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 generation in laser heating in relation to machining

Entropy generation during laser evaporative heating of solid substrate in relation to machining is considered and entropy generation rate due to different pulse intensities is computed. Energy method is used when simulating the phase change process and mushy zone formation across solid–liquid and liquid–vapor interfaces are accommodated. Since the heating duration is greater than the electron relaxation time, the Fourier heating model based on the equilibrium transport is employed in the simulations. Entropy generation in the substrate material is formulated during laser heating pulse. It is found that entropy generation rate in the surface region of the substrate material attains high values. Increasing power intensity ratio enhances the total entropy generation rate in a non-linear fashion.     

The effect of variable viscosity on the entropy generation and pumping power in a laminar fluid flow through a duct subjected to constant heat flux

Entropy generation and pumping power required for a laminar viscous flow in a duct subjected to constant heat flux has been investigated. The temperature dependence of the viscosity is taken into consideration. The ratio of pumping power to total heat flux decreases considerably and entropy generation increases along the duct length for viscous fluids. Therefore, it is shown that an optimum duct length may be obtained which minimizes total energy losses due to both entropy generation and pumping power. For low heat-flux conditions, entropy generation due to viscous friction becomes dominant and the dependence of viscosity on temperature must be considered in order to determine entropy generation accurately. Received on 17 May 1999     

A second law comparison for optimum shape of duct subjected to constant wall temperature and laminar flow

Various cross sectional duct geometries were compared from the point of view of entropy generation and pumping power requirement in order to determine the possible optimum duct geometry which minimizes the exergetic losses within the range of laminar flow conditions and constant wall temperature. Duct geometries used are; circular, square, equilateral triangle, rectangle with aspect ratio 1/2 and sinusoidal with aspect ratio . It is shown that the optimum duct geometry for constant thermophysical properties depends on the Reynolds number, however, the circular duct geometry is found to be the favorable one especially when the frictional contribution of entropy generation becomes dominant. Triangular and rectangular duct geometries are in general the worst choices for both entropy generation and pumping power requirement. Received on 17 June 1997     

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.     

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].     

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.     

Analysis of entropy generation and thermal stability in a long hollow cylinder with asymmetry convective cooling

The inherent irreversibility and thermal stability in a long hollow cylinder with temperature-dependent internal heating and asymmetric convective cooling at both inner and outer surfaces is investigated. Analytical solution is obtained for the governing equation and the expressions for the temperature field, thermal stability criterion, volumetric entropy generation number, and irreversibility distribution ratio are presented. With certain combinations of the heat transfer parameters, entropy generation rates can be minimized.     

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 in Double-Diffusive Convection in a Square Porous Cavity using Darcy–Brinkman Formulation

The article reports a numerical study of entropy generation in double-diffusive convection through a square porous cavity saturated with a binary perfect gas mixture and submitted to horizontal thermal and concentration gradients. The analysis is performed using Darcy–Brinkman formulation with the Boussinesq approximation. The set of coupled equations of mass, momentum, energy and species conservation are solved using the control volume finite-element method. Effects of the Darcy number, the porosity and the thermal porous Rayleigh number on entropy generation are studied. It was found that entropy generation considerably depends on the Darcy number. Porosity induces the increase of entropy generation, especially at higher values of thermal porous Rayleigh number.     

基于涡粘性模型的翼型湍流流场熵产率计算

利用有限体积法实现了基于非正交同位网格的SIMPLE算法。基于熵分析方法,采用涡粘性模型求解湍流熵产方程,系统研究了湍流模型对二维翼型绕流流场熵产率的影响。通过计算NACA0012翼型在来流雷诺数为2.88×10⁶时,0°攻角~16.5°攻角范围内的翼型表面压力系数分布和升阻力特性,验证了算法及程序的正确性。结果表明,选择不同湍流模型时,翼型流场熵产的计算结果存在差异,湍流耗散是引起流场熵产的主要原因;翼型流场的熵产主要发生在翼型前缘区、壁面边界层和翼型尾流区域,流场熵产率与翼型阻力系数线性相关;当产生分离涡时,粘性耗散引起的熵产下降。     

Entropy generation in parallel plate microchannels

In this study the entropy generation in microchannels in microdevices induced by the transient laminar forced convection in the combined entrance region between two parallel plates has been investigated numerically. The study considers the microscales in the region of Kn < 0.001. The effects of aspect ratio, Reynolds number, Prandtl number, Brinkman number, and the motion of the lower plate on the entropy generation during the simultaneously developing flow in a parallel-plates channel are investigated. The obtained results addressing all cases are thoroughly in good agreement with the expectations that the entropy generation has its highest value at channel with the smallest aspect ratio at counter motion of the lower plate with the highest Re, Pr and Br/Ω values considered in the problem. An erratum to this article can be found at     

Numerical investigation of turbulent flow,heat transfer and entropy generation in a helical coiled tube with larger curvature ratio

