This document discusses empirical correlations for mixed convection heat transfer through a fin array based on various orientations. It summarizes previous research on the effects of fin orientation and channel inclination angle on heat transfer. The current study investigates the effect of lateral and longitudinal channel inclination on heat transfer in a rectangular channel with longitudinal fins. Experimental results show that heat transfer is highest for a laterally inclined channel at 0 degrees and increases with longitudinal inclination angle. Empirical equations are developed to correlate Nusselt number with orientation angles, Reynolds number, and Grashof number.
Assessment of thermo-hydraulic performance of inward dimpled tubes with varia...CFD LAB
This paper presents a numerical investigation and assessment of thermal and hydraulic performance of dimpled
tubes of varying topologies at constant heat flux of 10 kW m2 and Reynolds numbers ranging from 2300 to
15,000. The performance of the tubes consisting of conical, spherical and ellipsoidal dimples with equivalent
flow volumes were compared using steady state Reynolds Averaged Navier Stokes simulations. The ellipsoidal
dimples, in comparison to other dimple shapes, demonstrated large increment in heat transfer rate. The variation
in the orientation of the ellipsoidal dimples was examined to further improve thermal and hydraulic performances of the tube. A 45° inclination angle of ellipsoidal dimple, from its major axis, increased the thermohydraulic performance by 58.1% and 20.2% in comparison to smooth tube and 0° ellipsoidal dimpled tube,
respectively. Furthermore, Large Eddy Simulations (LES) were carried out to investigate the role geometrical
assistance to fluid flow and heat transfer enhancement for the 45° and 90° ellipsoidal dimpled tubes. LES results
revealed a flow channel of connected zones of wakes which maximized fluid-surface contact and therefore
enhanced the thermal performance of the tube. In addition, correlations for Nusselt number and friction factor
for all angular topologies of ellipsoidal dimpled tube have been proposed.
Experimentation and analysis of heat transfer through perforated fins of diff...SharathKumar528
Engineering Project by Abhijath HB, Dashartha H S, Akshay Mohanraj and Sharath Kumar M S involving analysis of Fins( Heat exchanging extensions) with various geometrical perforations.
Assessment of thermo-hydraulic performance of inward dimpled tubes with varia...CFD LAB
This paper presents a numerical investigation and assessment of thermal and hydraulic performance of dimpled
tubes of varying topologies at constant heat flux of 10 kW m2 and Reynolds numbers ranging from 2300 to
15,000. The performance of the tubes consisting of conical, spherical and ellipsoidal dimples with equivalent
flow volumes were compared using steady state Reynolds Averaged Navier Stokes simulations. The ellipsoidal
dimples, in comparison to other dimple shapes, demonstrated large increment in heat transfer rate. The variation
in the orientation of the ellipsoidal dimples was examined to further improve thermal and hydraulic performances of the tube. A 45° inclination angle of ellipsoidal dimple, from its major axis, increased the thermohydraulic performance by 58.1% and 20.2% in comparison to smooth tube and 0° ellipsoidal dimpled tube,
respectively. Furthermore, Large Eddy Simulations (LES) were carried out to investigate the role geometrical
assistance to fluid flow and heat transfer enhancement for the 45° and 90° ellipsoidal dimpled tubes. LES results
revealed a flow channel of connected zones of wakes which maximized fluid-surface contact and therefore
enhanced the thermal performance of the tube. In addition, correlations for Nusselt number and friction factor
for all angular topologies of ellipsoidal dimpled tube have been proposed.
Experimentation and analysis of heat transfer through perforated fins of diff...SharathKumar528
Engineering Project by Abhijath HB, Dashartha H S, Akshay Mohanraj and Sharath Kumar M S involving analysis of Fins( Heat exchanging extensions) with various geometrical perforations.
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.
An Experimental Research on Heat Transfer Enhancement of a Circular Tube with...IRJESJOURNAL
ABSTRACT:- In the literature, internal tube baffles are widely studied. There is a lack of data for baffles mounted on outside of the tubes. This study aims to fill this gap. Therefore, the effect of baffle inclination angles on heat transfer improvement has been studied experimentally. The experiments were carried out for forced convection of air on a circular tube with inclined baffles. Air has been used as the cold fluid. Experimental results for eight different velocities of air flow (2 – 20 m/s) are presented. Pitch between baffles is 12 mm.The baffle inclination angles with respect to the tube axis were 45º, 60º and 80º. Water temperature is fixed as 65 °C. According to the experimental results, the baffles with an inclination angle of 45º enhance the heat transfer over 60º and 80º around 13.7 % and 10.5 %, respectively. However, pressure drop values for 45º and 60º are 18 % higher than pressure drop values for 80º. The empirical correlations of the Nusselt number have also been obtained for each angle.
EXPERIMENTAL STUDY OF HEAT TRANSFER FROM PLATE FIN ARRAY IN MIXED CONVECTION ...ijiert bestjournal
The work summarized in this paper presents an exper imental study of heat transfer from plate fin in mixed convection mode enhancement by the us e of plate fins is presented. After a brief review of the basic methods used to enhance the hea t transfer by simultaneous increase of heat transfer surface area as well as the heat tran sfer coefficient,a simple experimental method to assess the heat transfer enhancement is p resented. The method is demonstrated on plate fins as elements for the heat transfer enhanc ement,but it can in principle be applied also to other fin forms. That is varying various paramet ers (height,spacing). The order of the magnitude of heat transfer enhancement obtained exp erimentally,it was found that by a direct comparison of Nu and Re no conclusion regarding the relative performances could be made. This is because the dimensionless variables are int roduced for the scaling of heat transfer and pressure drop results from laboratory to large scal e but not for the performance comparison. Therefore a literature survey of the performance co mparison methods used in the past was also performed. Experiments will carried out on mix ed convection heat transfer from plate fin heat sinks subject to the influence of its geometry and heat flux. A total of 9 plate fins were pasted into the upper surface of the base plate. Th e area of the base plate is 150mm by 150mm. The base plate and the fins were made of alu minum. For all tested plate fin heat sinks,however,the heat transfer performance for h eat sinks with plate fins was better than that of solid pins.
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.
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.
Visualization of Natural Convection in a Vertical Annular Cylinder with a Par...IJERA Editor
In this work, we visualize the effect of varying wall temperature on the heat transfer by supplying the heat at
three different positions to the vertical annular cylinder embedded with porous medium. Finite element method
has been used to solve the governing equations. Influence of Aspect ratio 𝐴𝑟 , Radius ratio 𝑅𝑟 on Nusselt
number 𝑁 𝑢 is presented. The effect of power law exponent effect for different values of Rayleigh number is
discussed. The fluid flow and heat transfer is presented in terms of streamlines and isotherms.
