Entropy Generation Rate in Forced Convection Flow About Inclined Surfaces in a Porous Medium

2011 ◽  
Author(s):  
Bourhan Tashtoush ◽  
B. S. Yilbas
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Pressure Drop ◽  
Forced Convection ◽  
Entropy Generation ◽  
Operating Conditions ◽  
Generation Rate ◽  
Optimum Operating ◽  
Entropy Generation Rate ◽  
Thermal System

Entropy generation rate has been the attraction of research, since it provides information on the thermodynamic irreversibility associated with the thermal systems. The exergy distraction in the thermal system increases entropy generation rate while lowering the second law efficiency of the thermal system. The heat transferring devices, such as heat exchangers, operates better when temperature difference between the transferring device and the heat sink is maintained high. In addition, the use of porous material in these devices enhances the heat transfer rates due to the achievement of high heat transfer coefficients. However, the presence of the porous material also increases the pump power because of the high pressure drop in the flow system. This increases the operational costs. Consequently, entropy generation rate due to pressure drop needs to be minimized to reduce the cost; however, heat transfer rates from the thermal system needs to be enhanced to improve the thermal performance of the heat transferring device. Therefore, a balance between the entropy generation rates due to pressure drop and heat transfer needs to be attained to achieve optimum operating conditions of such devices. To investigate the optimum operating conditions, the forced convection problem about inclined surfaces (or wedges) in saturated porous medium is considered. The flow in the porous medium is described by the Darcy-Brinkman momentum equation. An exact analytical solution of the governing equations using Kummer function is developed for the velocity, temperature, Nusselt Number, and entropy generation rate for the case where the free stream velocity and wall temperature distribution of the inclined surface vary according to the same power function of distance x, along the plate. It is demonstrated that the entropy generation number is weakly dependent on the Brinkman-Darcy number for forced convection flow, which is particularly true near the wall region.

Genetic Algorithm-Based Optimal Design of Plate Fins Following Minimum Entropy Generation Considerations

2005 ◽  
Vol 219 (8) ◽  
pp. 757-765 ◽  
Author(s):  
R. K. Jha ◽  
S Chakraborty
Keyword(s):  
Heat Transfer ◽  
Genetic Algorithm ◽  
Optimal Design ◽  
Forced Convection ◽  
Entropy Generation ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Minimum Entropy ◽  
Minimum Entropy Generation ◽  
Continuous Plate

This paper deals with estimation of the optimal dimensions of arrays of plate fins cooled by forced convection. The optimization is achieved by minimizing the entropy generation rate using genetic algorithm-based evolutionary computing techniques. Results are presented for staggered plate fins configuration and continuous plate fins configuration. The effects of heat transfer and fluid friction on entropy generation rate are also reported.

Heat Transfer, Pressure Drop, and Entropy Generation in a Solar Collector Using SiO2/Water Nanofluids: Effects of Nanoparticle Size and pH

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Omid Mahian ◽  
Ali Kianifar ◽  
Ahmet Z. Sahin ◽  
Somchai Wongwises
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Heat Transfer Coefficient ◽  
Pressure Drop ◽  
Entropy Generation ◽  
Thermal Efficiency ◽  
Solar Collector ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Transfer Pressure

In this paper, an analytical study is carried out on the heat transfer, pressure drop, and entropy generation in a flat-plate solar collector using SiO2/water nanofluid with volume concentration of 1%. In the study, the effects of two different values of pH, i.e., 5.8 and 6.5, and two different sizes of nanoparticles, i.e., 12 nm and 16 nm, on the entropy generation rate in turbulent flow are investigated. The results are compared with the results obtained for the case of water. The findings show that by using the Brinkman model to calculate the viscosity instead of experimental data one obtains a higher heat transfer coefficient and thermal efficiency than that in the case of water, while, when the experimental data are used, the heat transfer coefficient and thermal efficiency of water are found to be higher than that of nanofluids. The results reveal that using nanofluids increases the outlet temperature and reduces the entropy generation rate. It is also found that for nanofluids containing the particles with a size of 16 nm, the increase in pH value would increase the entropy generation rate, while for nanoparticles with a size of 12 nm the increase in pH would decrease the entropy generation.

