International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Transient Three-dimensional Numerical Analysis of Forced Convection Flow and ...IOSR Journals
A three-dimensional transient numerical study of a constant property Newtonian fluid in curved pipe under laminar flow conditions is presented for a uniform wall temperature boundary condition. Numerical solutions were obtained using the control volume method described by Patankar for the range of. The working fluid was water. The transient flow pattern and the temperature distribution on the tube section were derived for different values of the Reynolds number. Graphical results for velocity and temperature are presented and analyzed. Results have shown that the maximum velocity in center of velocity profile increase with increasing of Reynolds number. In curved pipes, time averaged results exhibited Dean circulation and a strong velocity and temperature stratification in the radial direction. Flow and heat transfer were strongly asymmetric, with higher values near the outer pipe bend.
NUMERICAL INVESTIGATION OF LAMINAR NANOFLUID FLOW IN MICRO CHANNEL HEAT SINKS IAEME Publication
The effect of using nanofluids on heat transfer and aerodynamics characteristics in rectangular shaped micro channel heat sink (MCHS) is numerically investigated for Reynolds number range of (100-400 ) and different value of heat flux (50 , 100, 150 ) / . In this study,the MCHS performance using tow type of nanofluid with volume
fraction 10% was used as a coolant is examined. The three-dimensional steady, laminar flow and heat transfer governing equations are solved using The computational fluid dynamics code (FLUENT). The MCHS performance is evaluated in terms of temperature profile, heat transfer,velocity profile, pressure drop and friction factor.
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.
Obtain average velocity from a knowledge of velocity profile, and average temperature from a knowledge of temperature profile in internal flow.
Have a visual understanding of different flow regions in internal flow, and calculate hydrodynamic and thermal entry lengths.
Analyze heating and cooling of a fluid flowing in a tube under constant surface temperature and constant surface heat flux conditions, and work with the logarithmic mean temperature difference.
Obtain analytic relations for the velocity profile, pressure drop, friction factor, and Nusselt number in fully developed laminar flow.
Determine the friction factor and Nusselt number in fully developed turbulent flow using empirical relations, and calculate the heat transfer rate.
Convective heat transfer and pressure drop in v corrugatedMohamed Fadl
New energy system development and energy
conservation require high performance heat exchanger, so
the researchers are seeking to find new methods to enhance
heat transfer mechanism in heat exchangers. The objectives
of this study are investigating heat transfer performance
and flow development in V-corrugated channels, numerical
simulations were carried out for uniform wall heat flux
equal 290 W/m
2
using air as a working fluid, Reynolds
number varies from 500 to 2,000, phase shifts,
0 \ Ø \ 180, and channel heights (S = 12.5, 15.0, 17.5
and 20 mm). Governing equations of flow and energy were
solved numerically by using finite volume method. The
numerical results indicated that, wavy (V-corrugated)
channels have a significant impact on heat transfer
enhancement with increase in pressure drop though chan-
nel due to breaking and destabilizing in the thermal
boundary layer are occurred as fluid flowing through the
corrugated surfaces and the effect of corrugated phase shift
on the heat transfer and fluid flow is more significant in
narrow channel, the goodness factor (j/f) was increased
with increasing channel phase shift, the best performance
was noticed on phase shift, Ø = 180 and channel height,
S = 12.5 mm.
Transient Three-dimensional Numerical Analysis of Forced Convection Flow and ...IOSR Journals
A three-dimensional transient numerical study of a constant property Newtonian fluid in curved pipe under laminar flow conditions is presented for a uniform wall temperature boundary condition. Numerical solutions were obtained using the control volume method described by Patankar for the range of. The working fluid was water. The transient flow pattern and the temperature distribution on the tube section were derived for different values of the Reynolds number. Graphical results for velocity and temperature are presented and analyzed. Results have shown that the maximum velocity in center of velocity profile increase with increasing of Reynolds number. In curved pipes, time averaged results exhibited Dean circulation and a strong velocity and temperature stratification in the radial direction. Flow and heat transfer were strongly asymmetric, with higher values near the outer pipe bend.
NUMERICAL INVESTIGATION OF LAMINAR NANOFLUID FLOW IN MICRO CHANNEL HEAT SINKS IAEME Publication
The effect of using nanofluids on heat transfer and aerodynamics characteristics in rectangular shaped micro channel heat sink (MCHS) is numerically investigated for Reynolds number range of (100-400 ) and different value of heat flux (50 , 100, 150 ) / . In this study,the MCHS performance using tow type of nanofluid with volume
fraction 10% was used as a coolant is examined. The three-dimensional steady, laminar flow and heat transfer governing equations are solved using The computational fluid dynamics code (FLUENT). The MCHS performance is evaluated in terms of temperature profile, heat transfer,velocity profile, pressure drop and friction factor.
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.
Obtain average velocity from a knowledge of velocity profile, and average temperature from a knowledge of temperature profile in internal flow.
Have a visual understanding of different flow regions in internal flow, and calculate hydrodynamic and thermal entry lengths.
Analyze heating and cooling of a fluid flowing in a tube under constant surface temperature and constant surface heat flux conditions, and work with the logarithmic mean temperature difference.
Obtain analytic relations for the velocity profile, pressure drop, friction factor, and Nusselt number in fully developed laminar flow.
Determine the friction factor and Nusselt number in fully developed turbulent flow using empirical relations, and calculate the heat transfer rate.
Convective heat transfer and pressure drop in v corrugatedMohamed Fadl
New energy system development and energy
conservation require high performance heat exchanger, so
the researchers are seeking to find new methods to enhance
heat transfer mechanism in heat exchangers. The objectives
of this study are investigating heat transfer performance
and flow development in V-corrugated channels, numerical
simulations were carried out for uniform wall heat flux
equal 290 W/m
2
using air as a working fluid, Reynolds
number varies from 500 to 2,000, phase shifts,
0 \ Ø \ 180, and channel heights (S = 12.5, 15.0, 17.5
and 20 mm). Governing equations of flow and energy were
solved numerically by using finite volume method. The
numerical results indicated that, wavy (V-corrugated)
channels have a significant impact on heat transfer
enhancement with increase in pressure drop though chan-
nel due to breaking and destabilizing in the thermal
boundary layer are occurred as fluid flowing through the
corrugated surfaces and the effect of corrugated phase shift
on the heat transfer and fluid flow is more significant in
narrow channel, the goodness factor (j/f) was increased
with increasing channel phase shift, the best performance
was noticed on phase shift, Ø = 180 and channel height,
S = 12.5 mm.