Mixed Convection of Variable Properties Al2O3-EG-Water Nanofluid in a Two-Dim...A Behzadmehr
In this paper, mixed convection of Al2O3-EG-Water nanofluid in a square lid-driven enclosure is investigated numerically. The focus of this study is on the effects of variable thermophysical properties of the nanofluid on the heat transfer characteristics. The top moving and the bottom stationary horizontal walls are insulated, while the vertical walls are kept at different constant temperatures. The study is carried out for Richardson numbers of 0.01–1000, the solid volume fractions of 0–0.05 and the Grashof number of 104. The transport equations are solved numerically with a finite volume approach using the SIMPLER algorithm. The results show that the Nusselt number is mainly affected by the viscosity, density and conductivity variations. For low Richardson numbers, although viscosity increases by increasing the nanoparticles volume fraction, due to high intensity convection of enhanced conductivity nanofluid, the average Nusselt number increases for both constant and variable cases. However, for high Richardson numbers, as the volume fraction of nanoparticles increases heat transfer enhancement occurs for the constant properties cases but deterioration in heat transfer occurs for the variable properties cases. The distinction is due to underestimation of viscosity of the nanofluid by the constant viscosity model in the constant properties cases and states important effects of temperature dependency of thermophysical properties, in particular the viscosity distribution in the domain.
In this paper, the natural convection heat transfer in a cubic enclosure provided with
inclined baffles attached to the two adiabatic sides, heated from the bottom is studied
experimentally and numerically to assess the effect of the baffles on the heat transfer
process inside the enclosure. Two different configurations have been considered. The first
configuration corresponds to the heated from the bottom with uniform heat flux using two
baffles attached to the left and right walls, while the second configuration corresponding
that the enclosure’s floor has parallel bands that are heated to a constant, high
temperature and the bands are separated by gaps that are kept at a lower temperature
that is also constant and single baffle attached to the left wall. In both cases, the top wall
is kept at a lower temperature than the bottom wall and the inclined baffles are well
covered with an insulating material. The inclination angles of the baffles range as (0o ≤
and ≥ 150o). The governing parameter, Rayleigh number, is fixed within 2.6x1011. In
numerical solution, a commercial software package has been used for a 2-D computation,
and the effect of turbulence is modelled by using (k-ε) model. Depending on its
orientation, the partial baffle has been found to change significantly the flow field which
in turn causes a reduction to the heat exchange inside the enclosure due to the damping
caused to the flow field. For all cases, the insulated baffle with any inclination angle
caused a reduction to the heat exchange inside the enclosure due to the damping caused
to the flow field. Also, a good agreement has been obtained between experimental
measurements and numerical results
Natural Convection from Heated Rough Surface at the Bottom of Vented Rectangu...theijes
Natural convection heat transfer from tilted rectangular enclosure heated at the bottom rough surfaces wall and vented by uniform slots opening at top wall experimentally investigated. Rough surfaces of roughness 0.002 m are used to study their effect on the heat transfer characteristics. The experiments are carried out to study the effects of venting ratio, enclosure's tilt angle and Rayleigh number on the cooling of rough surface inside the enclosure. The experiments are carried out at a Rayleigh number ranging from 2 × 108 to 1.52× 109 for enclosure tilt angles ranging from 0º to 90. Top venting arrangement is studied at different venting ratios of 1, 0.75, 0.5 and 0.25. Roughness shows a large effect on heat transfer for the rectangular enclosure where the average Nusselt number increases with the increase of venting ratio and decrease enclosure's tilt angle at the same Rayleigh number. This can be attributed to the roughness may increase the blockage effect on the flow that can cause the buoyancy force to decrease, but on the other hand it increases the turbulence intensity resulting in a higher heat transfer. The results are compared with a smooth rectangular enclosure of the same surface area to study the effect of roughness on heat transfer. The average Nu of rough surface in rectangular enclosure is higher than that of smooth surface by the range from 12 % to 21% depending on Ra. Correlations are developed for the top venting arrangement to predict the average Nusselt number of the enclosure in terms of the Rayleigh number, venting ratio and enclosure tilt angle.
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.
An Experimental Research on Heat Transfer Enhancement of a Circular Tube with...IRJESJOURNAL
ABSTRACT:- In the literature, internal tube baffles are widely studied. There is a lack of data for baffles mounted on outside of the tubes. This study aims to fill this gap. Therefore, the effect of baffle inclination angles on heat transfer improvement has been studied experimentally. The experiments were carried out for forced convection of air on a circular tube with inclined baffles. Air has been used as the cold fluid. Experimental results for eight different velocities of air flow (2 – 20 m/s) are presented. Pitch between baffles is 12 mm.The baffle inclination angles with respect to the tube axis were 45º, 60º and 80º. Water temperature is fixed as 65 °C. According to the experimental results, the baffles with an inclination angle of 45º enhance the heat transfer over 60º and 80º around 13.7 % and 10.5 %, respectively. However, pressure drop values for 45º and 60º are 18 % higher than pressure drop values for 80º. The empirical correlations of the Nusselt number have also been obtained for each angle.
EXPERIMENTAL STUDY OF HEAT TRANSFER FROM PLATE FIN ARRAY IN MIXED CONVECTION ...ijiert bestjournal
The work summarized in this paper presents an exper imental study of heat transfer from plate fin in mixed convection mode enhancement by the us e of plate fins is presented. After a brief review of the basic methods used to enhance the hea t transfer by simultaneous increase of heat transfer surface area as well as the heat tran sfer coefficient,a simple experimental method to assess the heat transfer enhancement is p resented. The method is demonstrated on plate fins as elements for the heat transfer enhanc ement,but it can in principle be applied also to other fin forms. That is varying various paramet ers (height,spacing). The order of the magnitude of heat transfer enhancement obtained exp erimentally,it was found that by a direct comparison of Nu and Re no conclusion regarding the relative performances could be made. This is because the dimensionless variables are int roduced for the scaling of heat transfer and pressure drop results from laboratory to large scal e but not for the performance comparison. Therefore a literature survey of the performance co mparison methods used in the past was also performed. Experiments will carried out on mix ed convection heat transfer from plate fin heat sinks subject to the influence of its geometry and heat flux. A total of 9 plate fins were pasted into the upper surface of the base plate. Th e area of the base plate is 150mm by 150mm. The base plate and the fins were made of alu minum. For all tested plate fin heat sinks,however,the heat transfer performance for h eat sinks with plate fins was better than that of solid pins.
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.
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.
Visualization of Natural Convection in a Vertical Annular Cylinder with a Par...IJERA Editor
In this work, we visualize the effect of varying wall temperature on the heat transfer by supplying the heat at
three different positions to the vertical annular cylinder embedded with porous medium. Finite element method
has been used to solve the governing equations. Influence of Aspect ratio 𝐴𝑟 , Radius ratio 𝑅𝑟 on Nusselt
number 𝑁 𝑢 is presented. The effect of power law exponent effect for different values of Rayleigh number is
discussed. The fluid flow and heat transfer is presented in terms of streamlines and isotherms.
