Role of entropy generation minimization in thermal optimization

Thermal optimization is very important for improving the performances of thermal systems. In engineering, the entropy generation minimization(EGM) has been widely used to optimize and evaluate the performances of thermal systems.However, the consistency between the EGM and the optimization objective should be specified when the EGM is used.In this paper, we discuss the view angle of irreversibility of entropy generation, and show that entropy generation directly reflects the exergy destruction or the ability loss of doing work. As the design objective in a thermal system is not often consistent with the view angle of irreversibility of entropy generation, the EGM may not lead to the optimal value of the design objective. In heat transfer and heat-work conversion, the inconsistence between the design objectives and the EGM is shown with some examples, and the applicability of the EGM is found to be conditional. The "entropy generation paradox" in heat exchanger analyses is also discussed, and it is shown that there is no direct monotonic relation between the minimum entropy generation rate and the best heat transfer performance of heat exchangers.     

Predictions of Conjugate Heat Transfer in Turbulent Channel Flow Using Advanced Wall-Modeled Large Eddy Simulation Techniques

In this paper, advanced wall-modeled large eddy simulation (LES) techniques are used to predict conjugate heat transfer processes in turbulent channel flow. Thereby, the thermal energy transfer process involves an interaction of conduction within a solid body and convection from the solid surface by fluid motion. The approaches comprise a two-layer RANS–LES approach (zonal LES), a hybrid RANS–LES representative, the so-called improved delayed detached eddy simulation method (IDDES) and a non-equilibrium wall function model (WFLES), respectively. The results obtained are evaluated in comparison with direct numerical simulation (DNS) data and wall-resolved LES including thermal cases of large Reynolds numbers where DNS data are not available in the literature. It turns out that zonal LES, IDDES and WFLES are able to predict heat and fluid flow statistics along with wall shear stresses and Nusselt numbers accurately and that are physically consistent. Furthermore, it is found that IDDES, WFLES and zonal LES exhibit significantly lower computational costs than wall-resolved LES. Since IDDES and especially zonal LES require considerable extra work to generate numerical grids, this study indicates in particular that WFLES offers a promising near-wall modeling strategy for LES of conjugated heat transfer problems. Finally, an entropy generation analysis using the various models showed that the viscous entropy production is zero inside the solid region, peaks at the solid–fluid interface and decreases rapidly with increasing wall distance within the fluid region. Except inside the solid region, where steep temperature gradients lead to high (thermal) entropy generation rates, a similar behavior is monitored for the entropy generation by heat transfer process.     

Lattice Boltzmann simulation for hydrothermal analysis of free convection within dumbbell-shaped heat exchanger

The lattice Boltzmann simulation of nanofluid flow and heat transfer during natural convection within a dumbbell-shaped heat exchanger is carried out. The heat exchanger is filled with CuO–water. The KKL model is employed to predict the thermo-physical properties of nanofluid. In order to perform a comprehensive hydrothermal investigation, different post-processing approaches such as heatline visualization, total entropy generation, local entropy generation based on local fluid friction irreversibility and heat transfer irreversibility, average and local Nusselt variation are employed. In the present investigation, it is tried to present the impact of different influential parameters like Rayleigh number, solid volume fraction of nanofluid and thermal arrangement of internal fins-bodies on the fluid flow, heat transfer rate and entropy generation.     

Numerical modeling of nanofluid flow and heat transfer in a quartered gearwheel-shaped heat exchanger using FVM

The numerical modeling of natural convection fluid flow and heat transfer in a quarter of gearwheel-shaped heat exchanger is carried out. The heat exchanger is included with internal active square bodies. These bodies have hot and cold temperatures with different thermal arrangements. Three different thermal arrangements are considered and showed with Case A, Case B and Case C. The CuO-water nanofluid is selected as operating fluid. The Koo-Kleinstreuer-Li (KKL) correlation is utilized to estimate the dynamic viscosity and thermal conductivity. In addition, the shapes of nanoparticles are taken account in the analysis. The Rayleigh number, nanoparticle concentration and thermal arrangements of internal active bodies are the governing parameters. The impacts of these parameters on the fluid flow, heat transfer rate, local and total entropy generation and heatlines are studied, comprehensively. The results show that the heat transfer rate enhances with increasing of Rayleigh number and nanoparticle concentration. Moreover, the thermal arrangement of internal active bodies has considerable effect on the heat transfer between heat sources and heat sinks. On the other hand, the total entropy generation enhances and decreases with increasing of Rayleigh number and nanoparticle concentration, respectively.     