Experimental Study on Two-Phase Flow in Horizontal Rectangular Minichannel wi...IJERA Editor
An experimental study was conducted to investigate two-phase air-water flow characteristics, in horizontal
rectangular minichannel with Y-junction. The width (W), the height (H) and the hydraulic diameter (DH) of the
rectangular cross section for the upstream side of the junction are 4.60 mm, 2.50 mm and 3.24 mm, while those
for the downstream side are 2.36 mm, 2.50 mm and 2.43 mm. The entire test section was machined from
transparent acrylic block, so that the flow structure could be visualized. Liquid single-phase and air-liquid twophase
flow experiments were conducted at room temperature. The flow pattern, the bubble velocity, the bubble
length, and the void fraction were measured with a high-speed video camera. Pressure profile upstream and
downstream from the junction was also measured for the respective flows, and the pressure loss due to the
contraction at the junction was determined from the pressure profiles. Two flow patterns, i.e., slug and annular
flows, were observed in the fully-developed region apart from the junction. In the analysis, the frictional pressure
drop data, the two-phase frictional multiplier data, bubble velocity data, bubble length data and void fraction data
were compared with calculations by some correlations in literatures. In addition, new pressure loss coefficient
correlations for the pressure drop at the junction has been proposed. Results of such experiment and analysis are
described in the present paper.
The results show that, with proper selection of physical parameters, significant heat transfer
enhancements and pressure drop reductions can be achieved simultaneously with porous pin fins and
the overall heat transfer performances in porous pin fin channels are much better than those in
traditional solid pin fin channels. The effects of pore density are significant. As PPI increases, the
pressure drops and heat fluxes in porous pin fin channels increase while the overall heat transfer
efficiencies decrease and the maximal overall heat transfer efficiencies are obtained at PPI 20.
Furthermore, the effects of pin fin form are also remarkable. With the same physical parameters, the
overall heat transfer efficiencies in the long elliptic porous pin fin channels are the highest while they
are the lowest in the short elliptic porous pin fin channels
Numerical study of heat transfer in pulsating turbulent air flowMohamed Fadl
A numerical investigation of heat transfer
characteristics of pulsating turbulent flow in a circular
tube is carried out. The flow is thermally and
hydrodynamically fully developed and the tube wall is
subjected to a uniform heat flux. The flow inlet to the
pipe consists of fixed component and pulsating
component that varies sinusoidally with time. The flow
and temperature fields are computed numerically using
computational fluid dynamics (CFD) Fluent code.
Prediction of heat transfer characteristics is performed
over a range of 10 4 ≤ Re ≤ 4x10 4 and 0 ≤ ƒ ≤ 70 are
observed. Results showed little reduction in the mean
time-averaged Nusselt number with respect to that of
steady flow. However, in the fully developed
established region, the local Nusselt number either
increases or decreases over the steady flow-values
depending on the frequency parameter. These noticed
deviations are rather small in magnitude for the
computed parameter ranges. The characteristics of heat
transfer are qualitatively consistent with the available
experimental and numerical predictions.
Numerical Investigation of Mixed Convective Flow inside a Straight Pipe and B...iosrjce
The present study deals with a numerical investigation of steady laminar and turbulent mixed
convection heat transfer in a horizontal pipe and bend pipe using air as the working fluid.The thermal boundary
condition chosen is that of uniform temperature at the outer wall. Computations were performed to investigate
the effect of inlet Rayleigh number and Reynolds number in the velocity and temperature profile at inside of the
pipe. The secondary flow is more intense in the upper part of the cross-section. It increases throughout the
cross-section until its intensity reaches a maximum, and then it becomes weak at far downstream. For the
horizontal pipe the value of the L/D ratio becomes more than 10 the secondary flow effects are neutralized and
the velocity profile almost become constant throughout.
International Journal of Computational Engineering Research(IJCER)ijceronline
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
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.
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.
Presentación utilizada por Darío Pérez en la Jornada Orientación Profesional sobre el Perfil Profesional del Técnico de Consultoría.
Ciclo de Jornadas de Orientación Profesional organizadas por el ISM, el COBCM y ACA.
Experimental Study on Two-Phase Flow in Horizontal Rectangular Minichannel wi...IJERA Editor
An experimental study was conducted to investigate two-phase air-water flow characteristics, in horizontal
rectangular minichannel with Y-junction. The width (W), the height (H) and the hydraulic diameter (DH) of the
rectangular cross section for the upstream side of the junction are 4.60 mm, 2.50 mm and 3.24 mm, while those
for the downstream side are 2.36 mm, 2.50 mm and 2.43 mm. The entire test section was machined from
transparent acrylic block, so that the flow structure could be visualized. Liquid single-phase and air-liquid twophase
flow experiments were conducted at room temperature. The flow pattern, the bubble velocity, the bubble
length, and the void fraction were measured with a high-speed video camera. Pressure profile upstream and
downstream from the junction was also measured for the respective flows, and the pressure loss due to the
contraction at the junction was determined from the pressure profiles. Two flow patterns, i.e., slug and annular
flows, were observed in the fully-developed region apart from the junction. In the analysis, the frictional pressure
drop data, the two-phase frictional multiplier data, bubble velocity data, bubble length data and void fraction data
were compared with calculations by some correlations in literatures. In addition, new pressure loss coefficient
correlations for the pressure drop at the junction has been proposed. Results of such experiment and analysis are
described in the present paper.
The results show that, with proper selection of physical parameters, significant heat transfer
enhancements and pressure drop reductions can be achieved simultaneously with porous pin fins and
the overall heat transfer performances in porous pin fin channels are much better than those in
traditional solid pin fin channels. The effects of pore density are significant. As PPI increases, the
pressure drops and heat fluxes in porous pin fin channels increase while the overall heat transfer
efficiencies decrease and the maximal overall heat transfer efficiencies are obtained at PPI 20.
Furthermore, the effects of pin fin form are also remarkable. With the same physical parameters, the
overall heat transfer efficiencies in the long elliptic porous pin fin channels are the highest while they
are the lowest in the short elliptic porous pin fin channels
Numerical study of heat transfer in pulsating turbulent air flowMohamed Fadl
A numerical investigation of heat transfer
characteristics of pulsating turbulent flow in a circular
tube is carried out. The flow is thermally and
hydrodynamically fully developed and the tube wall is
subjected to a uniform heat flux. The flow inlet to the
pipe consists of fixed component and pulsating
component that varies sinusoidally with time. The flow
and temperature fields are computed numerically using
computational fluid dynamics (CFD) Fluent code.
