfer characteristics in plane fins and inverted notched fins. This investigation is also
extended over different types of notches and their effectiveness comparison. Fin spacing, fin height, fin length,
heater input, percentage of area removed in the form of inverted notch are the parameters under
consideration. This analysis is done numerically using CFD package (Fluent). It is found that the heat transfer
coefficient of inverted notch fin array is 25% to 35% higher as compared with normal fin array. Also we found
that the triangular shape notch gives better result than trapezoidal and rectangular shape notch.
Key words: Inverted Notched Fin, Chimney Flow, Natural Convection, Heat transfer coefficient enhancement.
I. Introduction
When available surface is found inadequate to transfer required quantity of heat with available
temperature gradient, fins are used Rate of heat dissipation from a fin configuration by convection heat transfer
depends on the heat transfer coefficient and the surface area of the fins. The surface area of the fins can also be
increased by adding more fins to the base material in order to increase the total heat transfer from the fins. But
the number of the fins should be optimized because it should be noted that adding more fins also decreases the
distance between the adjacent fins. Using fins is one of the cheapest and easiest ways to dissipate unwanted heat
and it has been commonly used for many engineering applications successfully. Rectangular fins are the most
popular fin type because of their low production costs and high effectiveness. Configuration of all fins
protruding from their bases is popular because they offer economical and trouble free solution to the problem.
Natural convection heat transfer is augmented by provision of rectangular fins on horizontal or vertical surfaces
in many electrical and electronic appliances. Because of reduction in surface area available for heat dissipation
and low heat transfer coefficient optimization of fin geometry becomes very important in natural convection
heat transfer. Now a days in electronic industries microminiaturization of electronic packages are in trend. The
thermal design problem is recognized as one of the factors limiting achievement of higher packaging densities.
Natural convection occurs due to temperature difference which produces the density difference. Generally in
natural convection heat transfer on horizontal fin array, we observe a chimney flow pattern which creates a
stagnant zone near the central bottom portion of fin channel. This stagnant zone created becomes less effective
or sometimes ineffective for heat transfer, because no air stream passes over this region. To optimize the fin
geometry some portion of this stagnant zone is removed in various shapes and sizes and its effect on other
parameters are studied in this investigation.
II. Model Analysis And Mathematical Formulation
2.1. Model Analysis:
Fig 2.1: Semantic diagram of rectangular notched fin array
An array of rectangular fins is set on aluminum sheet (This model was used by Suryabansi et al. 2009)
and a fixed amount of heat flux is given as in put to the base (Fig 2.1). Base is insulated from all sides except the
2. Numerical analysis of inverted notched fin array using natural convection
www.iosrjournals.org 48 | Page
on which fins are connected. Heat provided at the base is supposed to pass through the fins and the gap in
between them to a surrounding that is the atmosphere. A chimney flow pattern is observed and central bottom
region is untouched by this flow and become less effective. Further notches are created at the central bottom
portion of the fins for examining its effect on heat transfer. The chimney flow pattern flow is shown in fig 2.2
.This chimney flow occurs due to the density difference in natural convection.
Fig 2.2 vectorialrepresentation of chimney flow
For a rectangular fin array in natural convection heat transfer.
2.2 numerical models:
The natural convection flow under investigation is modeled by a set of partial differential equations
describing the conservation of mass, momentum, and energy in three Cartesian coordinates. The numerical
model is based on control volume finite difference formulation. The set of equations are integrated over each
control volume to obtain discretized linear algebraic equations, termed as finite volume equations. These
equations are solved by commercial CFD package, like FLUENT. Many numbers of fins with negligible
thickness is assumed. The fin surfaces with base are assumed as a source and held at uniform temperature.
Laminar natural convection is the mechanism for heat transfer from the fin array. The schematic drawing of fin
array under investigation with isothermal fin surface with base is shown in Fig 2.3. We are changing the
percentage of notch here and also change the shape of the notch like rectangle, triangle and trapezoidal. In
natural convection due to the density difference a stagnant zone is created at the central portion of fin.so we
remove that area which is not affected to the flow.
Fig 2.3: Numerical Model
The computational investigation is carried out for fin of length L, height H, fin spacing S. we are taking
horizontal fin array, changes space between fins accordingly the number of fin also changes given in table 2.1
.Constant heat flux given at the bottom wall shown in fig2.4.
3. Numerical analysis of inverted notched fin array using natural convection
www.iosrjournals.org 49 | Page
Table 2.1 Dimensions of rectangular fin array used for investigation.