Mixed Convection of Variable Properties Al2O3-EG-Water Nanofluid in a Two-Dim...A Behzadmehr
In this paper, mixed convection of Al2O3-EG-Water nanofluid in a square lid-driven enclosure is investigated numerically. The focus of this study is on the effects of variable thermophysical properties of the nanofluid on the heat transfer characteristics. The top moving and the bottom stationary horizontal walls are insulated, while the vertical walls are kept at different constant temperatures. The study is carried out for Richardson numbers of 0.01–1000, the solid volume fractions of 0–0.05 and the Grashof number of 104. The transport equations are solved numerically with a finite volume approach using the SIMPLER algorithm. The results show that the Nusselt number is mainly affected by the viscosity, density and conductivity variations. For low Richardson numbers, although viscosity increases by increasing the nanoparticles volume fraction, due to high intensity convection of enhanced conductivity nanofluid, the average Nusselt number increases for both constant and variable cases. However, for high Richardson numbers, as the volume fraction of nanoparticles increases heat transfer enhancement occurs for the constant properties cases but deterioration in heat transfer occurs for the variable properties cases. The distinction is due to underestimation of viscosity of the nanofluid by the constant viscosity model in the constant properties cases and states important effects of temperature dependency of thermophysical properties, in particular the viscosity distribution in the domain.
In this paper, the natural convection heat transfer in a cubic enclosure provided with
inclined baffles attached to the two adiabatic sides, heated from the bottom is studied
experimentally and numerically to assess the effect of the baffles on the heat transfer
process inside the enclosure. Two different configurations have been considered. The first
configuration corresponds to the heated from the bottom with uniform heat flux using two
baffles attached to the left and right walls, while the second configuration corresponding
that the enclosure’s floor has parallel bands that are heated to a constant, high
temperature and the bands are separated by gaps that are kept at a lower temperature
that is also constant and single baffle attached to the left wall. In both cases, the top wall
is kept at a lower temperature than the bottom wall and the inclined baffles are well
covered with an insulating material. The inclination angles of the baffles range as (0o ≤
and ≥ 150o). The governing parameter, Rayleigh number, is fixed within 2.6x1011. In
numerical solution, a commercial software package has been used for a 2-D computation,
and the effect of turbulence is modelled by using (k-ε) model. Depending on its
orientation, the partial baffle has been found to change significantly the flow field which
in turn causes a reduction to the heat exchange inside the enclosure due to the damping
caused to the flow field. For all cases, the insulated baffle with any inclination angle
caused a reduction to the heat exchange inside the enclosure due to the damping caused
to the flow field. Also, a good agreement has been obtained between experimental
measurements and numerical results
Natural Convection from Heated Rough Surface at the Bottom of Vented Rectangu...theijes
Natural convection heat transfer from tilted rectangular enclosure heated at the bottom rough surfaces wall and vented by uniform slots opening at top wall experimentally investigated. Rough surfaces of roughness 0.002 m are used to study their effect on the heat transfer characteristics. The experiments are carried out to study the effects of venting ratio, enclosure's tilt angle and Rayleigh number on the cooling of rough surface inside the enclosure. The experiments are carried out at a Rayleigh number ranging from 2 × 108 to 1.52× 109 for enclosure tilt angles ranging from 0º to 90. Top venting arrangement is studied at different venting ratios of 1, 0.75, 0.5 and 0.25. Roughness shows a large effect on heat transfer for the rectangular enclosure where the average Nusselt number increases with the increase of venting ratio and decrease enclosure's tilt angle at the same Rayleigh number. This can be attributed to the roughness may increase the blockage effect on the flow that can cause the buoyancy force to decrease, but on the other hand it increases the turbulence intensity resulting in a higher heat transfer. The results are compared with a smooth rectangular enclosure of the same surface area to study the effect of roughness on heat transfer. The average Nu of rough surface in rectangular enclosure is higher than that of smooth surface by the range from 12 % to 21% depending on Ra. Correlations are developed for the top venting arrangement to predict the average Nusselt number of the enclosure in terms of the Rayleigh number, venting ratio and enclosure tilt angle.
NATURAL CONVECTION HEAT TRANSFER INSIDE INCLINED OPEN CYLINDERIAEME Publication
Natural convection is investigated experimentally in an inclined open cylindrical passege heated under constant heat flux condition to study the effect of angle of inclination and heat flux on heat transfer. Heat transfer results are given for inclination angles of 0o (horizontal), 30o , 60o and 90o (vertical).Using cylinder diameter of 4.8 cm, cylinder length 50 cm and heat flux from 70 W/m2 to 600 W/m2 . Empirical correlations are given for the average Nusselt number as a function of the
Rayleigh number. The results show that the local and average Nusselt number increase as the heat flux increase and when angle of inclination changed from 0o (horizontal) to 90o
(vertical). An empirical correlations of average Nusselt number as a function of Rayleigh number were obtained.
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.
Cooling Of Power Converters by Natural ConvectionIJERA Editor
This paper discusses the numerical analysis of the effect of a discontinuous heat flux on heat transfer by natural convection along a vertical flat plate or in a rectangular channel. The objective of this study is to determine the effect of a discrete distribution of the heat flux on the cooling of twelve resistors, which represent electronic components, that are mounted on an aluminium vertical plate. The results of the simulations show that the distribution of the heat flux significantly influences the heat transfer.
HEAT TRANSFER AUGMENTATION IN A PLATE-FIN HEAT EXCHANGER: A REVIEWIAEME Publication
The improvement of the performance of heat exchangers with gas as the working fluid becomes particularly important due to the high thermal resistance offered by gases in general. In order to compensate for the poor heat transfer properties of gases, the surface area density of plate heat exchangers can be increased by making use of the secondary fins such as, off-set fins, triangular fins, wavy fins, louvered fins etc. In addition, a promising technique for the enhancement of heat transfer is the use of longitudinal vortex generators. The longitudinal vortices are produced due to the pressure difference generated between the front and back surface of the vortex generator.
Experimental Investigation on the Heat Transfer Coefficient of the Thermosyph...IJERA Editor
Two phase closed thermosyphon is a good heat transfer device. A large heat is transferred from evaporator to condenser with relatively a small temperature difference. In the present work, the heat transfer performance of two phase closed thermosyphon is analyzed experimentally with different cross section shape for the thermosyphon tube. A copper thermosyphon has been constructed with three different cross section shape (circular, square and rectangular) having the same hydraulic diameter and length. Methanol is used as the working fluid. The temperature distribution across the thermosyphon outer surface was measured and recorded using thermocouples. The results showed that the heat transfer coefficient increases with the increase of input power, thermal resistance is indirectly proportional to the input power. The maximum heat transfer coefficient (1815 W/m2C) for square cross section at the input power (500 W).