Prediction of heat transfer characteristics is performed
over a range of 10 4 ≤ Re ≤ 4x10 4 and 0 ≤ ƒ ≤ 70 are
observed. Results showed little reduction in the mean
time-averaged Nusselt number with respect to that of
steady flow. However, in the fully developed
established region, the local Nusselt number either
increases or decreases over the steady flow-values
depending on the frequency parameter. These noticed
deviations are rather small in magnitude for the
computed parameter ranges. The characteristics of heat
transfer are qualitatively consistent with the available
experimental and numerical predictions.
Numerical Investigation of Mixed Convective Flow inside a Straight Pipe and B...iosrjce
The present study deals with a numerical investigation of steady laminar and turbulent mixed
convection heat transfer in a horizontal pipe and bend pipe using air as the working fluid.The thermal boundary
condition chosen is that of uniform temperature at the outer wall. Computations were performed to investigate
the effect of inlet Rayleigh number and Reynolds number in the velocity and temperature profile at inside of the
pipe. The secondary flow is more intense in the upper part of the cross-section. It increases throughout the
cross-section until its intensity reaches a maximum, and then it becomes weak at far downstream. For the
horizontal pipe the value of the L/D ratio becomes more than 10 the secondary flow effects are neutralized and
the velocity profile almost become constant throughout.
International Journal of Computational Engineering Research(IJCER)ijceronline
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
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.
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.
Presentación utilizada por Darío Pérez en la Jornada Orientación Profesional sobre el Perfil Profesional del Técnico de Consultoría.
Ciclo de Jornadas de Orientación Profesional organizadas por el ISM, el COBCM y ACA.
AN EXPERIMENTAL STUDY OF EXERGY IN A CORRUGATED PLATE HEAT EXCHANGERIAEME Publication
In the present work an attempt has been made to investigate the performance of a 3 channel 1-1 pass, corrugated plate heat exchanger. The plates had sinusoidal wavy surfaces with corrugation angle of 450. Hot water at different inlet temperature ranging from 400C to 600C was made to flow in the central channel to get cooled by water in the outer channels.
NUMERICAL ANALYSIS OF THERMAL PERFORMANCE OF LOUVER FINijiert bestjournal
Louver fins are widely used in heat exchanger for a utomotive applications such as radiator,intercooler,condenser,heater core etc. This study presents numerical analysis of effect of variation of louver pitch on heat transfer rate of louver fins. The three dimensional governing equations for fluid flow and heat transfe r are solved using ANSYS Fluent 14.5 for air flow of 4 m/s to 9 m/s. The variations of t emperature,pressure and heat transfer rate are studied using computational model. The enhancem ent of heat rate is observed as louver pitch is reduced.
Helically Coiled Tube with Different Geometry and Curvature Ratio on Convecti...AM Publications
A helically coil-tube heat exchanger is generally applied in industry applications due to its compact structure, larger heat transfer area and higher heat transfer capability. Several studies from literature have also indicated that heat transfer rate in helically coiled tube are superior to straight tube due to complex flow pattern exist inside helical pipe. The concept behind compact heat exchanger is to decrease size and increase heat load which is the typical feature of modern helical tube heat exchanger. While the heat transfer characteristics of helical coil heat exchangers are available in the literature, This paper elaborates a brief review on different curvature ratio and geometry of tubes in heat transfer through heat exchangers.
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.
Numerical Investigation of Heat Transfer from Two Different Cylinders in Tand...IJERA Editor
A two dimensional technique has been studied numerically to predict the heat transfer from two different cylinders
in tandem arrangement (one is circular and the other is elliptical) using finite element technique with RNG k-ε turbulent
model, taking into consideration the effect of gap ratio (L/Deq ) and Reynolds number , where the distance between
the centers of cylinders is L (L=30 mm and 37 mm), the equivalent diameter of cylinder is Deq=22.5mm and
the range of Reynolds number is 2x103
< Reeq < 21x103 .The commercial CFD software FLUENT was used to get
the thermofluid characteristics (temperature, velocity, kinetic energy and pressure contours ,coefficient of friction ,
heat transfer coefficient , Stanton number …… etc) of the flow around cylinders. The dependency of the heat transfer
coefficient, Stanton number (Sta), pressure drop, and friction factor for circular and elliptical cylinders on the gap
ratio is clear from the results. Results show that, for circular cross section, the heat transfer coefficient is increased as
velocity, and gap ratio increase. On the other hand Sta decreased as velocity increase. The pressure drop and hence
the friction factor increase for circular cylinder as gap ratio increases. For elliptical tube the heat transfer and Sta are
relatively equal to that for circular one at the same gap ratio, but the overall power consumption and friction factor
for elliptical tube is lower than that of circular one. As the elliptical cylinder fixed on the second position the heat
transfer and Sta
increase, on the other hand the pressure drop and hence the friction factor decreases. For all studied
arrangements the highest heat transfer is observed for the arrangement of circular-first and elliptical-second cylinder
and the minimum pressure drop and hence the friction factor are for the elliptical one
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.
Experimental investigation of performance of plate heat exchanger for water a...eSAT Journals
Abstract
Compact heat exchangers are most widely used for heat transfer applications in industries. Plate heat exchanger is one such compact heat exchanger, provides more area for heat transfer between two fluids in comparison with shell and tube heat exchanger. Plate type heat exchangers are widely used for liquid-to-liquid heat transfer applications with high density working fluids. This study is focused on use of plate type heat exchanger for water as a working fluid. This research work deals with experimental investigation of plate type heat exchanger with evaluation of convective heat transfer coefficient, overall heat transfer coefficient, exchanger effectiveness. The heat exchanger used for carrying out this work consists of thin metal welded plates of stainless steel with 1mm thickness, rectangular geometry and distance between two plates is 7mm. This test setup consists of total 16 numbers of plates and it is designed to withstand with 850C temperature, pressure drop is neglected. Tests are conducted by varying operating parameters like mass flow rate, inlet temperatures of hot water. The main objective of this work is to find effects of these parameters on performance of plate heat exchanger with parallel flow arrangement. Results show that, overall heat transfer coefficient and convective heat transfer coefficient increases with increase in mass flow rate and Reynolds number. Also the effectiveness varies slightly with heat capacity ratio. In this study, maximum effectiveness achieved for plate heat exchanger with water as a working fluid is 0.48.Use of plate heat exchanger is more advantageous than the tube type heat exchanger with same effectiveness, as it occupies less space.
