Entropy generation in flow field subjected to a porous block in a vertical channel

Entropy generation in the flow field subjected to a porous block situated in a vertical channel is examined. The effects of channel inlet port height (vertical height between channel inlet port and the block center), porosity, and block aspect ratio on the entropy generation rate due to fluid friction and heat transfer in the fluid are examined. The governing equations of flow, heat transfer, and entropy are solved numerically using a control volume approach. Air is used as the flowing fluid in the channel. A uniform heat flux is considered in the block and natural convection is accommodated in the analysis. It is found that entropy generation rate due to fluid friction increases with increasing inlet port height, while this increase becomes gradual for entropy generation rate due to heat transfer for the inlet port height exceeding 0.03 m. The porosity lowers entropy generation rate due to fluid friction and heat transfer. The effect of block aspect ratio on entropy generation rate is notable; in which case, entropy generation rate increases for the block aspect ratio of 1:2.     

Entropy analysis of unsteady magneto-nanofluid flow past accelerating stretching sheet with convective boundary condition

The unsteady laminar magnetohydrodynamics(MHD) boundary layer flow and heat transfer of nanofluids over an accelerating convectively heated stretching sheet are numerically studied in the presence of a transverse magnetic field with heat source/sink. The unsteady governing equations are solved by a shooting method with the Runge-KuttaFehlberg scheme. Three different types of water based nanofluids, containing copper, aluminium oxide, and titanium dioxide, are taken into consideration. The effects of the pertinent parameters on the fluid velocity, the temperature, the entropy generation number, the Bejan number, the shear stress, and the heat transfer rate at the sheet surface are graphically and quantitatively discussed in detail. A comparison of the entropy generation due to the heat transfer and the fluid friction is made with the help of the Bejan number. It is observed that the presence of the metallic nanoparticles creates more entropy in the nanofluid flow than in the regular fluid flow.     

Entropy analysis for third grade fluid flow with Vogel model viscosity in annular pipe

The steady-state flow of a third grade fluid between concentric circular cylinders is considered and entropy generation due to fluid friction and heat transfer in the annular pipe is examined. Depending upon the fluid viscosity, entropy generation in the flow system varies. The third grade fluid is employed to account for the non-Newtonian effect while Vogel model is accommodated for temperature-dependent viscosity. The analysis is based on perturbation technique. The closed form solutions for velocity, temperature and entropy fields are presented. Entropy generation due to fluid friction and heat transfer in the flow system is formulated. The influence of viscosity parameters A and B on the entropy generation number is investigated. It is found that entropy generation number reduces with increasing viscosity parameter A, which is more pronounced in the region close to the annular pipe inner wall and opposite is true for increasing viscosity parameter B.     

Irreversibility investigation of Casson fluid flow in an inclined channel subject to a Darcy-Forchheimer porous medium:a numerical study

The heat transfer and entropy generation characteristics of the magnetohydrodynamic Casson fluid flow through an inclined microchannel with convective boundary conditions are analyzed.Further,the effects of the viscous forces,Joule heating,heat source/sink,and radiation on the flow are taken into account.The non-dimensional transformations are used to solve the governing equations.Then,the reduced system is resolved by the fourth-fifth order Runge-Kutta-Fehlberg method along with the shooting technique.The effects of different physical parameters on the heat transfer and entropy generation are discussed in detail through graphs.From the perspective of numerical results,it is recognized that the production of entropy can be improved with the Joule heating,viscous dissipation,and convective heating aspects.It is concluded that the production of entropy is the maximum with increases in the Casson parameter,the angle of inclination,and the Hartmann number.Both the Reynolds number and the radiation parameter cause the dual impact on entropy generation.     

Repercussion of Hall effect and nonlinear radiation on Couette-Poiseuille flow of Casson-Williamson fluid through upright microchannel

The main aim of the present work is to investigate the flow and heat transport properties of non-Newtonian Casson-Williamson fluid through an upright microchannel along with entropy generation analysis, and explore the effects of convective boundary conditions, Couette-Poiseuille flow, and nonlinear radiation. The movement of liquid is scrutinized with the Hall effect and exponential heat source. The rheological characteristics of the Casson-Williamson fluid model are also considered. By considering the desirable similarity variables, the equations of motion are reduced to nonlinear ordinary differential equations. The Runge-Kutta-Fehlberg fourth-fifth order method along with the shooting method is adopted to solve these dimensionless expressions. The detailed investigation is pictorially displayed to show the influence of effective parameters on the entropy generation and the Bejan number. One of the major tasks of the exploration is to compare the Casson fluid and the Williamson fluid. The results show that the rate of heat transfer in the Casson fluid is more remarkable than that in the Williamson fluid.     