Three-dimensional turbulent forced convective heat transfer and flow characteristics, and the non-dimensional entropy generation number in a helical coiled tube subjected to uniform wall temperature are simulated using the k–ε standard turbulence model. A finite volume method is employed to solve the governing equations. The effects of Reynolds number, curvature ratio, and coil pitch on the average friction factor and Nusselt number are discussed. The results presented in this paper cover a Reynolds number range of 2 × 10⁴ to 6 × 10⁴, a pitch range of 0.1–0.2 and a curvature ratio range of 0.1–0.3. The results show that the coil pitch, curvature ratio and Reynolds number have different effects on the average friction factor and Nusselt number at different cross-sections. In addition, the flow and heat transfer characteristics in a helical coiled tube with a larger curvature ratio for turbulent flow are different from that of smaller curvature ratio for laminar and turbulent flow in certain ways. Some new features that are not obtained in previous researches are revealed. Moreover, the effects of Reynolds number, curvature ratio, and coil pitch on the non-dimensional entropy generation number of turbulent forced convection in a helical coiled tube are also discussed.     

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.     

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.     

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.     

Analysis of Laminar Flow and Forced Convection Heat Transfer in a Porous Medium

The flow of an incompressible Newtonian fluid confined in a planar geometry with different wall temperatures filled with a homogenous and isotropic porous medium is analyzed in terms of determining the unsteady state and steady state velocities, the temperature and the entropy generation rate as function of the pressure drop, the Darcy number, and the Brinkman number. The one-dimensional approximate equation in the rectangular Cartesian coordinates governing the flow of a Newtonian fluid through porous medium is derived by accounting for the order of magnitude of terms as well as accompanying approximations to the full-blown three-dimensional equations by using scaling arguments. The one-dimensional approximate energy and the entropy equations with the viscous dissipation consisting of the velocity gradient and the square of velocity are derived by following the same procedure used in the derivation of velocity expressions. The one-dimensional approximate equations for the velocity, the temperature, and the entropy generation rate are analytically solved to determine the velocity, the temperature, and the entropy distributions in the saturated porous medium as functions of the effective process parameters. It is found that the pressure drop, the Darcy number, and the Brinkman number affect the temperature distribution in the similar way, and besides the above parameters, the irreversibility distribution ratio also affects the entropy generation rate in the similar way.     

Accuracy analysis of predicted velocity profiles of laminar duct flow with entropy generation method

The objective of this work is to estimate the accuracy of a predicted velocity profile which can be gained from experimental results, in comparison with the exact ones by the methodology of entropy generation. The analysis is concerned with the entropy generation rate in hydrodynamic, steady, laminar, and incompressible flow for Newtonian fluids in the insulated channels of arbitrary cross section. The entropy generation can be calculated from two local and overall techniques. Adaptation of the results of these techniques depends on the used velocity profile. Results express that in experimental works, whatever the values of local and overall entropy generation rates are close to each other, the results are more accuracy. In order to extent the subject, different geometries have been investigated. Also, the influence studied, and the distribution of volumetric geometries is drawn. of geometry on the entropy generation rate is local entropy generation rate for the selected geometries is drawn.     

Study on transient local entropy generation in pulsating fully developed laminar flow through an externally heated pipe

This study presents the investigation of transient local entropy generation rate in pulsating fully developed laminar flow through an externally heated pipe. The flow inlet to the pipe is considered as pulsating at a constant period and amplitude (only the velocity oscillates). The simulations are extended to include different pulsating flow cases (sinusoidal flow, step flow, and saw-down flow). To determine the effects of the mean velocity, the period and the amplitude of the pulsating flow on the entropy generation rate, the pulsating flow is examined for various cases of these parameters. Two-dimensional flow and temperature fields are computed numerically with the help of the fluent computational fluid dynamics (CFD) code. In addition to this CFD code, a computer program has been developed to calculate numerically the entropy generation and other thermodynamic parameters by using the results of the calculations performed for the flow and temperature fields. In all investigated cases, the irreversibility due to the heat transfer dominates. The step flow constitutes the highest temperature (about 919 K) and generates the highest total entropy rate (about 0.033 W/K) within the pipe. The results of this study indicate that in the considered situations, the inverse of square of temperature (1/T ²) is more dominant on the entropy generation than the temperature gradients, and that the increase of the mean velocity of the pulsating flow has an adverse effect on the ratio of the useful energy transfer rate to irreversibility rate.     

Numerical evaluation of entropy generation in isolated airfoils and Wells turbines

In recent years, a number of authors have studied entropy generation in Wells turbines. This is potentially a very interesting topic, as it can provide important insights into the irreversibilities of the system, as well as a methodology for identifying, and possibly minimizing, the main sources of loss. Unfortunately, the approach used in these studies contains some crude simplifications that lead to a severe underestimation of entropy generation and, more importantly, to misleading conclusions. This paper contains a re-examination of the mechanisms for entropy generation in fluid flow, with a particular emphasis on RANS equations. An appropriate methodology for estimating entropy generation in isolated airfoils and Wells turbines is presented. Results are verified for different flow conditions, and a comparison with theoretical values is presented.