2.3. Governing equation:
Continuity equation
( ) 0i
i
U
x
(1)
Momentum equation
ji i
i j j i
UD U Up
g
Dt x x x x
(2)
is the fluid density anywhere in the domain and is the buoyancy force per unit volume. The density
is taken to be a function of temperature according to ideal gas law.
Energy equation
Pr Pr
t
i t i
D T T
Dt x x
(3)
2.4 boundary conditions:
In natural convection flows, there is no information regarding the velocity and temperature fields
before the start of calculations. Since governing equations are invariably coupled, the temperature field causes
the velocity field to develop and in turn the velocity field affects the temperature field, with the promotion of
convective heat transfer. The boundary conditions can be visualized both in Fig. 2.4.Constant heat flux given at
the bottom wall of domain .pressure outlet boundary condition is given at top and one side of the domain.one
side of the fin is given as length symmetry boundary condition. The rest two side of fin is given as width
symmetry boundary condition. The lower portion of the fin is given as velocity inlet. We are taking symmetry
boundary condition like width symmetry, length symmetry because it is easy doing analysis.
Velocity inlet boundary conditions are used to define the flow velocity, along with all relevant scalar
properties of the flow, at flow inlets. In this case, the total (or stagnation) pressure is not fixed but will rise (in
response to the computed static pressure) to whatever value is necessary to provide the prescribed velocity
distribution. This boundary condition is equally applicable to incompressible and compressible flows. Pressure
outlet boundary conditions require the specification of a static (gauge) pressure at the outlet boundary. The value
of the specified static pressure is used only while the flow is subsonic. Should the flow become locally
Length of fin array, L (mm)150
Height, H(mm) 75
Spacing, S (mm) 4 5 6 9 13
No. of fins 15 13 12 9 7
Heater input (W) 50 100 150 200
Fig. 2.4 Schematic diagram of computational domain and boundary
conditions applied to it
4. Numerical analysis of inverted notched fin array using natural convection
www.iosrjournals.org 50 | Page
supersonic, the specified pressure will no longer be used; pressure will be extrapolated from the flow in the
interior. All other flow quantities are extrapolated from the interior. A set of "backflow'' conditions is also
specified should the flow reverse directionat the pressure outlet boundary during the solution process.
Convergence difficulties will be minimized if you specify realistic values for the backflow quantities. It is
known now, beyond any doubt, that a moving fluid in contact with a solid body will not have any velocity
relative to the body at the contact surface. This condition of not slipping over a solid surface has to be satisfied
by a moving fluid. This is known as the no-slip conditionSymmetryboundary conditions are used when the
physical geometry of interest, and the expected pattern of the flow/thermal solution, has mirror symmetry. They
can also be used to model zero-shear slip walls in viscous flows. This section describes the treatment of the flow
at symmetry planes and provides examples of the use of symmetry. You do not define any boundary conditions
at symmetry boundaries, but you must take care to correctly define your symmetry boundary locations.
Symmetry boundaries are used to reduce the extent of your computational model to a symmetric subsection of
the overall physical system.
2.5 .non dimensional parameter
We are calculating some non-dimensional parameter like Nusselt Number,
grashoff number, and Rayleigh number.
Nu =
hL
k
(Nusselt Number)
Gr =
gβ∆TL3
ν2 (Grashoffs Number)
Ra=Gr * Pr
Ra=
gβ∆TL3
ν2 ×
𝜇𝐶p
𝐾
We are calculating Nusselt number because if Nusselt number is high then that means convection is
more and it is directly propertional to the heat transfer coefficient and it also gives the heat transfer coefficient in
non-dimensional form. We are calculating Grashoffs Number because all variable of Grashoffs number is
depend upon temperature of fluid .if we found that at everywhere Grashoffs number is equal then the heat
transfer rate does not change when we remove the area. We are calculating Rayleigh number because it is a
function of Prandtl number and Grashoffs number. If the Rayleigh number is greater than the multiplication is
power nine then the flow is turbulent and if the multiplication is power six then the flow is turbulent.