The thermodynamic design of heat and mass transfer processes and devices

This review article places in perspective the new work devoted both to the analysis of the thermodynamic irreversibility of heat and mass transfer components and systems and to the design of these devices on the basis of entropy generation minimization. The review focuses on the fundamental mechanisms responsible for the generation of entropy in heat and fluid flow and on the design tradeoff of balancing the heat transfer irreversibility against the fluid flow irreversibility. Applications are selected from the fields of heat exchanger design, thermal energy storage, and mass exchanger design. This article provides a comprehensive, up-to-date review of second-daw analyses published in the heat and mass transfer literature during the last decade.     

Heat transfer and entropy generation analysis of non-Newtonian fluid flow through vertical microchannel with convective boundary condition

The entropy generation and heat transfer characteristics of magnetohydrodynamic(MHD) third-grade fluid flow through a vertical porous microchannel with a convective boundary condition are analyzed. Entropy generation due to flow of MHD non-Newtonian third-grade fluid within a microchannel and temperature-dependent viscosity is studied using the entropy generation rate and Vogel's model. The equations describing flow and heat transport along with boundary conditions are first made dimensionless using proper non-dimensional transformations and then solved numerically via the finite element method(FEM). An appropriate comparison is made with the previously published results in the literature as a limiting case of the considered problem.The comparison confirms excellent agreement. The effects of the Grashof number, the Hartmann number, the Biot number, the exponential space-and thermal-dependent heat source(ESHS/THS) parameters, and the viscous dissipation parameter on the temperature and velocity are studied and presented graphically. The entropy generation and the Bejan number are also calculated. From the comprehensive parametric study, it is recognized that the production of entropy can be improved with convective heating and viscous dissipation aspects. It is also found that the ESHS aspect dominates the THS aspect.     

Entropy generation and natural convection in square cavities with wavy walls

The aim of the present work is to study the entropy generation in the natural convection process in square cavities with hot wavy walls through numerical simulations for different undulations and Rayleigh numbers, while keeping the Prandtl number constant. The results show that the hot wall geometry affects notably the heat transfer rate in the cavity. It has been found in the present numerical study that the mean Nusselt number in the case of heat transfer in a cavity with wavy walls is lower, as compared to heat transfer in a cavity without undulations. Based on the obtained dimensionless velocity and temperature values, the distributions of the local entropy generation due to heat transfer and fluid friction, the local Bejan number, and the local entropy generation are determined and plotted for different undulations and Rayleigh numbers. The study is performed for Rayleigh numbers 10³ < Ra < 10⁵, irreversibility coefficients 10^?4 < φ < 10^?2, and Prandtl numbers Pr = 0.71. The total entropy generation is found to increase with increasing undulation number.     

A computational method for geometric optimization of enhanced heat transfer devices based upon entropy generation minimization

A computational fluid dynamics‐based optimization methodology is developed, appropriate for the geometric optimization of enhanced heat transfer devices based upon the principle of entropy generation minimization, in which the objective function is evaluated from a flow field obtained by computational simulation. A quasi‐Newton optimization procedure is employed, with computation of the objective function gradients based upon a finite difference approach. The optimization procedure is developed to be general with regard to the choice of objective function, the details of the problem under consideration, and the computational methodology employed in solving the fluid flow and heat transfer problems. A novel implementation of a Taylor series‐based procedure for the fast solution of nearby problems is presented, which is found to greatly benefit the efficiency of the present methodology. Finally, a numerical experiment is presented, illustrating the use of the present method in the geometric optimization of a practical enhanced heat transfer device on the basis of the criterion of entropy generation minimization. The optimization of the fin spacing of a simple plate fin heat sink is considered, and a comparison of the computational results with results obtained by analytical optimization based upon empirical friction factor and Nusselt number correlations is given. Copyright © 2012 John Wiley & Sons, Ltd.     

