Entropy generation analysis in a uniformly heated microchannel heat sink

Present investigation analyzes the issue of entropy generation in a uniformly heated microchannel heat sink (MCHS). Analytical approach used to solve forced convection problem across MCHS, is a porous medium model based on extended Darcy equation for fluid flow and two-equation model for heat transfer. Simultaneously, closed form velocity solution in a rectangular channel is employed to capture z-directional viscous effect diffusion and its pronounced effect on entropy generation through fluid flow. Subsequently, governing equations are cast into dimensionless form and solved analytically. Second law analysis of problem is then conducted on the basis of obtained velocity and temperature fields and expressions for local and average entropy generation rate are derived in dimensionless form. Average entropy generation rate is then utilized as a criterion for assessing the system performance. Finally, the effect of influential parameters such as, channel aspect ratio (α_S), group parameter (Br/Ω), thermal conductivity ratio (C) and porosity (ε) on thermal and total entropy generation is investigated. In order to examine the accuracy of the analysis, the results of thermal evaluation are compared to one of the previous investigations conducted for thermal optimization of MCHS.     

Second law analysis for optimal thermal design of radial fin geometry by convection

This paper presents a second law analysis for the optimal geometry of fin array by forced convection. The analytical analysis involves the achievement of a balance between the entropy generation due to heat transfer and entropy generation due to fluid friction. In the design of a thermal system, it is important to minimize thermal irreversibilities because the optimal geometry will be found when the entropy generation rate is minimized. In this paper, the entropy generation rate is discussed and optimum thickness for fin array is determined on the basis of entropy generation minimization subjected to the global constraint. In addition, the influence of cost parameters on the optimum thickness of fin array is also considered and presented in graphical form. It has been found that the increase in cross flow fluid velocity will enhance the heat transfer rate that will reduce the heat transfer irreversibility.     

传热强化管管内熵产分析与热力性能评价

根据热力学第二定律,对传热强化管管内热力过程进行熵产分析,建立了基于流动与传热过程熵增原理的管内传热熵产方程,导出恒热流和恒壁温2种常见工况下的无因次熵产数表达式.在不同雷诺数和进口温差条件下,对2种螺旋槽管和光管进行恒壁温工况的熵产分析和热力性能评价,分析了传热和流动摩阻引起的熵产变化规律及2种不可逆损失占总熵产的份额.结果表明,熵产分析可用于评价传热强化管的综合热力性能,确定合理的运行工况、结构参数及强化换热形式,为强化管的应用评估及优化设计提供参考.     

横掠不同型式光滑管束流动的热力学分析和比较

对横掠不同型式光滑管束的流动进行了热力学分析，在熵产分析的基础上对不同型式的光滑管比较了它们热力学性能的优劣，总结发现了一些规律性的结论，对于横掠光滑管束的优化设计具有重要的指导意义。     

Effect of Conjugate Heat Transfer on Entropy Generation in Slip-Driven Microflow of Power Law Fluids

We analyze the entropy generation characteristics in a non-Newtonian microflow under the influence of interfacial slip as modulated by the conjugate transport of heat. We consider power law model to represent the constitutive behavior of the non-Newtonian fluid. In this analysis, we analytically solve the transport equations employing the thermal boundary condition of the third kind at the exterior wall surface accounting for the effect of conjugate heat transfer. We demonstrate that the slip flow–driven alteration in convective transport of heat and its nonlinear interaction with viscous dissipation, as modulated by fluid rheology and conjugate transport of heat, gives rise to a minimum entropy generation rate of the system. We determine the optimum value of the geometrical parameter—that is, the channel wall thickness and the thermophysical parameters, such as the Biot number and Peclet number—leading to a minimum entropy generation rate in the system. The results of this analysis could be of helpful in designing microsystems/devices typically used for electronic cooling, micro-heat pipes, and micro-heat exchangers.     

Minimizing the entropy generation rate of the plate-finned heat sinks using computational fluid dynamics and combined optimization

The multi-parameter constrained optimization procedure integrating the design of experiments (DOE), response surface models (RSM), genetic algorithm (GA), mixed integer optimization (MOST), and computational fluid dynamics (CFD) is proposed to design the plate finned heat sinks by minimizing their rates of entropy generation. The results of three cases demonstrate that the combination optimization algorithm is feasible. In these cases, the overall rate of entropy generation decreases as the result of introducing the additional constrained variables into the optimization procedure. Consequently, the general thermal and fluid performance of the heat sink is dramatically improved.Based on the results derived by the optimization, the overall thermal and fluid performance of the plate finned heat sinks with both side and top bypass flow is investigated. In addition, two correlations describing Nusselt number and friction factor, as the functions of geometrical and operational parameters, are established by means of the multivariate non-linear regression analysis. The specific expressions to compute the thermal resistance and the rate of entropy generation are deduced.     