Experimental Investigation on Heat Transfer Analysis in a Cross flow Heat Ex...IJMER
Heat exchanger is devices used to exchange the heat between two liquids that are at different
temperature .These are used as a reheated in many industries and auto mobile sector and power
plants. The main aim of our project is thermal analysis of heat exchanger with waved baffles for
different types of materials at different mass flow rates and different tube diameters using FLOEFD
software and comparing the results that are obtained. The work is a simplified model for the study of
thermal analysis of shell-and-tubes heat exchangers having water as cold and hot fluid. Shell and
Tube heat exchangers are having special importance in boilers, oil coolers, condensers, pre-heaters.
They are also widely used in process applications as well as the refrigeration and air conditioning
industry. The robustness and medium weighted shape of Shell and Tube heat exchangers make them
well suited for high pressure operations. The project shows the best material, best boundary conditions
and parameters of materials we have to use for better heat conduction. For this we are chosen a
practical problem of counter flow shell and tube heat exchanger having water, by using the data that
come from cfd analysis. A design of sample model of shell and tube heat exchanger with waved baffles
is using Pro-e and done the thermal analysis by using FLOEFD software by assigning different
materials to tubes with different diameters having different mass flow rates and comparing the result
that obtained from FLOEFD software.
Similar to Empirical correlations for mixed convection heat transfer through a fin array based on various orientations (20)
A novel hybrid modelling structure fabricated by using Takagi-Sugeno fuzzy to forecast HVAC systems energy demand in real-time for Basra city
Raad Z. Homod
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
2. of inclination 0 ≤ Ө ≤ 60 and Pr = 0.72. The results show that at low
Rayleigh numbers, the heat transfer system is dominated by conduction
[11]. Huang et al. [12] they studied experimentally the heat transfer by
natural convection from square pin fin heat sinks subjected to the or-
ientation effect. A seven square pin fin heat sinks and a flat plate with
different arrangements were tested in a controlled environment. The
results show that the downward facing orientation gives the lowest
coefficient of heat transfer. Therefore, the coefficients of heat transfer
for sideways and upward orientations are of comparable magnitude.
The test was carried on a trapezoidal fin heat sink with various or-
ientations under a controlled environment.
Experiments on the heat transfer by natural convection from tra-
pezoidal fin array heat sinks subjected to the orientation effect were
carried out by Al-Azawi [15]. A trapezoidal fin heat sink with various
orientations was tested in a controlled environment. The author pointed
out that the sideways horizontal fin gave the lowest coefficient of heat
transfer, while the sideways vertical fin yield the best performance of
natural cooling. Of these experiments, Nu was defined as a function of
Ra at Pr = 0.7 for each direction, with Ra between 1400 and 3900. The
results showed that the heat transfer coefficients for sideways vertical
fins higher than those of upward fins by 12%, while higher than the
downward fins by 26% and by120% than of sideways horizontal fins.
Moreover, Naidu et al. [16] They studied theoretically and experi-
mentally the heat transfer problem by natural convection from a fins
array to find the effect of the base inclination of fins array on the rate of
heat transfer. A numerical model was developed by taking the can,
formed from a horizontal base and between two adjacent vertical fins.
All the governing equations for a fluid, together with the equations of
heat conduction in each fin, were resolved using the method of alter-
nate Direct Implicit. The experimental studies were carried out for five
different longitudinal inclinations, including 0°, 30°, 45°, 60°, and 90°.
In addition, the natural convection heat transfer from a heat sink with
narrow plate-fins and a parallel arrangement mounted on an inclined
base is experimentally investigated by Walunj and Palande [17]. The
rectangular base was tilted at an angle of 0°, 10°, 20°, 45°, 70°, 80°, and
90° while the fins were facing upwards. The results showed that the rate
of convection heat transfer decreases by increasing fin length and in-
creases by increasing fin height. Furthermore, the heat transfer is in-
creased by convection with an increase in the aspect ratio, but this
behavior was different for different tilt angles. In addition, Ahmed [18]
The CFD software Ansys/Fluent was used to study the effect of the
longitudinal inclination angle for a plate heat shield for different Rey-
nold numbers and different of fin heights on the hydraulic and thermal
performance of heat sink. The study showed that a variation of the
longitudinal inclination angle caused a complicated and substantial
flow field variation in space both upstream and downstream near a heat
sink. In addition, experimental simulations are performed by Maughan
and Incropera [19], to investigate the effects of longitudinal fins on
laminar mixed convection in airflow between parallel plates, with iso-
thermally heated for the bottom plate while the upper plate is cooled
with constant temperature. The results were that no secondary flow was
evident for conditions of fully developed on the without fins plate until
the Rayleigh number exceeded the critical value 1708. Beyond that,
longitudinal vortices were formed and persisted in decaying into tur-
bulence at Ra = 20,000. Dogan and Sivrioglu [20] and Taji et al. [21] A
similar experimental study was performed on heat transfer by mixed
convection from longitudinally arranged fins within a horizontal duct
to find highest heat transfer and find the optimal value for the ratio of
the fin height to the spacing between fins. An experimental study was
carried out to find the effect of spacing between fins and fin height as
well as the heat flux on combined convection heat transfer from a fins
array heated from the bottom inside a horizontal channel. Results
showed that the optimum spacing of the fins that gave the maximum
heat transfer is S = 8–9 mm and that the optimal spacing depends on
Ra*. Moreover, Yang et al. [22] Das et al. [23] They studied combined
convection heat transfer in an inclined parallel plates channel with
transverse fins attached to the bottom wall of the channel. Their results
indicated that, for Gr/Re = 10, the optimum aspect ratio increased with
an increase in the longitudinal angle of inclination, while the orienta-
tion effect on the optimum aspect ratio was not pronounced for Gr/
Re < 1.
Only a few information can be found in the available literature on
experiments of the heat transfer by mixed convection from a fins array
fitted in a horizontal duct. However, some transient convection heat
transfer studies by implemented within ducts with longitudinal angles,
but none of the previous studies represented the effect of the lateral tilt
angles of the channel on the heat transfer process. The current study
experimentally reports the effect of longitudinal inclination angles and
lateral tilt angles of the channel on a laminar mixed convection heat
transfer in three dimensions from a rectangular fins array attached to
Nomenclature
Ab surface area of plate, m2
Ac area of channel cross sectional, m2
Dh hydraulic diameter of the channel, m
g gravitational force, m/s2
hav the average of heat transfer coefficient, W/mK
H height of the channel, in
Hf height of the fin, m
I current, A
K conductivity, W/mK
L length, m
Lf length of the fin, m
Nuav average Nusselt number
P perimeter, m
qcon convection heat flux, W/m2
Qconv convection heat transfer rate, W
Qcond conduction heat transfer rate, W
Qrad the rate of radiation heat transfer, W
Qtotal total dissipation of the power, W
Ra Rayleigh number
Re Reynolds number
T temperature, °C
Tb bulk mean temperature, °C
Tin inlet emperature of the ah,°C
Tw average temperature of the aluminium plate surface, °C
Win mean longitudinal velocity, m/s
V voltage, V
W width, m
Greek symbols
α diffusivity, m2
/s
α lateral inclination angle
Θ longitudinal inclination angle
β coefficient or thermal expansion, 1/K
ε emissivity
μ dynamic viscosity, kg/ms
ν kinematic viscosity, m2
/s
σ Stefan–Boltzmann constant W/m2
K4
Subscripts
f fin
in inlet
w wall
R.Z. Homod et al. International Journal of Thermal Sciences 137 (2019) 627–639
628
3. the heated wall of the duct. In order to achieve the highest heat
transfer, the lateral tilt angles and longitudinal inclination angles are
considered to optimize them for a condition of constant heat flux [24].