Optimization of fin geometry in heat convection with entransy theory

The entransy theory developed in recent years is used to optimize the aspect ratio of a plate fin in heat convection.Based on a two-dimensional model,the theoretical analysis shows that the minimum thermal resistance defined with the concept of entransy dissipation corresponds to the maximum heat transfer rate when the temperature of the heating surface is fixed.On the other hand,when the heat flux of the heating surface is fixed,the minimum thermal resistance corresponds to the minimum average temperature of the heating surface.The entropy optimization is also given for the heat transfer processes.It is observed that the minimum entropy generation,the minimum entropy generation number,and the minimum revised entropy generation number do not always correspond to the best heat transfer performance.In addition,the influence factors on the optimized aspect ratio of the plate fin are also discussed.The optimized ratio decreases with the enhancement of heat convection,while it increases with fin thermal conductivity increasing.     

对流换热过程的热力学优化与传热优化

为了进一步明确对流换热过程中热力学优化与传热优化之间的差异,本文分别利用熵产最小原理、(火积)耗散极值原理针对两种边界条件下的对流换热问题进行分析,讨论熵产,(火积)耗散与有用能损失以及对流换热能力之间的关系.结果表明:熵产最小意味着系统的有用能损失最小,但并不反映系统的对流换热能力的强弱;而(火积)耗散取极值意味着系统的对流换热能力最强,但与系统的有用能损失不存在对应关系.因此,对于将降低有用能损失作为优化目标的换热问题应采用熵产最小原理进行分析;而对于需要将提高换热能力作为优化目标的对流换热问题应采用(火积)耗散极值原理进行分析.     

Verification of numerical simulation method for entropy generation of radiation heat transfer in semitransparent medium

The numerical simulation method of radiative entropy generation in participating media presented by Caldas and Semiao [Entropy generation through radiative transfer in participating media: analysis and numerical computation. JQSRT 2005;96:423-37] is extended to analyze the radiative entropy generation in the enclosures filled with semitransparent media. A discrete ordinates method is used to solve radiative transfer equation and radiative entropy generation. Two different examples are employed to verify the numerical simulation method of radiative entropy generation in the enclosure. Numerical results of dimensionless radiative entropy generation of enclosure are identical to that of entire thermodynamics analysis for the enclosure system. This numerical simulation method can be used in the entropy generation analysis of high-temperature systems such as boilers and furnaces, in which radiation is the dominant mode of heat transfer.     

A comparison of different entransy flow definitions and entropy generation in thermal radiation optimization

In thermal radiation, taking heat flow as an extensive quantity and defining the potential as temperature T or the black body emissive power U will lead to two different definitions of radiation entransy flow and the corresponding principles for thermal radiation optimization. The two definitions of radiation entransy flow and the corresponding optimization prin ciples are compared in this paper. When the total heat flow is given, the optimization objectives of the extremum entransy dissipation principles （EEDPs） developed based on potentials T and U correspond to the minimum equivalent temperature difference and the minimum equivalent blackbody emissive power difference respectively. The physical meaning of the definition based on potential U is clearer than that based on potential T, but the latter one can be used for the coupled heat transfer optimization problem while the former one cannot. The extremum entropy generation principle （EEGP） for thermal radiation is also derived, which includes the minimum entropy generation principle for thermal radiation. When the radiation heat flow is prescribed, the EEGP reveals that the minimum entropy generation leads to the minimum equivalent thermodynamic potential difference, which is not the expected objective in heat transfer. Therefore, the minimum entropy generation is not always appropriate for thermal radiation optimization. Finally, three thermal radiation optimization examples are discussed, and the results show that the difference in optimization objective between the EEDPs and the EEGP leads to the difference between the optimization results. The EEDP based on potential T is more useful in practical application since its optimization objective is usually consistent with the expected one.     

Entropy resistance analyses of a two-stream parallel flow heat exchanger with viscous heating

Heat exchangers are widely used in industry, and analyses and optimizations of the performance of heat exchangers are important topics. In this paper, we define the concept of entropy resistance based on the entropy generation analyses of a one-dimensional heat transfer process. With this concept, a two-stream parallel flow heat exchanger with viscous heating is analyzed and discussed. It is found that the minimization of entropy resistance always leads to the maximum heat transfer rate for the discussed two-stream parallel flow heat exchanger, while the minimizations of entropy generation rate, entropy generation numbers, and revised entropy generation number do not always.     