MHD Eyring–Powell nanofluid past over an unsteady exponentially stretching surface with entropy generation and thermal radiation

This study's primary objective is to analyze the entropy generation in an unsteady magnetohydrodynamics (MHD) Eyring–Powell nanofluid flow. A surface that stretched out exponentially induced flow. The influences of thermal radiation, thermophoresis, and Brownian motion are also taken into consideration. The mathematical formulation for the transport of mass, momentum, and heat described by a set of partial differential equation is used, which is then interpreted by embracing the homotopy analysis method and with a fourth-order precision program (bvp4c). Graphical results display the consequences of numerous parameters on velocity, temperature, concentration, and entropy generation. Moreover, escalating amounts of the magnetic parameter, thermal radiation parameter, Reynolds number, and Brinkman number improve the entropy profile of the nanofluid. The rate of heat flux and the mass flux conspicuously improves for non-Newtonian fluid as compared to Newtonian fluid.     

Second law analysis of a disturbed flow in a thin slit with wall suction or injection

Fully-developed laminar flow in a horizontal thin slit having plates at different temperature is considered for the case of lower plate movement and/or the pressure gradient-and-upper plate movement. The flow under these conditions is analyzed in terms of entropy generations as function of the Prandtl number, the Eckert number, cross-flow Reynolds number and dimensionless temperature difference. In this context, the governing equations for distributions of temperature, the dimensionless entropy generation number and Bejan number are analytically derived with the aid of expressions for velocity distributions. The effect of each parameter on the temperature and the entropy generation are investigated by varying one of the parameters and keeping the rest of them constant for each flow case. The effects of viscous dissipation, rates of mass suction/injection and dimensionless temperature differences on the fluid temperature and entropy generation are examined. The magnitudes of mass suction and/or injection have a large influence on the temperature profile of the fluid. It is observed that the Prandtl number and the Eckert number affect fluid temperature in similar way. It is found that an increase in values of the cross-flow Reynolds number (mass suction/injection) enhances the entropy generation in boundary layer. The velocity profiles are found to be in agreement with the distributions of the dimensionless entropy generation number (N_S) for two flow cases.     

Second law analysis and heat transfer in a cross-flow heat exchanger with a new winglet-type vortex generator

In this paper a second law analysis of a cross-flow heat exchanger (HX) is studied in the presence of a balance between the entropy generation due to heat transfer and fluid friction. The entropy generation in a cross-flow HX with a new winglet-type convergent–divergent longitudinal vortex generator (CDLVG) is investigated. Optimization of HX channel geometry and effect of design parameters regarding the overall system performance are presented. For the HX flow lengths and CDLVGs the optimization model was developed on the basis of the entropy generation minimization (EGM). It was found that increasing the cross-flow fluid velocity enhances the heat transfer rate and reduces the heat transfer irreversibility. The test results demonstrate that the CDLVGs are potential candidate procedure to improve the disorderly mixing in channel flows of the cross-flow type HX for large values of the Reynolds number.     

传热与流动系统熵产生的研究与进展

本文综述了熵产分析在传热与流动系统的研究与进展,包括对流传热传质、基本流动传热、换热器、热能贮存系统、绝热层布置等方面的研究与进展。     

Second‐law analysis and optimization of microchannel flows subjected to different thermal boundary conditions

Entropy generation and transfer in microchannel flows were calculated and analyzed for different thermal boundary conditions. Due to the small flow cross‐sectional area, fluid temperature variation in the lateral direction was neglected and a laterally lumped model was developed and used in the first‐ and second‐law analyses. Since the Peclet numbers of microchannel flows are typically low, heat conduction in the flow direction was taken into consideration. Computed fluid temperature and entropy generation rate were cast into dimensionless forms, thus can be applied to different fluids and channels of different sizes and configurations. Local entropy generation rate was found to be only dependent upon the temperature gradient in the flow direction. The optimization results of microchannel flows exchanging heat with their surroundings indicate the optimal fluid temperature distribution is a linear one. Copyright © 2004 John Wiley & Sons, Ltd.     