2.6 Numerical Solution Procedure:
Three-dimensional equations of mass, momentum and energy control volume. These equations were
discretized over the control volume using the finite volume technique to yield a set of algebraic equations which
could be solved by the algebraic multi grid solver of Fluent 13.1in an iterative manner by imposing the above
boundary conditions. A first order upwind scheme (for convective variables) was considered for the momentum
as well as for the energy equations. After a first-hand converged solution could be obtained, the scheme was
changed over to second order upwind so as to get a little better accuracy (heat transfer coefficient was changed
by only 0.5%). A detail description of the types and number of grids used and the effect of domain size have
been discussed separately in the results and discussions. The SIMPLE algorithm with a PRESTO (Pressure
Staggering Option) scheme for the pressure velocity coupling was used for the pressure correction equation.
Under relaxation factors of 0.3 for pressure, 0.7 for momentum and 1 for temperature were used for the
convergence of all the variables. Simple tetrahedral cells were used for the entire computational domain due to
the complexity of the geometry. Convergence of the discretized equations were said to have been achieved when
the whole field residual for all the variables fell below 10-3
for u, v, w, and p whereas for energy the residual
level was kept at 10-6
.Three-dimensional equations of mass, momentum and energy have been integrated over
the control volume and the subsequent equations have been discretized overthe control volume using the finite
volume technique to yield a set of algebraic equations which could be solved by the algebraic multi grid solver
of Fluent 12.1in an iterative manner by imposing proper boundary conditions. First order upwind scheme (for
convective variables) was considered for momentum as well as for the turbulent discretized equations. After a
first-hand converged solution could be obtained the scheme was changed over to second order upwind so as to
get little better accuracy. SIMPLE algorithm has been used for the pressure-velocity coupling for the pressure
correction equation and the cell face values of pressure could be obtained from simple arithmetic averaging of
centroid values. However, it is to be noted that if density becomes a function of temperature then the SIMPLE
algorithm for pressure velocity coupling will not work properly because the pressure variation from cell to cell
will not be smooth due to the presence of source term in the momentum equation. So in order to obtain the cell
face pressure new pressure interpolation technique is needed which is available through body force weighted or
5. Numerical analysis of inverted notched fin array using natural convection
www.iosrjournals.org 51 | Page
PRESTO (Pressure Staggered Option) scheme in Fluent. The body-force-weighted scheme computes the face
pressure by assuming that the normal gradient of the difference between pressure and body forces is constant.
This works well if the body forces are known a priori in the momentum equations (e.g., buoyancy and axi-
symmetric swirl calculations). The PRESTO (Pressure Staggering Option) scheme uses the discrete continuity
balance for a "staggered'' control volume about the face to compute the "staggered'' (i.e., face) pressure. This
procedure is similar in spirit to the staggered-grid schemes used with structured meshes. Note that for triangular,
tetrahedral, hybrid, and polyhedral meshes, comparable accuracy is obtained using a similar algorithm. The
PRESTO scheme for pressure interpolation is available for all meshes in Fluent. Under relaxation factors (0.3
for pressure, 0.7 for momentum and1for energy) were used for the convergence of all the variables. Fine grids
were used at the nozzle entrance as well as for louvers opening area to have better accuracy. The field variables
for all type of cells are stored at the cell center but to get cell face values, interpolation is needed from values
stored at the centroids. For triangular or tetrahedral cells a node based solution procedure is adopted which
evaluates the cell face values from centroid values by making some weighted mean average around the cell
center and the nodes. This procedure normally makes a smooth computation of the face values (for fluxes) and
helps in better convergence. Convergence of the discretized equations were said to have been achieved when the
whole field residual for all the variables fell below 10-3
.
III. Results and Discussions
3.1 Grid independent test and validation with other results:
We have started our numerical investigation with a rectangular fin array with fin spacing 4mm and 12
numbers of fins. Subsequently it is extended to different spacing and numbers. This fin array is placed in a
domain. The dimensions of the fin are length 150 mm. height 75 mm and thickness 3 mm. Fin materials is
aluminum. As mentioned above in our numerical modeling we have taken two half fins(length 75 mm and
thickness 1.5 mm) for simulation applying symmetry boundary condition and accordingly dimensions of domain
is taken (length 150mm,height 225mm ).
Fig 3.1:A general arrangement of meshes
Map mesh is taken here. First we have taken mesh spacing 0.003m and compare the simulation result with
existing experimental results. It is observed that it differs from the experimental result. Then we reduce the mesh
size to 0.002m and find that the resulting is approaching towards existing results. Then we further reduce the
size to 0.0015 and then to 0.001.we find the result is still approaching towards perfection and there is noticeable
difference between the results of mesh size 0.0015m and 0.001m. We also notice a remarkable change in
computation time is up to 6 hours in mesh size 0.001m. So we have tried to match our result with existing
experimental result of Suryabansi et al. (2009).We find our result match well with these experimental results. So
for further all simulations we have taken this mesh size (0.0015m).