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

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.     

Numerical Investigation into the Development Performance of Gas Hydrate by Depressurization Based on Heat Transfer and Entropy Generation Analyses

The purpose of this study is to analyze the dynamic properties of gas hydrate development from a large hydrate simulator through numerical simulation. A mathematical model of heat transfer and entropy production of methane hydrate dissociation by depressurization has been established, and the change behaviors of various heat flows and entropy generations have been evaluated. Simulation results show that most of the heat supplied from outside is assimilated by methane hydrate. The energy loss caused by the fluid production is insignificant in comparison to the heat assimilation of the hydrate reservoir. The entropy generation of gas hydrate can be considered as the entropy flow from the ambient environment to the hydrate particles, and it is favorable from the perspective of efficient hydrate exploitation. On the contrary, the undesirable entropy generations of water, gas and quartz sand are induced by the irreversible heat conduction and thermal convection under notable temperature gradient in the deposit. Although lower production pressure will lead to larger entropy production of the whole system, the irreversible energy loss is always extremely limited when compared with the amount of thermal energy utilized by methane hydrate. The production pressure should be set as low as possible for the purpose of enhancing exploitation efficiency, as the entropy production rate is not sensitive to the energy recovery rate under depressurization.     

Analyses of an air conditioning system with entropy generation minimization and entransy theory

In this paper,based on the generalized heat transfer law,an air conditioning system is analyzed with the entropy generation minimization and the entransy theory.Taking the coefficient of performance(denoted as COP) and heat flow rate Q~(out) which is released into the room as the optimization objectives,we discuss the applicabilities of the entropy generation minimization and entransy theory to the optimizations.Five numerical cases are presented.Combining the numerical results and theoretical analyses,we can conclude that the optimization applicabilities of the two theories are conditional.If Q~(out) is the optimization objective,larger entransy increase rate always leads to larger Q~(out),while smaller entropy generation rate does not.If we take COP as the optimization objective,neither the entropy generation minimization nor the concept of entransy increase is always applicable.Furthermore,we find that the concept of entransy dissipation is not applicable for the discussed cases.     

导热优化中的最小传递势容耗散与最小熵产

为了比较分析强化传热中存在的熵产最小化和传递势容耗散最小化两种不同的方法,针对体点问题,根据这两种方法对导热系数分布进行了优化。数值计算和理论分析的结果表明,根据最小传递势容耗散原理得到的结果优于最小熵产原理得到的结果。其原因在于传递势容耗散最小的优化目标是提高热量传递效率,而熵产最小的优化目标实际上是减少可用能损失。     

Entropy generation applications in flow of viscoelastic nanofluid past a lubricated disk in presence of nonlinear thermal radiation and Joule heating

Entropy generation is the loss of energy in thermodynamical systems due to resistive forces,diffusion processes, radiation effects and chemical reactions. The main aim of this research is to address entropy generation due to magnetic field, nonlinear thermal radiation, viscous dissipation, thermal diffusion and nonlinear chemical reaction in the transport of viscoelastic fluid in the vicinity of a stagnation point over a lubricated disk. The conservation laws of mass and momentum along with the first law of thermodynamics and Fick's law are used to discuss the flow, heat and mass transfer, while the second law of thermodynamics is used to analyze the entropy and irreversibility. The numbers of independent variables in the modeled set of nonlinear partial differential equations are reduced using similarity variables and the resulting system is numerically approximated using the Keller box method. The effects of thermophoresis,Brownian motion and the magnetic parameter on temperature are presented for lubricated and rough disks. The local Nusselt and Sherwood numbers are documented for both linear and nonlinear thermal radiation and lubricated and rough disks. Graphical representations of the entropy generation number and Bejan number for various parameters are also shown for lubricated and rough disks. The concentration of nanoparticles at the lubricated surface reduces with the magnetic parameter and Brownian motion. The entropy generation declines for thermophoresis diffusion and Brownian motion when lubrication effects are dominant. It is concluded that both entropy generation and the magnitude of the Bejan number increase in the presence of slip. The current results present many applications in the lubrication phenomenon,heating processes, cooling of devices, thermal engineering, energy production, extrusion processes etc.     

