Entransy flux of thermal radiation and its application to enclosures with opaque surfaces

Entransy is a new concept developed in recent years to measure the transport ability of heat at a temperature in conduction and convection. This paper develops the concept of entransy flux for thermal radiation in enclosures with opaque surfaces. The entransy balance equation and entransy dissipation function are derived. The minimum principle of radiative entransy loss is developed. The potentials and the heat fluxes distribution which meet the Stefan–Boltzmann’s law and the energy balance equation would make the radiative entransy loss minimum if the net heat flux of each surface or the thermal potentials of the surfaces are given. The extremum entransy dissipation principles (EEDP) for thermal radiation are developed. The minimum radiative entransy dissipation leads to the minimum average radiative thermal potential difference for prescribed total heat exchange and the maximum radiative entransy dissipation leads to the maximum heat exchange for prescribed average radiative thermal potential difference. The minimum and maximum principle can be concluded into the minimum thermal resistance principle (MTRP) for thermal radiation by defining the thermal resistance with the entransy dissipation. The EEDP or MTRP is proved to be reliable when they are used to optimize some radiative heat transfer problems, and a comparison is made between the minimum principle of entropy generation and the EEDP.     

Entransy expression of the second law of thermodynamics and its application to optimization in heat transfer process

Based on theories of thermodynamics, the energy equation in terms of entransy in heat transfer process is introduced, which not only describes the change of entransy, but also defines the entransy consumption rate. According to the regularity of entransy change in heat transfer process and the effect of entransy consumption rate on the irreversibility of heat transfer process, it can be found that entransy is a state variable, from which a new expression for the second law of thermodynamics is presented. Then by setting entransy consumption rate and power consumption rate as optimization objective and constraint condition for each other, the Lagrange conditional extremum principle is used to deduce momentum equation, constraint equation and boundary condition for optimizing flow field of convective heat transfer, which are applied to simulate convective heat transfer coupling with energy equation in an enclosed cavity. Through the numerical simulation, the optimized flow field under different constraint conditions is obtained, which shows that the principle of minimum entransy consumption is more suitable than the principle of minimum entropy generation for optimizing convective heat transfer process.     

基于火积理论的螺旋折流板换热器的优化结构分析

为了比较平面螺旋折流板换热器和折面螺旋折流板换热器的传热和阻力性能,应用了换热器常用评价标准PEC准则和火积理论对两种换热器实验结果进行了分析,同时采用火积耗散极值原理对两种换热器的传热火积耗散率、阻力火积耗散率以及总火积耗散率进行了对比。结果表明:火积耗散理论分析换热器性能的结果与传统换热器评价标准PEC准则相符,说明了火积耗散理论的可靠性;折面螺旋折流板换热器的综合性能得到了有效的改进,火积耗散率也均优于原始结构,表明折面螺旋折流板换热器的性能得到较大改善;两种换热器传热火积耗散率值要远远大于阻力火积耗散率,约为阻力火积耗散率的一千余倍,说明传热损失为换热器的主要不可逆损失。     

基于火积理论的多级套管式相变蓄热系统优化

本文基于最小火积耗散热阻原理,在考虑相变材料导热热阻以及非稳态传热过程的基础上,对多级套管式相变蓄热系统的融化温度进行了数值优化,获得了最优融化温度分布。在此基础上,研究了相变材料导热系数和传热管长度对最优融化温度、火积耗散热阻和平均蓄热速率的影响。研究结果表明,与现有理论优化方法相比,本文提出的数值优化方法具有更好的适用性;优化后多级套管式相变蓄热系统可有效提高相变蓄热系统的平均蓄热速率,降低火积耗散热阻;随着相变材料导热系数增大和传热管长度增加,多级套管式相变蓄热系统最优融化温度的温差愈加明显,其强化传热性能呈上升趋势。     

Experimental exergy and entransy analyses on designed and fabricated crossflow heat exchanger

A crossflow heat exchanger (CFHEx) is designed and fabricated in a workshop. For designing this heat exchanger (HEx), the number of passes, frontal areas, HEx volumes, heat transfer areas, free-flow areas, ratios of minimum free-flow area to frontal area, densities, mass flow rates of flowing fluids, maximum/minimum heat capacities, heat capacity ratio, outlet temperatures of hot/cold fluids, average temperatures, mass velocities, Reynolds numbers, and convective heat transfer coefficients are evaluated by considering Colburn/friction factors. After fabrication of the HEx, effectiveness, exergy destruction, entransy dissipation, entransy dissipation-based thermal resistance, entransy dissipation number, and entransy effectiveness for hot/cold fluids sides are found at different flow rates and inlet temperatures of fluids. By experimental results, optimum operating conditions are found, which gives maximum effectiveness and entransy effectiveness but minimum rates of exergy destruction, entransy dissipation, entransy dissipation-based thermal resistance, and entransy dissipation number for the fabricated CFHEx. This study is concluded as follows: minimum exergy destruction and entransy dissipation rates (ie, 3.061 kJ/s·K and 1125.44 kJ·K/s, respectively) are found during experiment 2. Maximum entransy effectiveness of hot/cold fluids (ie, 0.689/0.21) is achieved in experiment 1. Moderate values of entransy dissipation number (ie, 4.689), entransy dissipation-based thermal resistance (ie, 0.04 s·K/J), exergy destruction (ie, 3.845 kJ/s·K), and entransy dissipation (ie, 1374.04 kJ·K/s) rates are found during experiment 1. Maximum effectiveness (ie, 0.4) for the fabricated HEx is also obtained through experiment 1. After comparative analyses, it is found that experiment 1 provides optimum results, which shows the best performance of the fabricated HEx.     