Keywords: Plate heat exchanger, Convective heat transfer coefficient, Effectiveness, Overall heat transfer coefficient, Reynolds 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.
Pressure and Heat Transfer over a Series of In-line Non-Circular Ducts in a P...Carnegie Mellon University
Flow and heat transfer for two-dimensional laminar flow at low Reynolds number for five in-line ducts of various cross-sections in a parallel plate channel are studied in this paper. The governing equations were solved using finite-volume method. A commercial CFD software, ANSYS Fluent 14.5 was used to solve this problem. A total of three different non-conventional cross-sections and their characteristics are compared with that of circular cross-section. Shape-1, Shape-2 and Shape-3 performed better for heat transfer rate than the circular cross-section, but also offered higher resistance to the flow. Shape-1 offered less resistance to flow at Re < 200 but post Re = 200 the resistance equalled to that of the Shape-3. In overall, Shape-2 performed better when the heat transfer and resistance to flow were considered.
THE EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER AND HYDRO DYNAMICAL CHA...ijmech
Compact size and high heat transfer coefficient of helical coil heat exchangers causes them to have an
important role in various industrial applications. This paper investigate numerically on the influence of
different parameters such as coil radius, coil pitch and diameter of tube on the hydrodynamic and
heat transfer characteristics of helical double tube heat exchangers using the CFD software which is
based on the principles of heat transfer, fluid mechanics and thermodynamics. The results indicated that
heat transfer augmentation occurs by increasing of the inner Dean Number, inner tube diameter, curvature
ratio and by the reduction of the pitch of heat exchanger coil. By increasing the radius of coils, the
secondary flow effects due to centrifugal forces diminishes and flow of fluid through the coils tends to flow
in a straight path and as a result, the friction coefficient decreases consequently.
NUMERICAL INVESTIGATION OF NATURAL CONVECTION HEAT TRANSFERFROM SQUARE CYLIND...ijmech
The enhancement of natural convection heat transfer using nanofluids from horizontal square cylinder
placed in a square enclosure is investigated numerically. Water-based Cu is used as the working nanofluid.
The investigation covered a range of Rayleigh numbers of 104
- 106
, nanoparticles volume fraction of
(0<ϕ≤0.2), enclosure width to cylinder height ratio, W/H of 2.5. The investigation includes the solution of
the governing equations in the Vorticity-Stream function space with the aid of a body fitted coordinate
system. Algebraic grid generation is used in the initial transformations, followed by an elliptic
transformation to complete the grid generation to computational domain. The resulting discretized system
of equations is solved using an ADI method. The built code is validated and the results showed an increase
in average Nusselt number with increasing the volume fraction of the nanoparticles for the whole range of
Rayleigh number. The isotherms are nearly similar when the volume fraction of nanoparticles is increased
from 0 to 0.2 for each Rayleigh number but a change in the streamlines is observed.
Similar to International Journal of Engineering and Science Invention (IJESI) (20)
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
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International Journal of Engineering and Science Invention (IJESI)
1. International Journal of Engineering Science Invention
ISSN (Online): 2319 – 6734, ISSN (Print): 2319 – 6726
www.ijesi.org Volume 2 Issue 7 ǁ July. 2013 ǁ PP.17-29
www.ijesi.org 17 | Page
Entropy generation analysis for fully developed laminar
convection in hexagonal duct subjected to constant heat flux and
minimization of entropy generation by adjusting the shape of the
cross section.
Dipak P. Saksena
Assistant Professor, Mechancial Engg. Dept.Institute of Diploma Studies.Nirmaunieversity
ABSTRACT: The entropy generation of a fully developed laminar flow in a hexagonal duct is investigated in
this study. A constant heat flux condition was applied in this analysis. Two fluids, water and engine oil, were
used to study the effect of fluid properties on the entropy generation. The fluid properties were evaluated using
average temperature between inlet and outlet duct sections. The aspect ratio of the hexagonal duct was varied
to show its effect on the entropy generation. Attention was also given to the supplied heat flux affecting the
entropy generation. Finally, the entropy generation calculated from the hexagonal duct was compared with that
from rectangular and circular ducts having the same hydraulic diameter and cross sectional. Entropy
generation in fully-developed flow through a duct with heat transfer is discussed. Methods are presented to
minimize entropy generation by adjusting the shape of the duct’s cross-section. Choosing a different cross-
sectional shape allows for control of the competing fluid flow and heat transfer irreversibilities. By controlling
the competing irreversibilities, the total entropy generation rate can be minimized. Given the flow rate, heat
transfer rate, available cross-sectional area, and the fluid properties, a general design correlation is presented
that allows for a determination of the optimal shape of a duct. area.
I. INTRODUCTION
The entropy generation of a fully developed laminar flow in a hexagonal duct is investigated discussed
in this study.
A constant heat flux condition was applied in this analysis. Two fluids, water and engine oil, were used
to study the effect of fluid properties on the entropy generation. The fluid properties were evaluated using
average temperature between inlet and outlet duct sections. The aspect ratio of the hexagonal duct was varied to
show its effect on the entropy generation.
In the present study, the entropy generation for fully developed laminar convection through a hexagonal duct
with constant heat flux is investigated. Water and engine oil are the fluids used to observe the significance of
fluid viscosity and fluid properties on the entropy generation. Effects of aspect ratio and heat flux on the entropy
generation are studied. Based on the same hydraulic diameter and cross-sectional area, the entropy generation
for the hexagonal duct is compared to those for rectangular and circular ducts.
Forced convection heat transfer in a flow passage is affected by two types of losses, namely, loss
associated with heat transfer through a temperature difference and loss associated with fluid friction. Entropy
generation minimization has been proposed as a criterion for the design of flow passages in internal flow forced
convection heat transfer configurations. Because entropy is generated by friction encountered in flowing fluids
and by heat transfer through a temperature difference, a calculation of the overall entropy generation allows for
an evaluation of these losses on a common scale. Moreover, because the entropy generation is a direct measure
of the irreversibilities associated with heat transfer and fluid friction, the overall performance of a device
containing heat transfer passages can be improved by calculating and minimizing the total entropy generation of
the convective heat transfer process. A few past studies have attempted to compare the entropy generation in
ducts with different cross-sectional shapes and to determine the cross-sectional shape that will yield minimum
entropy generation [10–12]. Sahin finds that for high Reynolds number flows where fluid friction
irreversibility dominates, the optimal shape for a flow channel is the circular shape in both laminar flow with a
constant wall temperature [10] and in turbulent flow with constant wall heat flux [11].