6. Numerical analysis of inverted notched fin array using natural convection
www.iosrjournals.org 52 | Page
Heat transfer coefficient is plotted as a function of fin spacing (fig ). Average heat transfer coefficient is
calculated from average temperature difference between fin array and atmosphere. We have calculated heat
transfer coefficient (h) for different fin spacing (s) like 4mm, 5mm, 6mm, 9mm & 13mm and different heater
inputs (q) such as 50W, 100W & 150W. Heater inputs are given in the form of constant heat flux. We have
compared our result with experimental result of suryabansi et al (2009). Above figures shows the comparisons
of heat transfer coefficients at different spacing between numerical results and experimental results. They show
a good agreement with experimental results (with around ± 5% error).
Heat transfer coefficient is plotted as a function of percentage of area removed (fig 3.4). Average heat
transfer coefficient is calculated from average temperature difference between fin array and atmosphere. We
have calculated heat transfer coefficient (h) for different notch like (10% removal area of fin,20% removal of
area of fin,30% area removal of fin and 40% area removal of fin) with constant heater inputs (q) as 150W as
constant heat flux. We have compared our numerical result with existing experimental result of suryabansi et al
(2009). They show a good agreement with each other.
7. Numerical analysis of inverted notched fin array using natural convection
www.iosrjournals.org 53 | Page
3.2 Effect of Fin Spacing On Nusselt Number with Constant Heat Flux for Plain Fins
Variation of Nusselt Number with respect to fin spacing is plotted in fig no 3.5 & 3.6 for constant heat flux of
100W & 150W. Dimensions of fin are taken as length (L) 150mm, height (H) 75mm, and thickness (T) 3mm.
We found that with increase in fin spacing from 4 mm to 13 mm Nusselt Number increases. But rate of increase
of Nusselt Number decreases with increase in fin spacing which gives a parabolic curve. As Nusselt Number is
directly proportional to heat transfer coefficient and other parameters are almost constant so it gives a curve of
same nature as heat transfer coefficient, discussed earlier.
3.3 Effect of Notch on Nusselt Number
Rate of increase of heat transfer coefficient is sharper in case of notched fins than plain fins as discussed earlier.
The major cause is removal of area without hampering heat transfer rate. In fig no 3.7 variation of Nusselt
Number is plotted against percentage of area removed. And we find the Nusselt Number increases with increase
in notch size. This increment is very sharp and the plot is almost a straight line unlike for plain fins. Here we
have investigated on same fin structure with rectangular notches of different size starting from 10% of fin area
to 40%. We have tried to remove the unaffected zone by chimney flow. Here we find that if we remove the
unaffected zone i.e. up to 40% of the main fin area. We find Nusselt number is increasing which implies
increase in heat transfer coefficient but after that heat transfer rate is hampered. It shows that we can save up to
40% material of fins making the equipment more light and cheap.
4 6 8 10 12 14
20
25
30
35
40
45
Nusseltnumber
fin spacing
100 watt with out notch
4 6 8 10 12 14
20
25
30
35
40
45
Nusserltnumber
fin spacing
150 watt with out notch
10 15 20 25 30 35 40
28
30
32
34
36
38
40
42
44
Nusseltnumber
notch
100 watt with nutch
10 15 20 25 30 35 40
30
32
34
36
38
40
42
44
46
48
Nusseltnumber
notch
150 watt with notch
Fig 3.5 Nusselt number is a function of fin spacing
Fig 3.7 Nusselt number is a function of
percentage of area removed
q = 100 W, L = 150 mm, H
= 75 mm, t=0.003
q = 100 W, L = 150 mm,
H = 75 mm, t=0.003,
s=6mm
q = 150 W, L = 150
mm, H = 75 mm,
t=0.003, s=6mm
Fig 3.6 Nusselt number is a function of fin
spacing
Fig 3.8. Nusselt number is a function
of percentage of area removed
q = 150 W, L = 150
mm, H = 75 mm,
t=0.003
8. Numerical analysis of inverted notched fin array using natural convection
www.iosrjournals.org 54 | Page
3.4 Effect of Notch on Grashoffs Number
Fig 3.9.Grashoff number is a function of percentage of area removed
For optimization purpose we are removing the central bottom portion of the rectangular fin but it always carries
a greater importance to maintain the original heat transfer rate that we are getting with plane fins. From fig 3.9 it
is evident that Grashoffs number is almost constant with no notch condition to 40% notched. This implies the
fluid temperature near to fin array remains constant even we removed the central bottom portion of the fin up to
a certain extent. The constancy of fluid temperature shows that there is no appreciable change in fin
temperature. From the above analysis we can conclude that as the fin temperature is not changing, the rate of
heat transfer remains almost constant from no notch to 40% notch condition.