2. Experimental apparatus
An experimental setup description is presented with the experi-
mental procedure discussion. A wind tunnel is built with a longitudinal
fin array to investigate the performance of the tested fin array. A
schematic drawing is shown in Fig. 1. The orientations of the experi-
mental setup selected here are shown in Fig. 2, which include a long-
itudinal and lateral inclination.
2.1. Open air stream
The induced draft fan was used to drive the cooling medium (air),
which was controlled by a valve. The wind tunnel was made from
galvanized iron and contains a damping chamber made of a
20 × 30 × 50 cm and 20 cm long inlet nozzle. The outlet nozzle is
30 cm long. The fan is induced the air then enters the damping
chamber, to suppress the turbulence in order to achieve laminar flow
conditions with a steady and uniform velocity distribution at the
channel entrance. Airflow is passed through a 60 cm long entrance re-
gion and through a 60 cm test section and is then passed through a
30 cm long exit region. The air leaves through the outlet nozzle to the
fan by a flexible hose. The flow velocity is measured using the air flow
meter. The flow rate through the wind tunnel is measured with the
velocity varying between 0.1 and 0.23 m/s. The flow meter gauge is
calibrated using an orifice plate for several volume flow rates, and the
least square method is applied to obtain the relation flow rate, as shown
in Eq. (1). The temperature of the inlet air was measured by a ther-
mocouple located at the entrance. The wind tunnel is mounted on a
wooden board that allows the orientation of the wind tunnel to be
changed for a range of longitudinal inclination angles (0°–70°) and a
transverse lateral inclination in the range of (0°–90°).
= × + × × +Q Q Q Q1912.6 88.201 0.5581 0.0118ref exp
3
exp
2
exp
(1)
where Qref is the standard flow rate, and Qexp is the experimental flow
rate.
2.2. The test section
The test section is a rectangular heated base with longitudinal fins.
This section contains an aluminum plate that is 60 × 30 × 0.6 cm. The
fin array is made from aluminum with 2 mm thick, 60 mm length. This
array was installed on the aluminum plate by making 2 mm width
grooves and 3 mm deep. The fins are embedded into the grooves of the
aluminum base plate without clearance by pressing hard and forcing
the fins into the grooves. The fins are then fixed by spot-welding along
the aluminum plate, similar to how many studies embed longitudinal
fins into the grooves of the base plate without welding [14,20,25]. The
section view (A-A) in Fig. 1 of the rectangular duct is graphically dis-
played in Fig. 3 and shown photographically in Fig. 4. The insulated
with 15 cm glass wool and a wooden box were implemented on all sides
of the test section to insulate it from the ambient environment. Table 1
shows descriptions of the tested fin array.
2.3. Heater circuit
The test section bottom wall was constructed from a 6 mm alu-
minum plate heated with a heating element. A sheet heater was located
under the aluminum plate, which was distributed along the aluminum
plate, i.e., both have the same dimensions of 30 cm × 60 cm, as seen in
Fig. 5.
The variation in the heater plate was provided by an electric cur-
rent, providing the boundary condition of a constant heat flux for the
experimental study. The plate was heated using an electrical heater,
which consisted of a nickel-chrome wire that was wrapped up as par-
allel strips on an electrically isolated plate, but the heat-conductive was
made of mica and covered by another mica plates (inserted between
two mica sheets). The heater is situated in contact under of the base; the
thickness of the heating element is equal to nearly 3 mm. The test
section is completely insulated along all sides to drive all the heat to the
fin array.
2.4. Thermocouple circuit
The base plate temperature was measured by a thermocouples set
(type K NiCr-Ni) located inside an aluminum plate of thickness 6 mm.
The thermocouples are installed in the bottom wall inside holes drilled
in the aluminum plate, the diameter of drilling holes is 6 mm and the
depth is 5 mm. The number of thermocouples was 24, which were
Fig. 1. Schematic diagram of the experimental setup.
R.Z. Homod et al. International Journal of Thermal Sciences 137 (2019) 627–639
629
4. distributed on the aluminum plate.
2.5. The experimental data
From the experimental study can be measured the voltage drop
across the heater, temperature, electric current, and velocity. Then from
the heated plate can calculate the average Nusselt number as follows:
=Nu
h D
k
av
av h
air (2)
where hav: the average heat transfer coefficient.
Dh: characteristic length.
kair: thermal conductivity of air.
The average heat transfer coefficient expressed by Eq. (3) is fre-
quently used in experimental studies and represented by the average
surface temperature of the aluminum plate and air inlet temperature.
The experimental verifications of Eq. (3), previously identified and
adopted by many studies as an active method to determine the average
heat transfer coefficient, are given in Refs. [14,20,25,26]. Furthermore,
the channel hydraulic diameter Dh is known by Eq. (4).
=h
Q
A T T( )
av
convection
b w in (3)
=D
A4
h
c
(4)
where Ab = L*W is the unfinned area of the heated wall, Ac is the duct
cross-sectional area, Qconv. is the fluid convection heat transfer rate, Tw
is the average heated wall temperature, P is the summation of edges of
the duct and Tin is an air inlet temperature. The heat transfer from both
the fins and heated aluminum plate by convection (Qconvection) is cal-
culated by the energy balance [27–30], as follows:
= + +Q Q Q Qtotal convection conduction radiation (5)
where Qtotal is the total supplied power, Qradiation is the overall loss of
radiation from the heated base and fin areas, and Qconduction is the
overall heat loss from the isolation of the duct. Based on Ohm's law the
overall energy provided to the heater can be calculated.
= ×Q V Itotal (6)
Heat loss was calculated in isolating the test section, as shown
below:
Fig. 2. Photo image of the experimental setup. (a) Lateral inclination case, (b) Longitudinal inclination case.
Fig. 3. Schematic diagram of the test section (section A-A).
R.Z. Homod et al. International Journal of Thermal Sciences 137 (2019) 627–639
630
5. =Q k A
T
L
coduction insulation insulation
insulation
insulation (7)
where kinsulation is the insulation for the thermal conductivity, Tinsulation
is the inside and outside gradient temperature of the insulation.
Radiation losses are calculated from the following equation:
=Q FA T T( )radiation R w b
4 4
(8)
where F is the shape factor, AR is the radiation surface area, and σ is the
constant of Boltzmann, 5.67 × 10−8
W/m2
.K4
.