II. ENTROPY GENERATION IN STEADY STATE FLOW THROUGH DUCTS.
In this section, the formulation of entropy generation equation is derived. All thermal properties are
assumed to be uniform along the duct. The development of the entropy generation equation can be started by
considering the fluid, which flows through a constant cross-sectional area duct, subjected to constant heat flux,
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as shown in Fig. 1. From the energy balance of the control volume of length dx, the heat transfer rate to the fluid
inside the duct is:
Nomenclature for entropy generation
b, c, d duct sides, m
cp specific heat, J/kg K
Dh hydraulic diameter, m
f friction factor or Darcy friction factor
h heat transfer coefficient, W/m2 K
k thermal conductivity, W/m K
L duct length, m
m mass flow rate, kg/s
Nu Nusselt number
p pressure, Pa
P perimeter, m
q" heat flux, W/m2
Q heat rate, W
Re Reynolds number
s specific entropy, J/kg$K
S entropy rate, W/K
St Stanton number
Greek symbols
ΔT wall-bulk fluid temperature difference (T w-T)
γ aspect ratio of hexagonal duct
dimensionless entropy generation
θ hexagonal duct angle, degree
ρ fluid density, kg/m3
τ dimensionless temperature difference (τ=ΔT/T)
μ absolute viscosity, kg/m s
Superscripts
-
quantity per unit mole
Subscripts
gen generation
i inlet
o outlet
w wall
Nomenclatures for Entropy generation minimization
A cross-sectional area
Bo duty parameter
Cf coefficient in friction factor
Ch coefficient in Nusselt number
cp specific heat
Dh hydraulic diameter
dT
dx axial temperature gradient
f Darcy friction factor
k thermal conductivity
m mass flow rate
Nu Nusselt number
P perimeter
Pr Prandtl number
q' heat transfer rate per unit length
RA area based Reynolds number
Re Reynolds number
Sgen entropy generation per unit length
T temperature
Greek
α exponent in Nusselt number
β exponent in Nusselt number
γ exponent in friction factor
μ viscosity
ρ density
ϕ irreversibility distribution ratio
χ shape factor
Subscripts
opt at the optimum
min minimum value
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Entropy generation minimization by adjusting the shape of the cross section:
III. ENTROPY GENERATION IN STEADY-STATE FLOW THROUGH DUCTS:
Consider the general internal flow configuration shown in Fig. 1. Fluid flows through a duct with a
cross-sectional area A, a perimeter P, and a hydraulic diameter Dh = 4A/P. The shape of the crosssection is
arbitrary but constant over the entire length of duct. A single-phase, incompressible and Newtonian fluid flows
through the duct with a mass flow rate m at a bulk temperature T. Heat is transferred to the duct at a rate (per
unit length) of q' , through the duct wall to the fluid across a temperature difference ΔT. Following Bejan [2],
for T<<T, the entropy generation rate per unit length is given by
(1)
where Nu, f, q', and k are the Nusselt number, the Darcy friction factor, the fluid density, and the fluid thermal
conductivity, respectively.
Nu= Ch Reα
Pr
β
(2)
f = Cf Re-γ
(3)
Using the same notation as Ratts and Raut [4], the Nusselt number and friction factor for fully-developed
laminar or turbulent flow are generalized as
where Re=mDh/Aμ is the Reynolds number, Pr is the Prandtl number, and μ is the viscosity. The
parameters Ch, Cf, α, β, and γ are tabulated in Table 1 for the circular cross-section and for rectangular and
elliptical cross-sections with varying aspect ratios [13]. Additionally, in Table 1 the shape factor, defined as χ=
P/Dh or χ=P2/
4A = 4A/Dh2
, is shown for each cross-section. The shape factor is used throughout the following
analysis and in the interpretation of results.
After substitution of Eqs. (2) and (3) into Eq. (1), the entropy generation rate is given by
(4)
IV. DUCTS WITH SPECIFIED CROSS-SECTIONAL SHAPE
First, consider the entropy generation in a duct while holding constant the flow rate, the heat transfer rate, and
the fluid properties. Assume that the channel has a specified cross-sectional shape; that is, χ is specified.
Entropy generation can then be minimized by choosing the optimum cross-sectional size for the duct. For any
duct with a specified shape factor, the size is determined
by either the hydraulic diameter or the cross-sectional area, since these parameters are related through the shape
factor χ= 4A/Dh2
Furthermore, the definition of the shape factor is used to write.
Re=4m/ χ μDh (5)
For a constant flow rate, fluid properties, and cross-sectional shape, Eq. (5) shows that the Reynolds
number can only be varied by changing the size of the cross-section (through changes in the hydraulic diameter).
Thus, the optimum cross-sectional size can be found by determining the Reynolds number that minimizes
entropy generation. Using the definitions for the shape factor and Reynolds number, and substituting into Eq. (4),
(6)
The only parameter not held constant in the above equation is the Reynolds number. Differentiating
and setting the result equal to
zero, one finds that the optimum Reynolds number is given by
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(7)
where
(8)
is the duty parameter. From the optimum Reynolds number, the optimum irreversibility distribution
ratio (entropy generation due to fluid frictional losses divided by entropy generated by heat transfer through a
temperature difference, or, the last term in Eq. (6) divided by the first term in Eq. (6) evaluated at Reopt) is
evaluated as
(9)
Finally, the departure of the entropy generation from the optimum is evaluated as,
(10)
where S'gen,min is the minimum entropy generation rate evaluated when Re = Reopt.
Once the shape of the cross-section (the shape factor) is chosen, the generalized results above can be
used to find the optimum Reynolds number (or equivalently, the optimum size of a cross-section), the optimum
irreversibility distribution ratio, and the departure of the entropy generation from the optimum, provided that the
friction factor and Nusselt number correlations are known and can be described by Eqs. (2) and (3).
V. DUCTS WITH A FIXED CROSS-SECTIONAL AREA
Now consider a similar situation, where the entropy generation is minimized in a duct flow with
constant flow rate, constant heat transfer rate per unit length, and while holding the fluid properties constant.
Consider a channel with a specified cross-sectional area, A, and minimize entropy generation by choosing the
optimal crosssectional shape or shape parameter, χ , for the duct.