Thermodynamic analysis and optimization of air-cooled heat exchangers

In the present study, a thermodynamic second-law analysis was performed to investigate the effects of different geometry and flow parameters on the air-cooled heat exchanger performance. For this purpose, the entropy generation due to heat transfer and pressure loss of internal and external flows of the air-cooled heat exchanger was calculated; and it was observed that the total entropy generation has a minimum at special tube-side Reynolds number. Also, it was seen that the increasing of the tube-side Reynolds number resulted in the rise of the irreversibility of the air-cooled heat exchanger. The results also showed when air-side Reynolds number decreased, the entropy generation rate of the external flow reduced. Finally, based on the computed results, a new correlation was developed to predict the optimum Reynolds number of the tube-side fluid flow.     

Second law analysis of the 2D laminar flow of two-immiscible,incompressible viscous fluids in a channel

The laminar and fully developed flows of two immiscible fluids confined in a thin slit of constant wall heat fluxes are analyzed in terms of entropy generations due to irreversibility of forced convection heat transfer. The governing equations are analytically derived using expressions for velocity distributions. The derived equation for the dimensionless entropy generation number is used to interpret the relative importance of frictions to conduction by varying irreversibility distribution ratio ϕ. It is found that the minimum entropy generation takes place at the dimensionless half transverse distance (ξ) of 0.3 for values of ϕ higher than zero. The entropy generation near the plate increases more rapidly in fluid I than in fluid II as viscous dissipation effects becomes more important. The velocity profiles are found to be in agreement with the distributions of the dimensionless entropy generation number (N _S ) for two-immiscible incompressible flows in the slit.     

Entropy generation for pipe flow of a third grade fluid with Vogel model viscosity

The flow of fluid-solid mixtures in a pipe can be treated as non-Newtonian fluids of third grade. Depending upon the fluid viscosity, entropy generation in the flow system varies. In the present study, flow of third grade fluid in a pipe is considered. The Vogel model is introduced to account for the temperature-dependent viscosity. Entropy generation due to fluid friction and heat transfer in the flow system is formulated. The influence of viscosity parameters A and B on the entropy generation number is investigated. It is found that increasing viscosity parameter A reduces the entropy generation number and opposite is true for increasing viscosity parameter B.     

Entropy generation analysis of fully developed laminar forced convection in a helical tube with uniform wall temperature

In the present study, fully developed laminar flow and heat transfer in a helically coiled tube with uniform wall temperature have been investigated analytically. Expressions involving relevant variables for entropy generation rate contributed to heat transfer and friction loss, and total entropy generation rate have been derived. The effect of various flow and coil parameters like Reynolds number, curvature ratio, coil pitch, etc. on the entropy generation rate has been studied for two fluids- air and water. The results of the present study have been compared to the corresponding entropy generation values of straight pipe. Investigating the results, some optimum values for Reynolds number have been proposed and compared with the optimum Reynolds numbers of laminar flow inside a coiled tube subjected to constant heat flux boundary condition.     

Entropy generation analysis of natural convective radiative second grade nanofluid flow between parallel plates in a porous medium

The present article explores the entropy generation of radiating viscoelastic second grade nanofluid in a porous channel confined between two parallel plates. The boundaries of the plates are maintained at distinct temperatures and concentrations while the fluid is being sucked and injected periodically through upper and lower plates. The buoyancy forces, thermophoresis and Brownian motion are also considered due to the temperature and concentration differences across the channel. The system of governing partial differential equations has been transferred into a system of ordinary differential equations(ODEs) by appropriate similarity relations, and a shooting method with the fourth-order Runge-Kutta scheme is used for the solutions. The results are analyzed in detail for dimensionless velocity components. The temperature, concentration distributions, the entropy generation number, and the Bejan number corresponding to various fluid and geometric parameters are shown graphically. The skin friction, heat and mass transfer rates are presented in the form of tables. It is noticed that the temperature profile of the fluid is enhanced with the Brownian motion, whereas the concentration profile of the fluid is decreased with the thermophoresis parameter, and the entropy and Bejan numbers exhibit the opposite trend for the suction and injection ratio.     