Second law analysis of pseudo-plastic nanofluid stream past a stretching sheet with a sliding consequence

The entropy generation (second law of thermodynamics) analysis of gyrotactic microorganism flow of power-law nanofluid with slip effects and combined effect of heat and mass transfer past a stretching sheet has been studied. The flow is maintained with Lorentz force and thermal radiation. The governing nonlinear partial differential equations are transformed into ordinary differential equations using similarity transformations. The impact of different physical parameters, such as convective bouncy parameter, power-law parameter, Brownian motion parameter, thermophoresis parameter, and slip parameter for velocity and temperature on the entropy generation number (Ns) are plotted graphically with the help of MATLAB built in bvp4c solver technique. Further, the uniqueness of this study is to find out the ratios of various irreversibilities due to thermal and mass diffusions, momentum diffusion, and microorganism over the total entropy generation rate. Our results showed that the power-law parameter and Brownian motion parameter influenced entropy generation positively. The slip parameter for velocity and temperature and the thermophoresis parameter helps to reduce the entropy production.     

Analysis of entropy generation using nanofluid flow through the circular microchannel and minichannel heat sink

In this paper, different types of entropy generations in the circular shaped microchannel and minichannel are discussed analytically using different types of nanoparticles and base fluids. In this analysis, Copper (Cu), alumina (Al₂O₃) as the nanoparticle and H₂O, ethylene glycol (EG) as the base fluids were used. The volume fractions of the nanoparticles were varied from 2% to 6%. In this paper, the irreversibility or entropy generation analysis as the function of entropy generation ratio, thermal entropy generation rate and fluid friction entropy generation rate for these types of nanofluids in turbulent flow condition have been analyzed using available correlations. Cu–H₂O nanofluid showed the highest decreasing entropy generation rate ratio (36%) compared to these nanofluids flow through the microchannel at 6 vol.%. The higher thermal conductivity of H₂O causes to generate much lower thermal entropy generation rate compared to the EG base fluid. The fluid friction entropy generation rate decreases fruitfully by the increasing of volume fraction of the nanoparticles. Cu–H₂O and Cu–EG nanofluid gave the maximum decreasing rates of the fluid friction entropy generation rate are 38% and 35% respectively at 6% volume fraction of the nanoparticles. Smaller diameter showed less entropy generation in case of all nanofluids.     

A comparative study of viscous dissipation effect on entropy generation in single-phase liquid flow in microchannels

The influence of viscous dissipation on entropy generation in fully developed forced convection for single-phase liquid flow in a circular microchannel under imposed uniform wall heat flux has been studied. In the first-law analysis, closed form solutions of the radial temperature profiles for the models with and without viscous dissipation term in the energy equation are obtained. In the second-law analysis, for different Brinkman number and dimensionless heat flux, the variations of dimensionless entropy generation and Bejan number as a function of the radial distance are investigated. The two models are compared by analyzing their relative deviations in dimensionless entropy generation and Bejan number. Comparisons are also performed for average dimensionless entropy generation and average Bejan number. Contribution of heat transfer irreversibility and fluid friction irreversibility to the deviations is analyzed and discussed. It is found that, under certain conditions, the effect of viscous dissipation on entropy generation in microchannel is significant and should not be neglected.     

Entropy analysis of MHD flow of Jeffrey fluid in an inclined channel

This study is aimed at investigating the influence of entropy analysis of magnetohydrodynamic flow of Jeffrey fluid in an inclined micro-channel in the presence of thermal radiation and field suction/injection. We have improved the mathematical model of the physical problem under consideration. The designed equations have been solved by applying the shooting-based fourth-order, Runge–Kutta method with the boundary conditions, which describe velocity slip and temperature jump conditions at the fluid–wall inter-face. Numerical efforts are described graphically and mentioned quantitatively concerning different parameters such as Jeffery parameter, Bejan number, and entropy generation embedded in the problem. The numerical results for the expression of the irreversibility ratio are obtained. It is observed that the wall inclination strengthens the entropy production rate in the micro-channel, and the thermal buoyancy layer induces an increase in fluid velocity as suction.     

Entropy generation analysis of two-dimensional high-temperature confined jet

In high-temperature systems, thermal radiation becomes the dominant mode of heat transfer. The analysis of entropy generation mechanism is very important to optimize the second-law performance of these energy conversion devices. In this paper, the entropy generation in a two-dimensional high-temperature confined jet flow is analyzed. The computation of combined radiation and convection heat transfer is carried out with the help of a CFD code, and the entropy generation due to heat transfer and fluid friction is calculated as post-processed quantities with the computed data of velocity, temperature and radiative intensity. Numerical results show the entropy generation due to radiative transfer cannot be omitted in high-temperature systems such as boilers and furnaces, in which thermal radiation is one of the main modes of heat transfer. In the case that the temperatures of the inlet gas and the top and bottom are not changed, the total entropy generation number decreases with the increase of jet Reynolds number and Boltzmann number, respectively. For enhancing heat transfer and advancing energy conversion efficiency, large jet Reynolds number and Boltzmann number should be selected.     