Once again, using the definitions of the shape factor and the Reynolds number, Eq. (4) can be
arranged to read
(11)
Furthermore, the Reynolds number is
(12)
Holding constant the fluid properties, the heat transfer rate, the flow rate, for a duct with a fixed cross-
sectional area, and assuming that the coefficients and exponents in the Nusselt number and friction factor
correlations are only weakly dependent on the shape of the cross-section, the only variable in Eq. (11) is the
Reynolds number. The Reynolds number can only vary with variations in the shape of the cross-section. To
determine the optimal Reynolds number, or equivalently, the optimal shape for a cross-section, differentiate
with respect to the Reynolds number and set the result equal to zero. This gives
(13)
where RA is a Reynolds number based on the area of the cross-section, defined by
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(14)
An optimal shape factor for a given flow configuration is evaluated from Eqs. (12) and (13) as
(15)
Finally, while holding the cross-sectional area constant, the optimum irreversibility distribution ratio and the
departure of entropy generation from the minimum are given by
(16)
(17)
VI. RESULTS AND DISCUSSION
In this section, the entropy generation due to heat transfer and viscous friction is investigated for fully
developed laminar flow in the hexagonal duct with constant heat flux forwater and engine oil. Some parameter
values, employed in the calculations for both fluids, are shown in Table 1.
Fig. 2. Relating variables of (a) hexagonal and (b) rectangular ducts.
In the analysis, the calculations started with finding the fluid outlet temperature, in which the constant
specific heat of the fluid was initially assumed (for example, cp = 4186 J/kgK for water). The average of the
mean fluid temperature was found based on the initial specific heat. Next, the new specific heat value was
determined based on the calculated mean temperature. The new outlet temperature of the fluid was calculated
again using new specific heat value. The iterative procedure was continued until the difference of the average
mean temperature taken from the last two iterations was less than 0.1 K. The specific heat and outlet
temperature in the last iteration were adopted. For fully developed laminar flow through the hexagonal duct
with constant heat flux, the Nusselt number and the fanning friction factor (the friction factor is four times
greater than the fanning friction factor) are available in [18]. According to the reference, at a specific q (see Fig.
2a), both parameters are dependent on the aspect ratio, g. Finally Eq. (12) was used to calculate the entropy
generation. If the dimensionless of the entropy generation is preferred, Eq. (13) can be employed.
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6.1. The comparison of the entropy generation between water and engine oil
Table 2 The comparison of entropy generation components for water and engine oil at γ = 1.5.
Table 2 shows the comparison of the entropy generation due to heat transfer and viscous friction for
water and engine oil at γ =1.5.
Moreover, the dimensionless entropy generation is also expressed in the last column. From Table 2, it
can be observed that the entropy generation due to heat transfer contributes to almost 100% in the total entropy
generation. Similar result was also observed by Ben-Mansour and Sahin [19] for a circular pipe. When the
results from both fluids are compared, the total entropy generation for the case of engine oil is higher than that
for the case of water. Considering only the entropy generation due to heat transfer for engine oil, it is higher
than that for water. Similarly, the entropy generation due to viscous friction for engine oil is higher than that for
water. To investigate the reason, Eq. (12) has to be carefully considered. Although the same heat flux was
supplied to both fluids, the outlet temperature for water and engine oil was different because of the difference in
the specific heats. As mentioned, at a specific q, the Nusselt number is a function of the aspect ratio. Therefore,
the same duct geometry for both fluids results in the same Nusselt number. Engine oil has lower specific heat
value than that of water.
Therefore, with the same heat flux and inlet temperature, the outlet temperature of engine oil is higher
than that of water. However, the thermal conductivity of engine oil is lower than that of water. The
multiplication result leads to a lower denominator of the first term in Eq. (12) for the case of engine oil,
compared with that for the case of water. As a result, the entropy generation due to heat transfer in the case of
engine oil is higher than that in the case of water. Considering the entropy generation due to viscous friction,
high viscosity in the case of engine oil causes this entropy generation to dramatically increase. The entropy
generation due to viscous friction for the engine oil is about 530 times that for water, while the viscosity of
engine oil is 424 times that of water. The total entropy generation for water and engine oil, calculated according
to the above condition, are 2.90 x 10-1
W/K and 1.21 W/K, respectively. When these values are converted to
dimensionless entropy generation, these become 1.39 x 10-3
and 3.10 x 10-2
, respectively.
6.2: The effect of duct aspect ratio and supplied heat flux
The aspect ratio of the duct was varied from 0.25 to 3.50 to study its effect on the entropy generation.
The parameter c was fixed at 0.04 m. Since the duct aspect ratio changed, the parameter b also changed. The
parameter d was computed using Eq. (16) with a fixed θ =75º and varied value of the aspect ratio. The values of
the parameters, shown in Table 1, were used again in these calculations.
Fig. 3 shows the dimensionless entropy generation forwater and engine oil. It can be observed that the
entropy generations for both fluids rapidly decrease when the aspect ratio increases. However, when the aspect
ratio is higher than 2.0, the dimensionless entropy generations for both fluids are nearly constant. The reason is
that when the parameter cis fixed, increasing the aspect ratio reduces the perimeter and hydraulic diameter.
Consequently, the surface area of the duct is decreased. Even though the heat flux supplied to the fluid is
constant, the total heat rate reduces because of a decrease in the heat transfer area. From Eq. (11), reducing the
total heat rate significantly causes a decrease in the total entropy generation. If Eq. (12) is considered, the same
result (decreasing the entropy generation) is caused by the decreasing duct perimeter and hydraulic diameter.
However, the above explanation should be considered with the fact that the entropy generation due to viscous
friction has insignificant effect on the total entropy generation, as previously discussed. For an aspect ratio
higher than 2.0, increasing the aspect ratio results in a slowly decreasing duct perimeter. Therefore, the total heat
rate slightly decreases and this event results the small variation in the total entropy generation. Moreover, if the
result presented in Fig. 3 is carefully considered, it can be noticed that the dimensionless entropy generation for
each fluid has a minimum value. The minimum dimensionless entropy generation for the case of water and
the case of engine oil takes place at the aspect ratio of 2.642 and 2.627, respectively. The effect of heat flux on
the entropy generation was also investigated.Water is the fluid used for this study. The parameters, given in
Table 1 were again utilized, except for the heat flux. The
heat flux was varied from 1000 W/m2
to 3600 W/m2
with an increment of 200 W/m2
. The change in the
dimensionless entropy generation was observed. Fig. 4a presents the result for the aspect ratio less than 2.642
(the minimum point), while Fig. 4b shows the result for the aspect ratio higher than 2.642. The figures clearly
show the existence of a minimum point. For Fig. 4a, at a specific heat flux when the aspect ratio increases, the
dimensionless entropy generation decreases. However, when the aspect ratio is higher than 2.642, the value of
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dimensionless entropy generation increases with increasing aspect ratio, as shown in Fig. 4b. For the effect of
heat flux on the dimensionless entropy generation, both
figures obviously illustrate that the heat flux has a strong influence on the entropy generation. At a high
value of heat flux, the dimensionless entropy generation seems to linearly increase when
heat flux increases.