The Reynolds number:
=
w D
Re in h
air (9)
The Grashof number can be modified (Gr*) as:
=
=
Gr
g q D
k
con h
air air
4
2
(10)
where =qcon
Q
A
convection
b
is the mean heat flux transported by convection to
the air.
The properties of the fluid are calculated at an average of the heated
plate and fluid inlet
+
( )T T
2
w in
.
3. Calibration of thermocouples
The accuracy of commercial measurement devices is less than the
accuracy of equipped laboratory devices. To overcome this problem, a
calibration process is carried out. The measured value found from a
measuring tool is thus compared with the identified value of the test
standard under definite reference conditions using measuring proce-
dures.
The digital multimeter and its thermocouples were calibrated
against the standard digital thermocouples for several readings. Using
the least square method, the relation of the true temperature of the
digital temperature gauge was performed and is as follows:
=T T1.0778 1.013ref exp (11)
where Tref is the standard temperature, and Texp is the experimental
temperature.
The accuracy of the instruments applied to the case study is shown
in Table 2.
4. Uncertainty analysis
To calculate the validity of the experimental study, a validation and
uncertainty estimation (errors in measurements) is conducted on all
measured quantities of heat supplied, thermocouple values, and fin
array dimensions. According to Moffat's standard procedures [31,32],
the uncertainties are estimated. Nusselt number uncertainty is ap-
proximately ± 5% and, for the modified Grashof number uncertainty, is
approximately ± 3.5%. Reynolds number uncertainty is
Fig. 4. Photo image of the test section (section A-A).
Table 1
Design considerations of the test fin array.
Parameter Values
Thermal conductivity of fin, 237 W/m
kfin K
Duck width, W 30 cm
Duck height, H 10 cm
Fin number, Nfin 15
Fin length, Lfin 60 cm
Fin height, Hfin 6 cm
Fin thickness, tfin 2 mm
Fin spacing, S 17 mm
Fig. 5. Photograph of the heater element.
R.Z. Homod et al. International Journal of Thermal Sciences 137 (2019) 627–639
631
6. approximately ± 3%. The average heat transfer coefficient uncertainty
can be determined using Eq. (12) [33] and is approximately ± 1.74%.
Neglecting the conduction losses during the thin thermocouple
wires because of the diameter less than 0.18 mm. Heat losses such as
radiation, the thermal contact resistance of the fins, conduction losses
during the isolation and conduction losses through the thin thermo-
couple are calculated in Appendix A based on Eq. (5). These losses were
found to equal 12.07% to clarify that the maximum total heat losses do
not exceed 13% of the overall power consumed [14,20,25]. The re-
duction in the total losses is mainly due to the fact that the duct is well
insulated and that each fin was inserted by force into the groove and
pushed down to make contact with the bottom of the groove in the base
plate. Then fixed by spot-welding along aluminum plate beside, a
molten 2024-T6 aluminum alloy (k = 185 W/m.K) was poured into an
interface line between the fins and the bottom plate to reduce the
thermal contact resistance, as shown in Fig. 4(b).
= + +
h
h
Q
Q
A
A
T
T
( )
2 2 2
(12)
5. Results and discussion
An experimental study for a rectangular fin array with the heat
transfer of laminar mixed convection in a horizontal orientation with a
longitudinal and lateral inclination of the rectangular duct, in which the
lower wall is exposed to a uniform heat flux. Two different cases are
investigated. In case one, measurements are performed for the lateral
inclination angle, with a range α = 0°, 30°, 60°, and 90°. Case two is
achieved by studying both the longitudinal and lateral inclination ef-
fects, with the lateral inclination angle varying from 0° to 90° and the
longitudinal inclination range Ө = 0°, 30°, 60°, and 70°. The
experiments were conducted under various flow conditions, ranging
from Re = 1000 to 2300 and with a modified Grashof number
Gr* = 3 × 108
to 1 × 109
.
This paper seeks to test the more appropriate parameter to facilitate
comparisons with other similar studies that adopted the average heat
transfer coefficient hav [14,20,25]. Thus, the coefficient of heat transfer
has been considered the dependent variable. Furthermore, it is com-
paratively easier to calculate the coefficient of heat transfer than the
Nusselt number. Accordingly, there are many studies that adopted the
heat transfer coefficient as the dependent variable [34–37].
5.1. Case one: lateral inclination angles (α)
Fig. 6 illustrates the change of the local temperature of the heated
surface along the distance extended from the inlet to the outlet of the
test section for a lateral inclination angle α = 30°, Re = 2300 and
several Grashof numbers. It clear from this figure that the temperature
values in the entry of the test section have nearly the same inlet tem-
perature and represent forced convection thermal conditions. Then, the
temperature increases until it reached a maximum value of nearly
z = 0.4 m. This result refers to the intensity of the buoyancy secondary
flow. Furthermore, distribution of the local heat transfer coefficient for
the lateral inclination angle α = 30° at Re = 2300 and the different
modified Grashof numbers are shown in Fig. 6. In the entry zone of the
test section, the forced convection features seem clear on the behavior
of the heat transfer coefficient. After the short distance of the channel,
instability begins in the buoyancy secondary flow, which prevents the
continuance decline in the local heat transfer coefficient. This outcome
due to the buoyancy strength, which becomes sufficient to instability
the boundary layer.
Moreover, increasing in the heat transfer coefficient is dis-
tinguished. The mixed convection zone started after the secondary flow.
The variations of the Grashof number on the coefficient of local heat
transfer are presented in this figure. It can be seen that the heat transfer
coefficient increases with the Grashof number.
The Grashof number's effect on the average convection heat coef-
ficient distribution is shown in Fig. 7 for different Reynolds number and
lateral inclination angles. For all lateral inclination angle cases, a re-
markable change can be observed in the convection heat coefficient
produced by an increase in the Grashof number. It is noticed that as Gr*
increases above 3 × 108
, a buoyancy-driven secondary flow adjacent to
the heated walls develops, which quickly increases as Gr* continues to
Table 2
Measuring instrument list.
Mesured Paramter Instrument Range Accuracy
Air temperature (Ta) BES-01 -2-90 °C ± 0.5 °C
thermocouple K NiCr-Ni – ± 0.25%
multimeter BS471110 – ± 1%
air velocity Fluke 922 1–80 m/s ± 0.015 m/s
Airflow Meter Fluke 922 0–99 m3
/hr ± 1%
wattmeter BEEMET 0–2000 w ± 1%
Fig. 6. Variation in the local base temperature and heat transfer coefficient for different Grashof numbers at angle α = 30°, Re = 2300.
R.Z. Homod et al. International Journal of Thermal Sciences 137 (2019) 627–639
632
7. increase. The reason that a pressure gradient in the channel develops,
which is against the inertial and buoyancy forces, is that it assists the
secondary effect.