3.5 Effect of Rayleigh Number on Nusselt Number
Fig 3.10. Rayleigh number is a function of Nusselt number
Density plays a major role in natural convection heat transfer. The value of viscosity varies directly with
density. Viscosity determines the flow nature. It natural convection heat transfers the flow becomes turbulent at
certain Rayleigh Number range (Ra= Gr ×Pr) i.e.108
-109
. In our investigation we find the value of Ra lies in the
range of 106
. This conforms the flow set up due to density difference is in laminar zone. The fig3.10 shows the
variation of Ra with respect to different Nusselt Number. As Nusselt Number is directly proportional to heat
transfer co-efficient and heat transfer co-efficient to heat supplied so in our range of investigation we find a
laminar chimney flow pattern is seen in all different notches.
0 10 20 30 40
6510000
6520000
6530000
6540000
6550000
6560000
6570000
6580000
Grashoffsnumber
notch
150 watt
15 16 17 18 19 20 21 22 23
5.6x10
6
5.8x10
6
6.0x10
6
6.2x10
6
6.4x10
6
6.6x10
6
6.8x10
6
7.0x10
6
7.2x10
6
7.4x10
6
Rayleighnumber
Nusselt number
150 W/m
2
q = 150 W, L = 150 mm, H = 75
mm, t=0.003 s=6mm
Q = 150 W, L = 150 mm, H = 75 mm,
t=0.003 s=6mm
9. Numerical analysis of inverted notched fin array using natural convection
www.iosrjournals.org 55 | Page
3.7 Effect of Notch on Heat Transfer Coefficient for Constant Heat Flux with Different Shape of
Notch
From the previous investigation we found that heat transfer co-efficient in case of notched fin is more than plane
fins. Here we have tried to optimize the notch to get better heat transfer co-efficient with same effort. So we
studied the effect of different notch shape of same size on heat transfer co-efficient. We have analyzed two more
types of notches (triangular & trapezoidal) along with rectangular notch. We compared heat transfer co-efficient
of different notches at different sizes. It is observed for same conditions triangular notch give better heat transfer
coefficient followed by trapezoidal and rectangular notch respectively due to more effective removal of fin area
in stagnant zone. So for better optimization of fin geometry we can switch over to the above types of notches
with certain limitations (Limitation like triangular and trapezoidal notch can’t be made more than 20% of main
fin area).
IV. Conclusions
Fin geometry and orientation plays a vital role in natural convection heat transfer. Our investigation
deals with natural convection heat transfer on rectangular fin array. Here we have tried to optimize a rectangular
fin array on the basis of cost and usefulness. We have optimized above fin array based on natural convection
heat transfer numerically using CFD package fluent with laminar model. Our model has been validated with
existing experimental result of Suryavansi et al. we have measured heat transfer coefficients and other non-
dimensional parameters as a function of heat transfer coefficient. The investigation is based on rectangular fin
array and the results obtained are the function of notch size and shape. The following conclusion can be derived
from the present investigation: Nusselt number is increasing if we increase the fin spacing at constant heat flux
for plane fins. Because Resistance to the flow due to density difference, decreases for increase in fin spacing.
Nusselt Number increases with increase in notch size 10% to 40% for constant heat flux. Because the fin area
decreases retaining constant heat transfer rate.TheGrashoffs Number is almost remaining same with no notch
condition to 40% notch condition. This implies the fluid temperature is not changing with the change of notch
size. That means the fin temperature does not change, which refers to constant Heat transfer rate. Rayleigh
Number remains almost constant with increase in Nusselt Number for constant heat flux. Which gives the value
of Rayleigh number gives in the order 106
.This shows the flow setup due to variation in density is laminar. The
heat transfer coefficient is maximum in case of triangular (In the limit up to 20%) shape notch followed by
trapezoidal (In the limit up to 20%) and Rectangular shaped notch (In the limit up to 20%) at constant heat flux
due to effective removal of stagnant zone fin area.