A new approach to analysis and optimization of evaporative cooling system II: Applications

After introducing the concepts of moisture entransy, moisture entransy dissipation and thermal resistance based on moisture entransy dissipation (TRMED) in part I of this study, we further analyze several direct/indirect evaporative cooling processes based on the above concepts in this part. The nature of moisture entransy, moisture entransy dissipation and TRMED during evaporative cooling processes was reexamined. The results demonstrate that it is the moisture entransy, not the enthalpy, that represents the endothermic ability of a moist air, and reducing the entransy dissipation by both enlarging the thermal conductance of heat and mass transfer, and decreasing the temperature potential of the moist air, i.e. the difference between the dry-bulb temperature of moist air over its dew-point temperature, will result in a smaller system TRMED, and consequently a better evaporative cooling performance. Then, a minimum thermal resistance law for optimizing evaporative cooling systems is developed. For given mass flow rates of both moist air and water, with prescribed moist air and water conditions, minimizing the TRMED will actually lead to the most efficient evaporative cooling performance. Finally, the thermal conductance allocation for an indirect evaporative cooling system is optimized to illustrate the application of the proposed minimum thermal resistance law.     

Optimization principles for convective heat transfer

Optimization for convective heat transfer plays a significant role in energy saving and high-efficiency utilizing. We compared two optimization principles for convective heat transfer, the minimum entropy generation principle and the entransy dissipation extremum principle, and analyzed their physical implications and applicability. We derived the optimization equation for each optimization principle. The theoretical analysis indicates that both principles can be used to optimize convective heat-transfer process, subject to different objectives of optimization. The minimum entropy generation principle, originally derived from the heat engine cycle process, optimizes the convective heat-transfer process with minimum usable energy dissipation focusing on the heat–work conversion. The entransy dissipation extremum principle however, originally for pure heat conduction process, optimizes the heat-transfer process with minimum heat-transfer ability dissipation, and therefore is more suitable for optimization of the processes not involving heat–work conversion. To validate the theoretical results, we simulated the convective heat-transfer process in a two-dimensional foursquare cavity with a uniform heat source and different temperature boundaries. Under the same constraints, the results indicate that the minimum entropy production principle leads to the highest heat–work conversion while the entransy dissipation extremum principle yields the maximum convective heat-transfer efficiency.     

Two energy conservation principles in convective heat transfer optimization

Improving heat transfer performance is very beneficial to energy conservation because heat transfer processes widely existed in energy utilization systems. In this contribution, in order to effectively optimize convective heat transfer, such two principles as the field synergy principle and the entransy dissipation extremum principle are investigated to reveal the physical nature of the entransy dissipation and its intrinsic relationship with the field synergy degree. We first established the variational relations of the entransy dissipation and the field synergy degree with the heat transfer performance, and then derived the optimization equation of the field synergy principle and made comparison with that of the entransy dissipation extremum principle. Finally the theoretical analysis is then validated by the optimization results in both a fin-and-flat tube heat exchanger and a foursquare cavity. The results show that, for prescribed temperature boundary conditions, the above two optimization principles both aim at maximizing the total heat flow rate and their optimization equations can effectively obtain the best flow pattern. However, for given heat flux boundary conditions, only the optimization equation based on the entransy dissipation extremum principle intends to minimize the heat transfer temperature difference and could get the optimal velocity and temperature fields.     

Application of EoEP principle with variable heat transfer coefficient in minimizing entropy production in heat exchangers

A more realistic application of the entropy minimization principle EoEP is presented. This principle dictates uniform local entropy generations along the heat exchanger in order to minimize the total entropy generation rate due only to heat transfer. For a certain heat duty and area of an existing exchanger, this is done by changing the temperatures of one fluid while the temperatures of the other fluid are held constant. Since the heat duty is fixed, the change in the temperatures of the fluid after the change, however, may sometimes cause a drastic change in its flow rate. This may cause considerable changes in the overall heat transfer coefficient (U) and, consequently, in the entropy generation rate. Depending on the choice of the fluid for changing, the new entropy generation rates may be higher or lower than those based on constant U as is the case in papers recently published. So, the classical application of the EoEP principle needs to be modified to achieve more realistic entropy generation rates. In this study, the principle of EoEP with variable U is applied to some cases of heat exchange, and a simple method is presented as a criterion for the proper choice of the fluid to be changed.     