Fig.3. The dimensionless entropy generations for water and engine oil versus duct aspect ratio.
6.3: The comparison of the entropy generations for hexagonal duct and duct with different geometries:
In this section, the entropy generation for the hexagonal duct is compared with that for ducts having
different geometries (rectangular and circular ducts). Two cases are considered. For the first case, the hydraulic
diameter is the same for all duct geometrics. For the second case, the cross-sectional area is the same. The
Nusselt numbers and the friction factors for the rectangular and circular ducts are available in [20].
Fig. 4. The dimensionless entropy generation versus supplied heat flux, (a) for γ <=2:642, (b) for γ <= 2:642.
8. Entropy generation analysis for fully…
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Considering the first case (the same hydraulic diameter) the parameters, shown in Table 1, were used
again in the calculation. The hydraulic diameter for different geometries was adjusted to make them have the
same values. For example, for the rectangular duct, one side was fixed to be equal to 2c (see Fig. 2b). The other
side (2X) was calculated according to the equivalent hydraulic diameter condition. In the case of circular duct,
its diameter was set to have the same value as hydraulic diameter of hexagonal duct. The calculationwas carried
out and the result is shown in Fig. 5. The figure shows that, with the same hydraulic diameter, the circular duct
is the best for this comparison. The use of circular duct results in the lowest dimensionless entropy generation
through this examination range.
Fig. 5. The comparison of the dimensionless entropy generation for hexagonal, rectangular, and circular ducts
with the equivalent hydraulic diameter condition.
For the hexagonal and rectangular ducts, the dimensionless entropy generations are not much different
and they are slightly higher than that of circular duct for lower hydraulic diameter. However, when the hydraulic
diameter increases, the dimensionless entropy generations for the hexagonal and rectangular ducts substantially
increase and diverge from that of circular
duct.
Fig. 6. The comparison of the dimensionless entropy generation for hexagonal, rectangular, and circular ducts
with the equivalent cross-sectional area condition.
From the comparison, it can be implied that the circular duct is better than the rectangular and
hexagonal ducts if the comparison is based on the entropy generation. The rectangular geometryis an inferior
choice. This conclusion has also been mentioned in [6]. For the hexagonal duct, its dimensionless entropy
generation is generally less than that of the rectangular. Nevertheless, for Dh < 0.036 m, the rectangular
geometry is a little better than hexagonal geometry in the context of thermodynamic irreversibility. The circular
duct gives the lowest dimensionless entropy generation. High thermodynamic irreversibility was observed from
the case of the rectangular duct. For the hexagonal geometry, it has the dimensionless entropy generation higher
than that of the circular geometry, but generally less than that of the rectangular one.
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6.4 Ducts with specified cross-sectional shape:
Bejan determined the entropy generation, the irreversibility distribution ratio, and the departure of the
entropy generation from the minimum for a circular cross-section in both laminar and turbulent flow [3]. In
Bejan’s analysis with the circular tube, the mass flow rate, the heat transfer rate per unit length, and the fluid
properties were held constant and the tube diameter was adjusted to minimize entropy generation. Using the
values from Table 1 in Eqs. (7) and (9) for the circular tube carrying laminar flow, one finds that Reopt = 0 and
that ϕopt = 0. As suggested by Bejan, for a circular tube with laminar flow, the tube diameter should be large
enough so that the entropy generation is dominated by the heat transfer contribution, which will result in a small
value for the irreversibility distribution ratio, ϕ. As discussed above, this behavior for laminar tube flow is
confirmed by the generalized expression in Eq. (9).
Using Table 1 and Eqs. (7), (9), and (10) for turbulent flow in a circular tube, the following are
evaluated:
(18)
(19)
(20)
These equations are identical to those of Bejan. In both laminar and turbulent flow in circular tubes, the
generalized results presented here reduce to expressions that are identical to the expressions derived by Bejan
for circular tubes.
The generalized expressions in Eqs. (7), (9), and (10) can be used to determine the optimal size (to
minimize entropy generation) of ducts with any cross-sectional shape, provided that the information contained
in Table 1 are known for the flow through the particular cross-section chosen.
Fig.2. The shape factor that minimizes entropy generation for flow in a duct with specified flow rate, heat
transfer rate, cross-sectional area and fluid properties. The figure is generated for circular, χ = π, and rectangular
χ = 4.5 and χ =10.125, cross sections in laminar and turbulent flow. The figure is for fluids with Pr = 0.7.
Fig. 3. The shape factor that minimizes entropy generation for flow in a duct with specified flow rate, heat
transfer rate, cross-sectional area and fluid properties. The figure is generated for circular, χ = π,, and elliptical, χ
= 5.79 and χ = 19.71, cross sections in laminar and turbulent flow. The figure is for fluids with Pr = 0.7.
10. Entropy generation analysis for fully…
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6.4: Ducts with a fixed cross-sectional area
For the case of internal convective heat transfer in a duct with a specified cross-sectional area, Eq. (15)
is used to determine an optimal shape factor (a shape factor that minimizes entropy generation). To illustrate
the determination of the optimal shape, results from Eq. (15) are presented graphically in Figs. 2 and 3.
Eq. (15) can be manipulated to give
(21)
As shown in Figs. 2 and 3, Eq. (15) results in straight lines on logarithmic scales when the parameters are
plotted on the abscissa and ordinate, respectively.
(22)
Fig. 2. The shape factor that minimizes entropy generation for flow in a duct with specified flow rate, heat
transfer rate, cross-sectional area and fluid properties. The figure is generated for circular, v = p, and
rectangular, v = 4.5 and v = 10.125, crosssections in laminar and turbulent flow. The figure is for fluids with Pr
= 0.7.
Fig. 3. The shape factor that minimizes entropy generation for flow in a duct with specified flow rate, heat
transfer rate, cross-sectional area and fluid properties. The figure is generated for circular, v = p, and elliptical,
v = 5.79 and v = 19.71, crosssections in laminar and turbulent flow. The figure is for fluids with Pr = 0.7.
