Second law analysis of an array of vertical plate-finned heat sink undergoing mixed convection

Second law analysis of an array of vertical plate-finned heat sink undergoing mixed convective heat transfer is investigated. The fluid flow and temperature fields are evaluated numerically solving the mass, momentum and energy conservation equations. The effects of Grashof number, inlet velocity, clearances, and fin spacing on entropy generation, Nusselt number, pumping power ratio and by-pass factor are presented. Total dimensionless entropy generation continuously decreases with clearances for all fin spacing, while Nusselt number shows an optimum value, especially at higher inlet velocities. There exists an optimum range of fin spacing at which Nusselt number is maximum for all Grashof numbers. The pumping power ratio shows significantly higher value for smaller fin spacing and at optimum fin spacing it decreases approximately by an order of magnitude. At optimum clearance, flow by-pass is significantly low.     

Entropy analysis in MHD Couette flow of chemically reacting viscoelastic fluid past a deformable porous channel

Here, an investigation of MHD Couette flow of a chemically reacting viscoelastic fluid past a deformable porous layer with entropy generation using Walters liquid model has been considered. A binary, homogeneous, and isotropic mixture of fluid and solid phases in the porous medium is considered. The impact of heat source parameter and Soret effect are taken into account. The governing equations are solved analytically to obtain the expressions for solid displacement, fluid velocity, temperature, and concentration. The impact of relevant parameters on the flow system, temperature, concentration, mass transfer flux, entropy generation number, and Bejan number are discussed graphically. It is observed that solid displacement enhances due to the growth of drag and viscoelastic parameter, while it reduces due to rising volume fraction parameter. Fluid velocity rises when the volume fraction parameter increases. Rising Brinkmann number enhances the temperature, while Brinkmann number and Soret number reduces the species concentration. The irreversibility of heat transfer dominates the flow near the channel plates, while the effect of fluid friction irreversibility can be observed within the channel centerline region.     

Optimal package design of stacks of convection-cooled printed circuit boards using entropy generation minimization method

Thermal optimization of a stack of printed circuit boards using entropy generation minimization (EGM) method is presented. The study consists of two parts. One is focused on the entropy generation of a module in periodically fully-developed channel flow (PDF), while the other is the optimization applied to electronic packages composed of a stack of printed circuit boards. In the process of optimizing electronics packaging, consideration is given to two constraints which are the maximum junction temperature specified by a chip manufacturer and the allowable pressure difference across the channel maintained by cooling fans. Governing thermal-fluid flow equations in the laminar-flow regime are numerically integrated subject to the appropriate boundary conditions. After the flow and temperature fields are solved, the volumetric rate of local entropy generation in the PDF is integrated to determine the total entropy generation rate in the system which consists of two components, one by heat transfer and the other by viscous friction. The Reynolds number, block geometry and bypass flow area ratio are varied to search for an optimal channel spacing using the EGM method whose validity is borne out by comparing with those obtained by the conventional thermal optimization (or overall thermal conductance) method. A dimensionless optimal board spacing parameter C is derived which involves the relative migration speed (or time) of heat transfer and viscous friction over the PDF channel length. A correlation equation is derived which expresses C in terms of the Reynolds number and block geometry. This equation can be employed in the optimal design of electronic packages.     

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.     

Entropy generation minimization in turbulent mixed convection flows

This paper reports the results of a numerical investigation of turbulent mixed convection from a symmetrically heated vertical channel, bathed by a steady upward flow of cold air. The computations have been performed using FLUENT 6.2 by employing the k–ε model for turbulence with enhanced wall treatment. The entropy generation rates due to (i) heat transfer across a finite temperature difference and (ii) irreversibility due to fluid friction have been calculated as post-processed quantities with the computed velocity and temperature profiles. Optimal inlet velocities at which the total entropy generation rate reaches a minimum value are found to exist, for every set of heat flux and aspect ratio. Further, this optimum velocity turns out to be independent of the aspect ratio and increases linearly with the heat flux. Simple and easy to use correlations for the optimum Reynolds number and the dimensionless average wall temperatures corresponding to the optima are developed. Plots of total entropy generation rate against the velocity clearly demonstrate that near the optimum conditions, buoyancy does not have a significant role to play in deciding the optimum. For the range of parameters considered in this study, it is seen that for optimum conditions, the ratio of the entropy generation due to fluid friction to total entropy generation rate, known in literature as the Bejan number, varies within a narrow band (0.14–0.22).     