It is observed from this figure that the convection heat transfer
coefficient with an orientation α = 60°, Re = 1000 and Re = 1800 is
higher than other orientation angles when Grashof number
Gr* = 9 × 108
. Additionally, the convection heat transfer coefficient in
the lateral inclination angle α = 30° and Re = 2300 it has the max-
imum heat transfer rate at Gr* = 9 × 108
. The low heat transfer
process with a high orientation angle is due to the impeding air, which
is generated by changing the angle so that the heated air that enters
between the fins will hit the surface of the fins before leaving the sides.
The thickness of the thermal boundary layer increases with a re-
duction in Re. Because of this layer, heat transfer from the heated wall
surface and the fin is decreased. There is a fluid flow entering the duct
and passing through a channel between the fins. The heat exchanging
takes place between the fresh air and the heated plate and goes out at
the exit. As a result, hav increases with increasing Re.
Fig. 8 Shows the change of the temperature in the heated wall Twz
and the local heat transfer coefficient hz for lateral inclination angles
α = 0° and 90° at Re = 2300, respectively.
It is observed from Fig. 8 that the base temperature increases with
an increasing Gr* and lateral inclination angle. With an increasing Gr*,
the values of the surface temperature increase when the angle is
changed from an upward orientation (α = 0°) to a sideways orientation
(α = 90°). It is also clear from Fig. 8 that the coefficient of heat transfer
diminishes as the heat sink is laterally inclined from the horizontal
(upward orientation) α = 0° to the vertical (sideways orientation) or-
ientation α = 90°. For the orientation angle α = 90°, the fluid between
the fin channels becomes hotter than the fluid above the tip fins. This
Fig. 7. Shows the change of average h with Reynolds number for several Grashof numbers and lateral inclination angles.
Fig. 8. Presented the local base temperature and h for different Gr* number and α = 0°, α = 90° at Re = 2300.
R.Z. Homod et al. International Journal of Thermal Sciences 137 (2019) 627–639
633
8. outcome leads to a reduction in the coefficient of heat transfer.
It can be observed from this figure that the local heat transfer
coefficient has the highest value at inlet due to a thin boundary layer
and supremacy forced convection. Then, the coefficient of heat transfer
is gradually decreased because there is a balance between the effect of
all convection and buoyancy. Thus the buoyancy effect controls over
the forced convection effect at the end part of the test section, leading
to an increase in the local heat transfer rate.
Fig. 9 displays the variant of the average convection heat coefficient
with regard to Re for lateral inclination angles α = 30°, α = 60°, and
Gr* = 6 × 108
. The orientation angle of fins α = 60° gives a coefficient
of heat transfer less than that of α = 30° orientation. It is, therefore,
concluded the rising heat transfer coefficient with decreasing α is due to
the buoyant force produced by the change in air density when the
temperature difference occurs. This outcome leads to more air entering
between the fin channels for low values of α, which leads to an efficient
heat exchange. Then air is heated in the course of the fin channels and
goes up, while, with an increase in the lateral inclination angle, some of
the hot air remains confined between the fins. Therefore, α = 30° or-
ientation delivers the best performance for natural cooling.
Furthermore, the heat transfer coefficient is affected by the or-
ientation as shown in Fig. 9 for different Reynolds numbers with lateral
inclination angles α = 0° and α = 90° and Gr* = 6 × 108
. The upward
orientation (α = 0°) have higher values of heat transfer coefficient than
that for the sideways orientation (α = 90°). The sideways orientation
(α = 90°) causes the thermal boundary layer to concentrate on the fin
surfaces. Therefore, there is a concentration of the boundary layers,
resulting in a decrease in the fluid inflow velocity during fin arrays,
avoiding the entry of fresh fluid into the fin channels. Therefore, the hot
fluid remains longer among fin passages.
5.2. Case two: longitudinal inclination (Ө) and lateral inclination angle
case (α = 90°)
This experiment was conducted to demonstrate the effect of both
the longitudinal and lateral inclination angles on the heat transfer
features of mixed convection laminar flow from fins inside a rectan-
gular duct oriented with a lateral inclination angle α = 90° and long-
itudinal inclination ranges (Ө = 0°, 30°,60°,70°).
Fig. 10 shows the change of the local base temperature and
Fig. 9. Shows the change of average h with Reynolds number for lateral inclination angles α = 30°, α = 60°, and Gr* = 6 × 108
.
Fig. 10. Variation of local base temperature and convection heat coefficient for different Gr* at Ө = 60°, α = 90° and Re = 1000.
R.Z. Homod et al. International Journal of Thermal Sciences 137 (2019) 627–639
634
9. coefficient of heat transfer for various Grashof numbers at longitudinal
inclination angle Ө = 60°, Re = 1000, and a lateral inclination angle
α = 90°. In the entrance part of the test section, the temperature is low
and mostly, it is affected by the inlet temperature. Then, after some
distance, the temperature increases because of the influence of mixed
convection before decreasing from the mixing of hot and cold fluids.
At Gr* = 3 × 108
, heat transfer occurs by conduction, which
overcomes the convection mechanism. At Gr* = 6 × 108
, the heat
transfer mechanism through the duct is both forced convection and
natural convection. As Gr* increases to 9 × 108
, natural convection
becomes the predominant heat transfer mechanism. It is detected that
the base temperature rises with an increasing Gr*. As a result, the heat
transfer coefficient increases, as can be noticed in Fig. 10.
To study the influence of the longitudinal inclination angle on the
mechanisms of heat transfer for a horizontal and longitudinal inclined
duct, in the heat transfer process exist three mechanisms that play an
important role in heat transfer for the longitudinal inclined case. The
convection is forced by these three mechanisms due to the uniform
mainstream, where the direct free convection as a result of the com-
ponent of the gravity vector parallel to the heated wall and the indirect
free convection due to the component of the gravity vector normalized
to the heated plate [38].
The effect of Gr* on the average heat transfer coefficient was stu-
died in Fig. 11 for several Re and longitudinal inclination angles. The
trend of the curves displays that the average heat transfer coefficient
hav rises with increasing Re and Gr* for all longitudinal inclination
angles. In addition, the average heat transfer coefficient hav rises with
increasing longitudinal inclination angles Ө because the buoyant force
is working in the flow direction, which will be improved with an in-
creasing longitudinal inclination angle and the natural convection ef-
fect.
The average heat coefficient changes with the longitudinal in-
clination angle for different Reynolds numbers and Gr* = 6 × 108
and
Gr* = 9 × 108
is shown in Fig. 12. From the figure, it is observed that
Fig. 11. Displays the convection heat coefficient with Re number for various Gr* number and Ө at α = 90.
Fig. 12. Exhibits that the average of heat convection with Ө for several Re numbers and Gr numbers, with α = 90°.
R.Z. Homod et al. International Journal of Thermal Sciences 137 (2019) 627–639
635
10. the coefficient of heat transfer increases as the longitudinal inclination
angle rises. It is known that, as the longitudinal inclination angle varies
from 0° to 70°, the strongest buoyancy force appears at higher long-
itudinal inclination angles (Ө > 0°) and the weakest at horizontal
conditions (Ө = 0°).