Output power analyses of an endoreversible Carnot heat engine with irreversible heat transfer processes based on generalized heat transfer law

In this paper, an endoreversible Carnot heat engine with irreversible heat transfer processes is analyzed based on generalized heat transfer law. The applicability of the entropy generation minimization, exergy analyses method, and entransy theory to the analyses is discussed. Three numerical cases are presented. It is shown that the results obtained from the entransy theory are different from those from the entropy generation minimization, which is equivalent to the exergy analyses method. For the first case in which the application preconditions of the entropy generation minimization and entransy loss maximization are satisfied, both smaller entropy generation rate and larger entransy loss rate lead to larger output power. For the second and third cases in which the preconditions are not satisfied, the entropy generation minimization does not lead to the maximum output power, while larger entransy loss rate still leads to larger output power in the third case. For the discussed cases, the concept of entransy dissipation is not applicable for the analyses of output power.The problems in the negative comments on the entransy theory are pointed out and discussed. The related researchers are advised to focus on some new specific application cases to show if the entransy theory is the same as some other theories.     

Thermal-exergetic behavior of a vertical double-tube heat exchanger with bubble injection

The use of air bubbles as a heat transfer improvement technique for heat exchangers has been proposed by some researchers. The vertical motion of tiny bubbles because of density difference with liquid provides extra vibration, eddies, turbulences, and consequently further heat transfer rate. The variety of affected parameters, such as injection method, air mass flow rate, bubbles size, number of perforations that forms bubbles, etc., has added to the complexity of this phenomena so that any change in the said parameters significantly influences the thermal-exergetic behavior of the heat exchanger. The quality and quantity of the impact of bubbles on the thermal performance of heat exchangers are different for any type of them. Moreover, each type of heat exchanger requires a specific injection method depending on the heat exchanger structure. In the present research, an injection way is proposed for vertical double-tube heat exchangers, and the effect of bubbles on thermal-exergetic characteristics is experimentally studied and discussed, which have not been performed before. Nondimensional exergy destruction, number of heat transfer units, and effectiveness are the main evaluated parameters in the present paper. Results showed a significant thermal improvement of the heat exchanger under the bubble injection.     

Entropy generation analysis for peristaltically driven flow of hybrid nanofluid

Present study investigates entropy generation analysis for peristaltic motion of hybrid nanofluid. Hybrid nanofluid is composed of iron-oxide and copper nanoparticles suspended in water. Effects of Hall current, Ohmic heating and mixed convection are taken into account. Governing equations are simplified by utilizing lubrication approach. The numerical solutions for resulting system of differential equations are obtained with the aid of Shooting method. Attention has been given to the analysis of hybrid nanoparticles, Hall parameter and Grashoff number on entropy generation, heat transfer rate, velocity profile and pressure gradient. Outcomes reveal that insertion of nanoparticles decreases the temperature of hybrid nanofluid. It is found that increase in Hall parameter reduces the heat transfer rate at wall. Increment in Hall parameter reduces the entropy generation. Velocity and pressure gradient increases by enhancing Grashoff number. It is believed that the present flow model can prove useful in improving the efficiency of similar thermodynamical systems.     

孤立系内热传导过程(火积)耗散的解析解

(火积)耗散与熵增均可以作为传热不可逆性的度量, 当前(火积)理论的反对者认为(火积)是不必要的. 为说明(火积)的必要性, 从有效性的角度进行了论证, 即在描述传热过程不可逆性的变化上, (火积)的严格解析解存在, 而熵的严格解析解难以得到. 本文构建了孤立系内的一维及多维热传导模型, 求解了温度及其梯度的级数型解析解, 将其代入(火积)耗散的求解式, 得到其最初的形式为一多重级数的多重积分, 交换积分与级数计算顺序, 并利用特征函数的正交性, 将(火积)耗散求解式中的积分运算求出, 并使级数的维数降低, 最终将其表示为一稳态项与一瞬态项加和的形式, 其极限与文献中的结果一致. 通过对孤立系内(火积)耗散解析解的求解可以得出: 由于热传导过程熵与(火积)的解析解求解难度不同, 在描述传热过程不可逆性变化上, (火积)更加有效; 对于孤立系内不同维数的热传导问题, 只要温度场解析解存在, (火积)耗散解析解均可以应用特征函数正交性求解得到.