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Eq. (21) shows that, regardless of the shape of the cross-section, the slope of the lines on the plot will
be constant and will be determined by the exponents in the Nusselt number and friction factor correlations
(although the slopes for laminar and turbulent flow may be different from one another). Fig. 2 was generated
using the exponents and coefficients for the Nusselt number and friction factor correlations in Table 1 for the
circular tube and the rectangular cross-sections. Fig. 3 was generated using the values in Table 1 for the
elliptical cross-sections. Although the lines in Figs. 2 and 3 have a constant slope regardless of the shape of the
cross-section, both the shape factor and the value of the Prandtl number (Figs. 2) and 3 were generated for Pr =
0.7) of the fluid will shift the position of the line on the plane. Most importantly, if one considers a flow with a
constant heat transfer rate per unit length and with constant fluid properties, the parameter on the horizontal axis
scales directly with the cross-sectional area of the duct and the parameter on the vertical axis scales directly with
the mass flow rate. For a particular convective flow with a given heat transfer rate, as soon as the flow rate and
cross-sectional area are chosen, Figs. 2 and 3 can be used to determine the optimal shape factor. By way of
example, consider a convective flow for which Pr = 0.7, (Bo/RA)2
= 1012
, and Bo = 1010
, and assume that we will
use either a circular cross-section or a rectangular cross-section. In Fig. 2, this flow is represented by a point
near the turbulent flow line of constant χopt =π. These results would suggest that, for this particular flow, a
circular cross-section (with χopt =π) is the optimal cross-section to minimize entropy generation.
Now consider the same flow, however, double the available cross-sectional area. The flow parameters
are now Pr = 0.7, (Bo/RA)2
= 2 x 1012
, and Bo=1010
. Notice that by increasing only the cross-sectional area we
move horizontally to the right in Fig. 2 Eq. (22) shows that Bo remains constant after changing only the area).
With an available cross-sectional area that is twice as large as in the previous example, the optimal shape factor
is near χopt= 10.125, suggesting that a rectangle with an aspect ratio of 8 is an optimal shape of the cross-section
for the larger flow area duct rather than the circular cross-section. When the available cross-sectional area of the
flow channel is doubled, the resistance to flow in the duct is reduced, thereby reducing the entropy generation
associated with fluid friction. However, Eq. (16) indicates that in both examples above, the optimal
irreversibility distribution ratio is
(23)
for these turbulent flows. To maintain this optimal irreversibility distribution ratio after an increase in
the cross-sectional area (and the associated reduction in fluid friction), the entropy generation associated with
heat transfer must also be reduced. The reduction in entropy generation associated with heat transfer is
accomplished by choosing a cross-section with a larger perimeter compared to its cross-sectional area (a cross-
section with a larger shape factor). Choosing a cross-sectional shape with a large perimeter increases the surface
area available for heat transfer, reducing the entropy generation associated with heat transfer and restoring the
balance required by Eq. (23) for minimum entropy generation. This example is continued by now considering a
flow with half the available cross-sectional area as in the original example, so that Pr = 0.7, (Bo/RA ) 2
= 5 x 1011
,
and Bo = 1010
. Referring again to Fig. 2, we find ourselves at a point to the left of the constant χopt = π line.
From Eq. (15), one calculates for these flow parameters, χopt = 0.48. Because the circular cross-section has the
smallest possible shape factor with χopt = π, a circle would be used in this flow configuration to minimize
entropy generation, although the true minimum could never be achieved. Figs. 2 and 3 show that flows with
small flow rates generally require channels with larger shape factors to minimize entropy generation. For
convective heat transfer with a low flow rate in a channel with a large cross-sectional area (the lower right
portions of Figs. 2 and 3), the contribution to the total entropy generation by fluid friction is relatively low. In
this situation, the total entropy generation is dominated by entropy generation due to heat transfer. To minimize
entropy generation, the shape factor can be increased by introducing a geometry with more surface area
available for heat transfer.
Next, consider an adiabatic flow , for which q́ =0. Circular or nearly circular cross-sections are used
throughout engineered and natural systems to transport fluids while minimizing flow losses (flow resistance) in
adiabatic flows [14]. In the case of an adiabatic flow, Bo = 0. In either laminar or turbulent flow, Eq. (15)
suggests that χopt = 0 for the adiabatic flow case. Again, because the smallest possible shape factor can be
achieved with the circular cross-section, the entropy generation minimization analysis of Eq. (15) suggests that a
circle is the most efficient cross-section for adiabatic flow.
Although Eq. (15) does reproduce the well-known result that the circular cross-section is the optimal
shape for adiabatic flow through a duct, the entropy generation minimization presented here also provides a new
result for ducts with forced convection heat transfer. The correlation in Eq. (15) and the examples shown
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above suggest that for flows dominated by heat transfer irreversibility (i.e., flows with large heat transfer rates,
small flow rates, and large available cross-sectional area, or equivalently, flows with large Bo and small RA) the
circular cross-section is not ideal and large aspect ratio channels should be used to minimize entropy generation.
VII. CONCLUSIONS
The entropy generation for fully developed laminar convection through a hexagonal duct with constant
heat flux is investigated. The result shows that the fluid properties strongly affect the entropy generation. The
total entropy generation, for the case of engine oil, is about 4.2 times of that for the case of water. The analysis
indicated that when the aspect ratio increases, the dimensionless entropy generation decreases. This is because,
at constant heat flux, when the parameter c is fixed and the aspect ratio increases, the total heat transfer rate
decreases. Consequently, the entropy generation due to heat transfer reduces. However, for aspect ratio that are
higher than 2.642 and 2.627 (for the case of water and engine oil, respectively), the dimensionless entropy
generation slightly increases with increasing aspect ratio. The comparison, based on the same hydraulic
diameter and crosssectional area conditions, illustrates that the circular duct has the lowest dimensionless
entropy generation, while the rectangular geometry generally causes the highest dimensionless entropy
generation. For the case of the hexagonal duct, its dimensionless entropy generation is usually in the middle.
Entropy generation in fully-developed convective heat transfer has been investigated. Generalized correlations
to determine the optimum cross-sectional shape of a flow passage to minimize entropy production have been
presented. The equations confirm the well-known conclusion that in adiabatic flow, the circular crosssection
will minimize flow resistance, which is reflected by a minimization of the entropy generation. However, in
flows with heat transfer, the correlations developed suggest that the circular cross-section may not always be
ideal. In situations where the heat transfer irreversibility dominates (with low flow rates, large available cross-
sectional areas, and high heat transfer rates), a duct with a large wetted perimeter (for example, a rectangular
channel with a large aspect ratio) will increase the surface area available for heat transfer and will minimize the
overall entropy generation.
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