Second-Law Analysis on Wavy Plate Fin-and-Tube Heat Exchangers

1998 ◽  
Vol 120 (3) ◽  
pp. 797-800 ◽  
Author(s):  
W. W. Lin ◽  
D. J. Lee
Keyword(s):  
Entropy Generation ◽  
Operating Conditions ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Second Law ◽  
Spanwise Direction ◽  
Minimum Entropy ◽  
Tube Heat Exchanger ◽  
Second Law Analysis ◽  
Minimum Entropy Generation

Second-law analysis on the herringbone wavy plate fin-and-tube heat exchanger was conducted on the basis of correlations of Nusselt number and friction factor proposed by Kim et al. (1997), from which the entropy generation rate was evaluated. Optimum Reynolds number and minimum entropy generation rate were found over different operating conditions. At a fixed heat duty, the in-line layout with a large tube spacing along streamwise direction was recommended. Furthermore, within the valid range of Kim et al.’s correlation, effects of the fin spacing and the tube spacing along spanwise direction on the second-law performance are insignificant.

scholarly journals Analytical Analysis of Heat Transfer and Entropy Generation in a Tube Filled with Double-Layer Porous Media

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1214 ◽  
Author(s):  
Kun Yang ◽  
Wei Huang ◽  
Xin Li ◽  
Jiabing Wang
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Nusselt Number ◽  
Double Layer ◽  
Entropy Generation ◽  
Single Layer ◽  
Entropy Generation Rate ◽  
Total Entropy ◽  
Interfacial Radius

The heat transfer and entropy generation in a tube filled with double-layer porous media are analytically investigated. The wall of the tube is subjected to a constant heat flux. The Darcy-Brinkman model is utilized to describe the fluid flow, and the local thermal non-equilibrium model is employed to establish the energy equations. The solutions of the temperature and velocity distributions are analytically derived and validated in limiting case. The analytical solutions of the local and total entropy generation, as well as the Nusselt number, are further derived to analyze the performance of heat transfer and irreversibility of the tube. The influences of the Darcy number, the Biot number, the dimensionless interfacial radius, and the thermal conductivity ratio, on flow and heat transfer are discussed. The results indicate, for the first time, that the Nusselt number for the tube filled with double-layer porous media can be larger than that for the tube filled with single layer porous medium, while the total entropy generation rate for the tube filled with double-layer porous media can be less than that for the tube filled with single layer porous medium. And the dimensionless interfacial radius corresponding to the maximum value of the Nusselt number is different from that corresponding to the minimum value of the total entropy generation rate.

Lower Entropy Generation in Microchannels With Laminar Single Phase Flow

2010 ◽  
Author(s):  
E. Galvis ◽  
J. R. Culham
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Pressure Drop ◽  
Transfer Coefficient ◽  
Entropy Generation ◽  
Entropy Generation Rate ◽  
Channel Geometry ◽  
Micro Channels ◽  
Optimum Channel

In this study the entropy generation minimization method is used to find the optimum channel dimensions in micro heat exchangers with a uniform heat flux. With this approach, pressure drop and heat transfer in the micro channels are considered simultaneously during the optimization analysis. A computational model is developed to find the optimum channel depth knowing other channel geometry dimensions and coolant inlet properties. The flow is assumed laminar and both hydrodynamically and thermally fully developed and incompressible. However, to take into account the effect of the developing length in the friction losses, the Hagenbach’s factor is introduced. The micro channels are assumed to have an isothermal or isoflux boundary condition, non-slip flow, and fluid properties have dependency on temperature accordingly. For these particular case studies, the pressure drop and heat transfer coefficient for the isoflux boundary condition is higher than the isothermal case. Higher heat transfer coefficient and pressure drop were found when the channel size decreased. The optimum channel geometry that minimizes the entropy generation rate tends to be a deep, narrow channel.

Numerical Investigation of Local Entropy Generation for Laminar Flow in Rotating-Disk Systems

2010 ◽  
Vol 132 (9) ◽  
Author(s):  
Mohammad Shanbghazani ◽  
Vahid Heidarpoor ◽  
Marc A. Rosen ◽  
Iraj Mirzaee
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Laminar Flow ◽  
Entropy Generation ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Bejan Number ◽  
Local Entropy ◽  
Fluid Friction ◽  
Local Entropy Generation

The entropy generation is investigated numerically in axisymmetric, steady-state, and incompressible laminar flow in a rotating single free disk. The finite-volume method is used for solving the momentum and energy equations needed for the determination of the entropy generation due to heat transfer and fluid friction. The numerical model is validated by comparing it to previously reported analytical and experimental data for momentum and energy. Results are presented in terms of velocity distribution, temperature, local entropy generation rate, Bejan number, and irreversibility ratio distribution for various rotational Reynolds number and physical cases, using dimensionless parameters. It is demonstrated that increasing rotational Reynolds number increases the local entropy generation rate and irreversibility rate, and that the irreversibility is mainly due to heat transfer while the irreversibility associated with fluid friction is minor.