Gas-phase entropy generation during transient methanol droplet combustion

A numerical model was used to investigate gas-phase entropy generation during transient methanol droplet combustion in a low-pressure, zero-gravity, air environment.A comprehensive formulation for the entropy generation in a multi-component reacting flow is derived. Stationary methanol droplet combustion in a low ambient temperature (300 K) and a nearly quiescent atmosphere was studied and the effect of surface tension on entropy generation is discussed. Results show that the average entropy generation rate over the droplet lifetime is higher for the case that neglects surface tension. Entropy generation during the combustion of methanol droplets moving in a high-temperature environment (1200 K), as seen in a typical spray combustion system, is also presented. Entropy generation due to chemical reaction increases and entropy generation due to heat and mass transfer decreases with an increase in initial Reynolds number over the range of initial Reynolds numbers (1–100) considered. Contributions due to heat transfer and chemical reaction to the total entropy generation are greater than the contribution due to mass transfer. Entropy generation due to coupling between heat and mass transfer is negligible. For moving droplets, the lifetime averaged entropy generation rate presents a minimum value at an initial Reynolds number of approximately 55.     

系统参数对超临界水冷堆子通道熵产影响分析

利用流体力学计算软件CFX,采用结构化网格,研究系统参数如系统压力、热流密度以及质量流率对超临界水冷堆堆芯子通道内熵产行为的影响。湍流模型选择SSG雷诺应力模型,近壁面采用加强壁面处理方法。研究结果表明:系统压力对子通道熵产的影响有限,而热流密度和质量流率的影响则更为显著。随着热流密度的升高,传热对熵产的贡献增大,子通道内主流熵产增加;随着质量流率的升高,流体摩擦阻力对熵产的贡献增大,子通道内主流熵产减少。为了从热力学角度综合评估系统参数对主流熵产行为的影响,引入无量纲熵产数,进一步获得合理的热流密度和质量流率的系统参数设计方案,为超临界水冷反应堆的概念设计提供一定的理论指导。     

Entropy generation on MHD flow of a Casson fluid over a curved stretching surface with exponential space-dependent heat source and nonlinear thermal radiation

The present model concentrates on entropy generation on a steady incompressible flow of a Casson liquid past a permeable stretching curve surface through chemical reaction and magnetic field effects. The exponential space-dependent heat source cum heat and mass convective boundary conditions are accounted for. The resulting nonlinear boundary layer model is simplified by the transformation of similarity. Chebyshev spectral technique is involved for obtaining numerical results of the converted system of the mathematical models. Behavior of the determining thermo-physical parameters on the profiles of velocity, temperature, concentration, skin friction, heat, mass transfer rate, rate of entropy generation, and finally the Bejan number are presented. The major point of the present investigation show that the curvature term weakens the mass transfer profile as the fluid temperature reduces all over the diffusion regime. A decrease in heat generation strengthens the species molecular bond, which prevents free Casson particle diffusion. Furthermore, the mass transfer field diminishes in suction and injection flow medium.     

Entropy generation and its relation to heating and cooling requirements of a metal hydride hydrogen storage reactor

In this paper a metal hydride hydrogen storage reactor is analyzed from heat and mass transfer and entropy generation points of view. A transient two dimensional energy equation along with suitable reaction kinetics and entropy balance equation is solved numerically. Results are obtained keeping hydrogen flow rates constant during absorption and desorption. For a fixed mass of metal hydride in the reactor the amount of hydrogen transferred and the time in which the transfer takes place are kept fixed. Using the mathematical model the entropy generated during the process and the external cooling and heating fluid requirements are obtained. Results show how improvement in the design and/or operating conditions leads to reduced cooling and heating requirements and lower entropy generation. For the system considered in the study the internal heat transfer characteristics of the hydride bed are seen to influence the reactor performance significantly. With improved bed heat transfer the required heat transfer fluid temperature during desorption can be reduced and that during absorption can be increased significantly. This automatically leads to lower entropy generation and a more economic system operation. It is expected that the methodology proposed and the results presented in this study will be useful in the optimal design of metal hydride reactors for a variety of practical applications, including hydrogen storage.     

S型流道冷板的流体域熵产分析及流道优化

粘性流体在流动和传热过程中,由于粘性耗散和热传导的存在造成能量损失。为分析流体流动和传热过程的能量损失并得到冷板的最优流道形式,本文以某电子器件用S型流道液冷冷板为分析对象,通过数值模拟,得到S型流道液冷冷板的流体域熵产率随工质流量的变化规律,对流体域充分发展的直段和弯段内熵产率大小进行了比较,并在固定流量下,分析了熵产率大小沿工质流动方向上的变化情况。提出冷板流道优化方案,并从换热表现、压头损失和总能量损失三方面对不同流道形式的冷板进行了综合评价和比较,得到了冷板流道的最优形式,为工程实际提供参考。     

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.     