Entropy generation in laminar jet: effect of velocity profiles at nozzle exit

Laminar free jet flow finds wide application in industry. Although considerable research studies were carried out in the past, but the irreversibility associated with the flow field due to heat transfer and viscous dissipation needs further investigation. In the present study, laminar free jet is considered and volumetric entropy generation in the flow field is computed. The normalized entropy ratio (entropy ratio generated in one-fourth of the jet length to total entropy generation), irreversibility, and the Merit number are determined for different velocity profiles leaving the nozzle. It is found that the uniform velocity profile results in less entropy generation due to viscous dissipation as compared to its counterpart corresponding to triangular velocity profile; however, the entropy generation due to heat transfer increases for the uniform profile.     

Effect of Richardson number on entropy generation over backward facing step

The flow over a backward facing step (BFS) has been taken as a useful prototype to investigate intrinsic mechanisms of separated flow with heat transfer. However, to date, the open literature on the effect of Richardson number on entropy generation over the BFS is absent yet, although the flow pattern and heat transfer characteristic both will receive significant influence caused by the variation of Richardson number in many practical applications, such as in microelectromechanical systems and aerocrafts. The effect of Richardson number on entropy generation in the BFS flow is reported in this paper for the first time. The entropy generation analysis is conducted through numerically solving the entropy generation equation. The velocity and temperature, which are the inputs of the entropy generation equation, are evaluated by the lattice Boltzmann method. It is found that the distributions of local entropy generation number and Bejan number are significantly influenced by the variation of Richardson number. The total entropy generation number is a monotonic decreasing function of Richardson number, whereas the average Bejan number is a monotonic increasing function of Richardson number.     

Entropy minimization in micro-scale evaporating thin liquid film in capillary tubes

An analysis has been provided for the entropy generated for the micro/nano scale heat and mass transfer in a capillary tube in terms of the gradients of velocity, temperature and concentration as well as the physical properties of the fluid. The heat and mass transfer rates are assumed to be uniform on the surface of the capillary tube. The optimum tube diameter that corresponds to the minimization of entropy generated and minimization of fluid flow resistance is about 1 mm. We have applied the method of thermodynamic optimization to capillary driven systems. The objective was to identify the geometric configuration that maximized performance by minimizing the entropy generated when the flow rate is prescribed.     

Thermal analysis of a flow of immiscible couple stress fluids in a channel

An analytical study of the entropy generation rate and heat transfer in a flow of immiscible couple stress fluids between two horizontal parallel plates under a constant pressure gradient is performed. Both plates are kept at different and constant temperatures higher than that of the fluid. The Stokes couple stress flow model is employed. The classical no-slip condition is prescribed at the plates, and continuity of the velocity, rotation, couple stress, shear stress, temperature, and heat flux is imposed at the interfaces. The velocity and temperature distributions are found analytically, and they are used to compute the entropy generation number and Bejan number. The effects of the couple stress parameter and Reynolds number on the velocity, temperature, entropy generation number, and Bejan number are investigated. It is observed that the friction near the plates in couple stress fluids decreases as the couple stress increases.     

Effects of temperature-dependent viscosity variation on entropy generation,heat and fluid flow through a porous-saturated duct of rectangular cross-section

Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [12], is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Peclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio (width to height ratio). These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case by Ratts and Raut [14].     

Natural convection of SiO_2-water nanofluid in square cavity with thermal square column

A square with a thermal square column is a simple but nontrivial research prototype for nanofluid research. However, until now, the effects of the temperature of the square column on the heat and mass transfer of nanofluids have not been revealed comprehensively, especially on entropy generation. To deepen insight into this important field, the natural convection of the SiO_2-water nanofluid in a square cavity with a square thermal column is studied numerically in this study. The effects of the thermal column temperature(T = 0.0, 0.5, 1.0, 1.5), the Rayleigh number(ranging from 10~3 to 10~6),and the volume fraction of the nanoparticle(varying from 0.01 to 0.04) on the fluid flow,heat transfer, and entropy generation are investigated, respectively. It is found that, no matter at a low or high Rayleigh number, the volume fraction of the nanoparticle shows no considerable effects on the flow field and temperature field for all the temperatures of the thermal column. With an increase in the volume fraction, the mean Nusselt number increases slightly. At the same time, it is found that, with an increase in the temperature of the thermal column, the average Nusselt number gradually decreases at all values of the Rayleigh number. Meanwhile, it is found that, at a high Rayleigh number, the heat transfer mechanism is the main parameter affecting the increase in the total entropy generation rather than the volume fraction. In addition, no matter at a high or low Rayleigh number, when T = 0.5, the total entropy generation is the minimum.