Reference
[1]. Starner K. E, and McManus H. N, 1963, “An Experimental Investigation of Free Convection Heat Transfer From Rectangular Fin
Arrays,” Trans. ASME,Ser. C: J. Heat Transfer, 85, pp. 273–278.
[2]. Sane N. K, and Sukhatme S. P, 1974, “Natural Convection Heat Transfer from Short Horizontal Rectangular Fin Arrays,” Fifth
International Heat Transfer Conference, Tokyo, Sept.
[3]. Sane N. K, Kittur M. B, and Magdum J. D., 1995, “Natural Convection Heat Transfer From Horizontal Rectangular Fin Arrays With
a Rectangular Notch at the Center,” Seventh ISHMT Conference, Suratkal.
[4]. Sane, N. K, Tikekar, A. N, and Morankar, K. P., 2000, “Natural Convection Heat Transfer From Vertical Arrays With Rectangular
Notched Fins,” ME thesis, Shivaji University, Kolhapur, India
[5]. Baskaya, S, Sivrioglu, M, and Ozek, M, 2000, “Parametric Study of Natural Convection Heat Transfer from Horizontal Rectangular
Fin Arrays,” Int. J. Therm. Sci., 39, pp. 797–805.
[6]. Jones, C. D, and Smith, L. F, 1970, “Optimum Arrangement of Rectangular Fins on Horizontal Surface for Free Convection Heat
Transfer,” ASME Paper No. 69-HT-44.
4 6 8 10 12 14 16
4.6
4.8
5.0
5.2
5.4
5.6
5.8
6.0
6.2
heattransfercoefficient
% of area removed
rectangle
trapizoidal
triengle
Fig 3.11. Heat transfer coefficient is a function of percentage of area removed
q = 150 W, L = 150 mm,
H = 75 mm, t=0.003
S=6mm
10. Numerical analysis of inverted notched fin array using natural convection
www.iosrjournals.org 56 | Page
[7]. Harahap, F, and McManus, H. N, 1967, “Natural Convection Heat Transfer From Horizontal Rectangular Fin Arrays,” Trans. ASME,
Ser. C: J. Heat Transfer, 89, pp. 32–38.
[8]. Sanjeev D. Suryawanshi,Narayan K. SaneNatural Convection Heat Transfer From Horizontal Rectangular Inverted Notched Fin
Arrays.
[10]. A similar experimental study was conducted by Welling .1965 Bridge on rectangular vertical fins. They reported optimum values of
the ratio of fin height to spacing. In the previous two studies the fin length was constant. International journal of heat and mass
transfer.
[11]. Rao V.D, Naidu S.V, Rao B.G, Sharma K.V, Heat transfer from a horizontal fin array by natural convection and radiation,
International journal of heat and mass transfer, 2006,Vol. 49, pg. 3379-3391
[12]. Yüncü H. and Anbar G, “An Experimental Investigation on Performance of Rectangular Fins on a Horizontal Base in Free
Convection Heat Transfer”, Heat and Mass Transfer 33, 507-514, (1998).
[13]. Guglielminiin 1986 he investigated that the heat transfers by natural convection and radiation between an isothermal vertical surface,
having a staggered array of discrete vertical plates of finite thickness, and the surroundings. International journal of heat and mass
transfer
[14]. Vollaro A.D.L, Grignaffini S, Gugliermetti F, “Optimum Design of Vertical Rectangular Fin Arrays”, International Journal of
Thermal Sciences 38, 525-259, (1999).
[15]. Leung C.W, Prober S.D. and Shilston M.J. “Heat Exchanger: Optimal Separation for Vertical Rectangular Fins Protruding from a
Vertical Rectangular Base”, Applied Energy, 77-85, (1985).
[16]. Kundu B, Das P.K, “Performance and Optimum Design Analysis of Convective Fin Arrays Attached to Flat and Curved Primary
Surfaces”, International Journal of Refrigeration, 1-14, (2008). 92
[17] Güvenc A, “An Experimental Investigation on Performance of Rectangular Fins on a Vertical Base in Free Convection Heat
Transfer”, M.S. Thesis in Mechanical Engineering, Middle East Technical University , Ankara (1999).
[18]. Orhan Aydin.2009 He takes natural convection of air in a two dimensional rectangular enclosure with localized heating from bellow
and symmetrical cooling from the inside has been numerically investigated. International journal of mass transfer.