Maximum exergy input rate from a hot stream in solar‐driven refrigerators

The authors believe that reducing the size of solar‐driven refrigerators and air conditioning systems will make them more attractive to potential users. This paper presents a contribution to understanding the behaviour of such systems with a view to determining the manner in which refrigeration rate, mass flows and heat transfer areas are related. The intention is to make possible the identification of preliminary design rules. The basic thermodynamic problem of how to obtain maximum exergy input rate in a solar‐driven refrigerator is considered. The existence of an optimal refrigerant flow rate for maximum refrigeration is investigated. The analysis proceeds by relating the entropy generation rate, the physical and operating parameters, and the constraints of the system, through well‐established heat transfer relationships. Finally, a thermodynamic analysis determines the optimal characteristics that lead to minimum entropy generation. The second law efficiency is identified as the appropriate figure of merit for the thermodynamic optimum. Copyright © 2001 John Wiley & Sons, Ltd.     

Heat transfer and entropy generation for laminar forced convection flow of graphene nanoplatelets nanofluids in a horizontal tube

The results are reported of an investigation of the heat transfer characteristics and entropy generation for a graphene nanoplatelets (GNP) nanofluid with specific surface area of 750 m²/g under laminar forced convection conditions inside a circular stainless steel tube subjected to constant wall heat flux. The analysis considers constant velocity flow and a concentration range from 0.025 wt.% to 0.1 wt.%. The impact of the dispersed nanoparticles concentration on thermal properties, convective heat transfer coefficient, thermal performance factor and entropy generation is investigated. An enhancement in thermal conductivity for GNP of between 12% and 28% is observed relative to the case without nanoparticles. The convective heat transfer coefficient for the GNP nanofluid is found to be up to 15% higher than for the base fluid. The heat transfer rate and thermal performance for 0.1 wt.% of GNP nanofluid is found to increase by a factor of up to 1.15. For constant velocity flow, frictional entropy generation increases and thermal entropy generation decreases with increasing nanoparticle concentration. But, the total entropy generation tends to decrease when nanoparticles are added at constant velocity and to decrease when velocity rises. Finally, it is demonstrated that a GNP nanofluid with a concentration between 0.075 wt.% and 0.1 wt.% is more energy efficient than for other concentrations. It appears that GNP nanofluids can function as working fluids in heat transfer applications and provide good alternatives to conventional working fluids in the thermal fluid systems.     

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.     

Local entropy generation and exergy analysis of the condenser in a direct methanol fuel cell system

This paper aims to identify the irreversibilities in the condenser of a direct methanol fuel cell (DMFC) system and present possible enhancements in its design through local entropy generation analysis (L-EGA). For this purpose, the local entropy generation terms originating from heat and mass calculated from results of a pseudo two-phase computational fluid dynamic (CFD) model of the condenser. Through this analysis, the total irreversibilities due to heat and mass transfer are calculated locally (e.g., film boundary layer, vapour-gas boundary layer) under the variable operating conditions of a DMFC (undersaturated, saturated, and supersaturated conditions of the cathode exhaust gas). Moreover, the exergy destruction ratio of condenser is found to estimate the exergy performance of the condenser. The results show that in the case of supersaturated cathode exhaust gas (CEG) flow, the entropy generation rate due to mass transfer in the film region is found as 0.032 W/(m·K) which is 18 times higher than that for the undersaturated CEG flow. However, entropy generation rate due to mass transfer decreases significantly when the hot flow is just over the film region. In the film region, the entropy generation rates originating from heat transfer are found as 0.0055 W/(m·K) (for the undersaturated case), 0.0032 W/(m·K) (for the saturated case), and 0.0015 W/(m·K) (for the supersaturated case). Moreover, the maximum exergy destruction ratio is found as 0.72 when the CEG is undersaturated and the CEG velocity is 0.18 m/s, while the lowest exergy destruction ratio is calculated as 0.28 when the CEG is saturated.     