Finned Metal Foam Heat Sinks for Electronics Cooling in Forced Convection

2002 ◽  
Vol 124 (3) ◽  
pp. 155-163 ◽  
Author(s):  
A. Bhattacharya ◽  
R. L. Mahajan
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Heat Transfer Coefficient ◽  
Pressure Drop ◽  
Transfer Coefficient ◽  
Forced Convection ◽  
Metal Foam ◽  
Experimental Results ◽  
Heat Sinks ◽  
The Heat Transfer Coefficient

In this paper, we present recent experimental results on forced convective heat transfer in novel finned metal foam heat sinks. Experiments were conducted on aluminum foams of 90 percent porosity and pore size corresponding to 5 PPI (200 PPM) and 20 PPI (800 PPM) with one, two, four and six fins, where PPI (PPM) stands for pores per inch (pores per meter) and is a measure of the pore density of the porous medium. All of these heat sinks were fabricated in-house. The forced convection results show that heat transfer is significantly enhanced when fins are incorporated in metal foam. The heat transfer coefficient increases with increase in the number of fins until adding more fins retards heat transfer due to interference of thermal boundary layers. For the 20 PPI samples, this maximum was reached for four fins. For the 5 PPI heat sinks, the trends were found to be similar to those for the 20 PPI heat sinks. However, due to larger pore sizes, the pressure drop encountered is much lower at a particular air velocity. As a result, for a given pressure drop, the heat transfer coefficient is higher compared to the 20 PPI heat sink. For example, at a Δp of 105 Pa, the heat transfer coefficients were found to be 1169W/m2-K and 995W/m2-K for the 5 PPI and 20 PPI 4-finned heat sinks, respectively. The finned metal foam heat sinks outperform the longitudinal finned and normal metal foam heat sinks by a factor between 1.5 and 2, respectively. Finally, an analytical expression is formulated based on flow through an open channel and incorporating the effects of thermal dispersion and interfacial heat transfer between the solid and fluid phases of the porous medium. The agreement of the proposed relation with the experimental results is promising.

Forced Convection in a Porous Channel With Localized Heat Sources

1994 ◽  
Vol 116 (2) ◽  
pp. 465-472 ◽  
Author(s):  
A. Hadim
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Pressure Drop ◽  
Heat Source ◽  
Forced Convection ◽  
Numerical Study ◽  
Porous Channel ◽  
Heat Sources ◽  
Porous Layers ◽  
Channel Configuration

A numerical study is performed to analyze steady laminar forced convection in a channel filled with a fluid-saturated porous medium and containing discrete heat sources on the bottom wall. Hydrodynamic and heat transfer results are reported for two configurations: (1) a fully porous channel, and (2) a partially porous channel, which contains porous layers above the heat sources and is nonporous elsewhere. The flow in the porous medium is modeled using the Brinkman-Forchheimer extended Darcy model. Heat transfer rates and pressure drop are evaluated for wide ranges of Darcy and Reynolds numbers. Detailed results of the evolution of the hydrodynamic and thermal boundary layers are also provided. The results indicate that as the Darcy number decreases, a significant increase in heat transfer is obtained, especially at the leading edge of each heat source. For fixed Reynolds number, the length-averaged Nusselt number reaches an asymptotic value in the Darcian regime. In the partially porous channel, it is found that when the width of the heat source and the spacing between the porous layers are of the same magnitude as the channel height, the heat transfer enhancement is almost the same as in the fully porous channel while the pressure drop is significantly lower. These results suggest that the partially porous channel configuration is a potentially attractive heat transfer augmentation technique for electronic equipment cooling, an end that motivated this study.

Entropy Generation Minimization in a Pressure-Driven Microflow of Viscoelastic Fluid With Slippage at the Wall: Effect of Conjugate Heat Transfer

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Rajkumar Sarma ◽  
Pranab Kumar Mondal
Keyword(s):  
Heat Transfer ◽  
Viscoelastic Fluid ◽  
Entropy Generation ◽  
Conjugate Heat Transfer ◽  
Applied Pressure ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Minimum Entropy ◽  
Viscoelastic Parameter ◽  
Entropy Generation Minimization

We focus on the entropy generation minimization for the flow of a viscoelastic fluid through a parallel plate microchannel under the combined influences of applied pressure gradient, interfacial slip, and conjugate heat transfer. We use the simplified Phan–Thien–Tanner model (s-PTT) to represent the rheological behavior of the viscoelastic fluid. Using thermal boundary conditions of the third kind, we solve the transport equations analytically to obtain the velocity and temperature distributions in the flow field, which are further used to calculate the entropy generation rate in the analysis. In this study, the influential role of the following dimensionless parameters on entropy generation rate is examined: the viscoelastic parameter (εDe2), slip coefficient (k¯), channel wall thickness (δ), thermal conductivity of the wall (γ), Biot number (Bi) and Peclet number (Pe). We show that there exists a particular value of the abovementioned parameters that lead to a minimum entropy generation rate in the system. We believe the results of this analysis could be of helpful in the optimum design of microfluidic system/devices typically used in thermal management, such as micro-electronic devices, microreactors, and microheat exchangers.

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