Heat Transfer and Entropy Generation Analysis of an Intermediate Heat Exchanger in ADS

The intermediate heat exchanger for enhancement heat transfer is the important equipment in the usage of nuclear energy. In the present work, heat transfer and entropy generation of an intermediate heat exchanger (IHX) in the accelerator driven subcritical system (ADS) are investigated experimentally. The variation of entropy generation number with performance parameters of the IHX is analyzed, and effects of inlet conditions of the IHX on entropy generation number and heat transfer are discussed. Compared with the results at two working conditions of the constant mass flow rates of liquid lead-bismuth eutectic (LBE) and helium gas, the total pumping power all tends to reduce with the decreasing entropy generation number, but the variations of the effectiveness, number of transfer units and thermal capacity rate ratio are inconsistent, and need to analyze respectively. With the increasing inlet mass flow rate or LBE inlet temperature, the entropy generation number increases and the heat transfer is enhanced, while the opposite trend occurs with the increasing helium gas inlet temperature. The further study is necessary for obtaining the optimized operation parameters of the IHX to minimize entropy generation and enhance heat transfer.     

The second law analysis in fundamental convective heat transfer problems

Second law characteristics of heat transfer and fluid flow due to forced convection of steady-laminar flow of incompressible fluid inside channel with circular cross-section and channel made of two parallel plates is analyzed. Different problems are discussed with their entropy generation profiles and heat transfer irreversibility characteristics. In each case, analytical expression for entropy generation number (N_S) and Bejan number (Be) are derived in dimensionless form using velocity and temperature profiles.     

Heat transfer and entropy generation optimization of forced convection in porous-saturated ducts of rectangular cross-section

We investigate analytically the first and the second law characteristics of fully developed forced convection inside a porous-saturated duct of rectangular cross-section. The Darcy–Brinkman flow model is employed. Three different types of thermal boundary conditions are examined. Expressions for the Nusselt number, the Bejan number, and the dimensionless entropy generation rate are presented in terms of the system parameters. The conclusions of this analytical study will make it possible to compare, evaluate, and optimize alternative rectangular duct design options in terms of heat transfer, pressure drop, and entropy generation.     

Irreversibility scrutinization on EMHD Darcy–Forchheimer slip flow of Carreau hybrid nanofluid through a stretchable surface in porous medium with temperature-variant properties

The significance of hybrid nanofluids in controlling heat transmission cannot be overemphasized. Therefore, this article scrutinizes the electromagnetized flow of Carreau hybrid nanofluid towards a stretching surface in a Darcy–Forchheimer porous medium with the occurrence of slip conditions. To form the hybrid nanofluid, the amalgamation of silver and alumina nanoparticles (NPs) embedded in water as conventional fluid is assumed. For accurate interception of the rate of heat and mass transport, thermal conductivity and mass diffusion conductance are presumed to be temperature variants. The modeling system of partial differential equations has been translated into a nondimensional form by means of suitable similarity conversions. Then, the subsequent system of ordinary differential equations is handled using overlapping domain decomposition spectral local linearization method to acquire numerical solutions. The choice of the method has been justified through the provision of errors, condition numbers, and computation time. The behavior of distinct fluid parameters on the flow features, quantities of engineering curiosity, and entropy is analyzed. Findings of paramount importance constitute that the superior thermal conductivity, heat transfer efficiency, and low production cost can be achieved through the hybridization of silver and alumina NPs. The role of thermal radiation and temperature-variant thermal conductivity is to enhance the thermal transport performance of Carreau hybrid nanofluids. The velocity, energy, and mass profiles grow with the utilization of injection effects. The principal aspiration of the second law of thermodynamics (minimizing the rate of entropy generation) can be achieved by considering shear-thinning Carreau fluid while reducing the porosity parameter and Brinkman number in the existence of velocity slip conditions in the flow system. Outcomes of the current flow model can play a significant role in biomedical, technological, and various manufacturing processes. The approximation of entropy contributes towards power engineering and aeronautical propulsion to anticipate the smartness of the overall system.