For the lower longitudinal inclination angle of Ө = 30°, there are
weak buoyancy forces, and fluid streams above the fin section prevent
the hot fluid from escaping from the fin arrays. These phenomena lead
to less in the performance of heat transfer. Additionally, for the higher
longitudinal inclination angle Ө = 70°, the largest average heat transfer
coefficient can be attained for all Re.
With increasing the Reynolds number, the velocity increases, which
prevents the power of the secondary flow condition and decreases the
development of the thermal boundary layer. A higher Re produces
smaller variations in hav. These features are noticed for Re = 2300,
where secondary flow conditions are mostly absent, and the forced
convection is the dominant mode.
Fig. 13 displays the change of the average heat transfer coefficient
Fig. 13. Shows the change of the average heat coefficient with Gr* number for different Ө and Re numbers and α = 90°.
Fig. 14. Comparison of the correlation found from the data set and experimental consequences for lateral inclination angles.
= + =Nu Re Gr( ) ( ) 0.912(1 0.0174 sin( )) for 70av
0.256 0.136 2.12
(13a)
= + =Nu Re Gr( ) ( ) 1.074(1 0.0857 sin( )) for 60av
0.183 0.098 1.96
(13b)
= + =Nu Re Gr( ) ( ) 0.852(1 0.1018 sin( )) for 30av
0.206 0.101 1.73
(13c)
= + =Nu Re Gr( ) ( ) 0.69(1.17 0.098 sin( )) for 0av
0.318 0.137 2.74
(13d)
R.Z. Homod et al. International Journal of Thermal Sciences 137 (2019) 627–639
636
11. with various Gr* and Re. From this figure, for the longitudinal in-
clination angle Ө = 30°, a lower value of hav is obtained. This result
occurs because the effects of buoyancy, which are induced by natural
convection, diminish, leading to in a low coefficient of heat transfer.
Furthermore, it is clear from this figure that the optimal angle for
the desired heat transfer is while the longitudinal inclination angle
Ө = 70°. This result is because of the body force component that ac-
celerates the fluid because of it acts in the direction of axial flow, re-
sulting from an increase in the heat transfer coefficient; this has an
important role in the heat sink cooling. It can be deduced that the heat
transfer coefficient increases when the fins are longitudinally inclined
from a horizontal orientation. The fins orientation also plays a sig-
nificant role in heat transfer enhancement.
5.3. Empirical correlations for the average Nusselt number
The variation of the heat transfer coefficient for the fins is due to the
two tilting orientations that have been previously observed. This out-
come gives a primary indicator as to how the Nusselt number will be
changed based on how the two angles change. The empirical equations
to correlate the mean Nusselt number are derived based on the
Reynolds number, modified Grashof number, and the longitudinal and
lateral inclination angles. Accordingly, the results are as expected, as
shown in Fig. 14. Fig. 14 explains the empirical equations derived for
the adoption of the lateral inclination angle as a dependent variable.
The correlation can be written as follows:with the following ranges:
1000 ≤ Re ≤ 2300, 3 × 108
≤ Gr*≤ 1 × 109
and 0°≤ α ≤ 90°, a
relative error of 9% and a correlation factor = 0.913.
Additionally, empirical equations are derived for case two (lateral
inclination angles α and longitudinal inclination angle θ) to associate
the average Nusselt number with the Reynolds number and modified
Grashof number. Fig. 15 explains these equations. The correlation can
be written as follows:
= + =Nu Re Gr( ) ( ) (1.25 sin( )) for 90av
0.248 0.136 2.011
(14a)
= + =Nu Re Gr( ) ( ) 1.08(1.06 sin( )) for 60av
0.188 0.177 2.108
(14b)
= + =Nu Re Gr( ) ( ) 1.14(1.89 sin( )) for 30av
0.156 0.229 1.937
(14c)
= + =Nu Re Gr( ) ( ) 0.81(1.15 sin( )) for 0av
0.203 0.197 2.018
(14d)
with the following ranges: 1000 ≤ Re ≤ 2300, 3 × 108
≤ Gr*≤
1 × 109
and 0° ≤ θ ≤ 70°, α = 90°, a relative error not exceeding 9%
and a correlation factor = 0.995.
6. Conclusions
Experimental studies were carried out for mixed convection heat
transfer, laminar flow with fins inside a horizontal and inclined duct
subjected to uniform heat flux at the bottom surface.
From the experimental study, the following can be concluded.
1 The results illustrate that the average heat transfer coefficient in-
creased with Re and the Grashof number for all inclination angles.
2 Smaller fluctuations in hav are observed with higher Re due to the
absence of the secondary flow effects and the forced convection in
the dominant mode.
3 A greater coefficient of heat transfer is observed at the highest
longitudinal inclination angles.
4 The heat transfer coefficient decreases with an increasing lateral
inclination angle.
5 As the longitudinal inclination angle increases, the buoyancy effect
increases, which causes an unstable secondary flow and results in a
fluctuation of the distribution of hav.
6 From the experimental results, the equations of correlations are
obtained to relate four main variables, independent variables
(modified Grashof number, longitudinal and lateral inclination an-
gles, and Reynolds number) and the dependent variable (the
average Nusselt number) as shown in equations (13a)-(14d).
Appendix A
To prove the validity of the experimental system, its output result is compared with its input power, and the convection losses have been
determined with good accuracy. The thermal balance equation can be expressed as follows [39].
=Q V*I m*cp*(T T )o in (1A)
Fig. 15. The data set and experimental results for inclination angles are implemented to show a comparison of the correlation.
R.Z. Homod et al. International Journal of Thermal Sciences 137 (2019) 627–639
637
12. where Q, V and I are the power, voltage and electric current for the heater circuit, respectively, m is the air mass flow rate, cp is the specific heat of
the air, and To and Tin are the temperature at the outlet and inlet, respectively.
=Q A * * *cp*(T T )c m o in (2A)
where Ac is the cross-sectional area of the duct, m is the mean velocity of the air, and is the air density. cp and are determined by the base
temperature Tb.
=
+
=
+ +
T
T T
2
T T T
2
b
o in
(3A)
= ° = °T 28.3 C, T 35.4341 Cin o
=
+
= °T
T T
2
31.867 Co in
=
+
=
+
= ° =T K
T T
2
42.329 31.867
2
37.098 C 310.098 310b
= = =T KCp 1.00546
kJ
kg. k
and 1.1406
kg
m
at 310b3
=
m
s
0.188m
=Q m
m
s
j
kg k
k
m
k(0.1*0.3) 0.188 1.00546 10
.
1.1406 (308.434 301.3)2 3
3
=Q
j
s
46.14348
= Q AV*I b
= =
loss
220*0.226
0.13
49.68
0.13
46.14348
=loss 0.1207
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