Entropy analysis for heat transfer in a rectangular channel with suction

The purpose for this paper is to study heat transfer in a rectangular channel with suction applied at the adjacent two side walls. A two‐dimensional laminar viscous fluid flow is generated due to the application of suction/injection. The other two opposite sides are kept at a constant temperatures, and the walls with suction are maintained at a constant heat flux. The streamlines thus obtained due to the flow and isothermal lines and heat function are analyzed. The regions of high and low frictions are found by drawing contours of the entropy generation number and the Bejan number. The biharmonic equation for stream function is numerically solved by the Finite Difference Method (FDM) using a 13‐point formula, and a five‐point formula is used to solve for all other harmonic equations for temperature, heat function, and pressure. For derivative boundary conditions, the central difference formula with fictitious nodes is used. In the analysis, we note that the corner points are regions of high energy dissipation. The least dissipation of energy is near the wall, where the nondimensional temperature is 1. This paper analyzes heat transfer in the rectangular channel through the heat function and entropy generation number.     

Analysis of Entropy Generation of Combined Heat and Mass Transfer in Internal and External Flows with the Assumption of Local Thermodynamic Equilibrium

ＡｎａｌｙｓｉｓｏｆＥｎｔｒｏｐｙＧｅｎｅｒａｔｉｏｎｏｆＣｏｍｂｉｎｅｄＨｅａｔａｎｄＭａｓｓＴｒａｎｓｆｅｒｉｎＩｎｔｅｒｎａｌａｎｄＥｘｔｅｒｎａｌＦｌｏｗｓｗｉｔｈｔｈｅＡｓｓｕｍｐｔｉｏｎｏｆＬｏｃａｌＴｈｅｒｍｏｄｙｎａｍｉｃＥｑｕｉｌｉ...     

Entropy generation in transpiration cooling of concentric spherical shells

The present paper deals with transpiration cooling of two concentric spherical shells. The analysis includes the calculation for the radial distribution of temperature and volumetric entropy generation, and the total rate of entropy generation in the thermal system. Standard air is considered as the cooling fluid. Results showed that the entropy generation increases with increasing temperature difference between the sphere surfaces. Variation of either mass flow rate or radius ratio affects volumetric entropy distribution and the total rate of entropy generation of the processes. The increase of mass flow rate or radius ratio increases the total rate of entropy generation. The performance of the system is analyzed by calculating irreversibility to heat transfer ratio at both inner and outer sphere surfaces. It was found that irreversibility to heat transfer ratio at the inner sphere surface increases with increasing mass flow rate, or decreasing radius ratio. The opposite is true for the outer sphere surface.     

Optimal Porosity in an Air Heater Conduit Filled with a Porous Matrix

In the present study, flow and forced convective heat transfer in an air heater conduit filled with a porous matrix with a uniform constant solar heat flux has been investigated analytically, based on minimal entropy generation principle. While trying to decrease entropy generation due to heat transfer, pressure loss entropy generation increases, which indicates that an optimal porosity value exists. The influence of Reynolds number, fluid properties, constant uniform heat flux, flow, and geometry of the system on the optimum matrix porosity has been investigated. It was revealed that optimum matrix porosity values increase as Reynolds number increases. In the range of the present study, a correlation predicting optimal matrix porosity was proposed using least squares analysis.     

Thermodynamic optimisation of the integrated design of a small‐scale solar thermal Brayton cycle

The Brayton cycle's heat source does not need to be from combustion but can be extracted from solar energy. When a black cavity receiver is mounted at the focus of a parabolic dish concentrator, the reflected light is absorbed and converted into a heat source. The second law of thermodynamics and entropy generation minimisation are applied to optimise the geometries of the recuperator and receiver. The irreversibilities in the recuperative solar thermal Brayton cycle are mainly due to heat transfer across a finite temperature difference and fluid friction. In a small‐scale open and direct solar thermal Brayton cycle with a micro‐turbine operating at its highest compressor efficiency, the geometries of a cavity receiver and counterflow‐plated recuperator can be optimised in such a way that the system produces maximum net power output. A modified cavity receiver is used in the analysis, and parabolic dish concentrator diameters of 6 to 18 m are considered. Two cavity construction methods are compared. Results show that the maximum thermal efficiency of the system is a function of the solar concentrator diameter and choice of micro‐turbine. The optimum receiver tube diameter is relatively large when compared with the receiver size. The optimum recuperator channel aspect ratio for the highest maximum net power output of a micro‐turbine is a linear function of the system mass flow rate for a constant recuperator height. For a system operating at a relatively small mass flow rate, with a specific concentrator size, the optimum recuperator length is small. For the systems with the highest maximum net power output, the irreversibilities are spread throughout the system in such a way that the internal irreversibility rate is almost three times the external irreversibility rate. Copyright © 2011 John Wiley & Sons, Ltd.