Entropy generation and Carnot efficiency comparisons of high temperature heat transfer fluid candidates for CSP plants

Heat transfer fluid is a critical component in a concentrating solar power plant. A large quantity of heat transfer fluid is required to transfer heat between the solar collector and the power block, thus it is crucial to select the most appropriate heat transfer fluid in order to maximize the system performance. The present study compared the performances of five molten-salt eutectic mixtures in regarding with the entropy generation rate and the Carnot efficiency of using them as heat transfer fluids. All the five molten-salt eutectic mixtures have thermal stability temperatures above 600 °C. Effects of the tube lengths in the steam generation heat exchanger and the receiver heat exchanger as well as the heat transfer fluid flow rate on both the entropy generation rate and the Carnot cycle efficiency were investigated. The results indicate that the carbonate salts has the worst performances compared to the other eutectic mixtures. The three chloride salts have slightly higher entropy generation rate and 5% higher Carnot efficiency than the Solar Salt. Therefore the three chloride salts are suggested to be used in advanced concentrating solar power tower plants as potential high temperature heat transfer fluids.     

Assessment of Bejan’s heat exchanger allocation model under the influence of generalized thermal resistance,relaxation effect,bypass heat leak and internal irreversibility

This article reports an analytical investigation of the optimal heat exchanger allocation and the corresponding efficiency for maximum power output of a Carnot-like heat engine. To mimic a real engine, the generalized power law for the resistance in heat transfer external to the engine, relaxation effect in heat transfer, bypass heat leak and finally internal irreversibility of the power producing compartment of the engine is taken into consideration. From the engineering perspective the temperature ratio of the heat source and sink as well as to that of hot end and cold side of the working fluid is considered not to be the controllable parameters. A parametric study is presented for the other possible controllable variables. Selection of a power law over a linear model has a significant effect on the optimal heat exchanger allocation for maximum power output and the corresponding efficiency. For a higher degree of relaxation effect the drop in the maximum power efficiency is prominent along with the shift of equipartitioned allocation of heat exchanger inventory. Bypass heat leak and internal irreversibility exhibits relatively less pronounced effects on the maximum power efficiency and on the optimal heat exchanger allocation. Thus the endoreversible formulation of thermodynamic model is physically realistic. Strikingly when the optimal allocation of the heat exchanger inventory obeys the principle of equipartition in macroscopic organization for the linear law of the external heat resistance, the thermal efficiency appears to assume the representative documented value. Hence the linear model due to Bejan is also capable of capturing the essential features of a real power plant.     

An entransy dissipation-based optimization principle for building central chilled water systems

The recently developed entransy theory is introduced in this paper to tackle the heat transfer processes in building central chilled water systems so as to improve their energy efficiency. We first divide the irreversible heat transfer processes into four categories: (1) air mixing processes; (2) heat transfer processes between chilled water and air; (3) chilled water mixing processes; and (4) heat transfer processes between chilled water and refrigerant. The formulas of entransy dissipation rates for each irreversible process are derived, and then the total entransy dissipation rate in the whole chilled water systems is obtained, which connects the geometrical structures of each heat exchanger and the operating parameters of each fluid directly to the demands of users and the supply of refrigerating unit. Based on the formula of entransy dissipation rate together with the conditional extremum method in mathematics, two optimization equation groups are deduced theoretically. Simultaneously solving such equation groups will easily find the optimal central chilled water system with the highest energy efficiency. Finally, a simple building central chilled water system with two users is taken as an example to illustrate the applications of the newly proposed optimization principle.     

Effect of maximum and minimum heat capacity rate on entropy generation in a heat exchanger

This paper presents a theoretical analysis of a heat exchanger with a negligible fluid flow pressure drop to determine whether it is better to operate the heat exchanger with the minimum or maximum heat capacity rate of the hot fluid from entropy generation point of view. Entropy generation numbers are derived for both cases, and the results show that they are identical, when the heat exchanger is running at a heat capacity ratio of 0.5 with heat exchanger effectiveness equaling 1. An entropy generation number ratio is defined for the first time, which has a maximum value at ε = 1/(1+R) for any inlet temperature ratio. When R equals 0.1, 0.5 and 0.9, the entropy generation number ratio receives a maximum value at an effectiveness equaling 0.91, 0.67 and 0.526, respectively. When R=0.9, the entropy generation number ratio is the same for all inlet temperature ratios at ε=0.8. The results show that the entropy generation number ratio is far from 1 depending on the inlet temperature ratio of the cold and hot fluid. The results are valid for parallel‐flow and counterflow heat exchangers. Copyright © 2010 John Wiley & Sons, Ltd.     

Improvement of constructal tree-like network for “volume-point” heat conduction with variable cross-section conducting path and without the premise of optimal last-order construct

The constructal “tree-like” network has been proved an effective way for “volume-point” heat conduction. This paper aims to further improve the constructal “tree-like” network with the optimization objectives of minimizations of maximum thermal resistance and entransy dissipation rate respectively. By removing the constraint that the last-order construct must be optimal, and using variable cross-section conducting path, the maximum thermal resistance and entransy dissipation rate can be greatly reduced. It is also found that the optimal construct for minimum peak temperature is similar to the optimal one for minimum entransy dissipation rate. They hold the same shape and configuration, and the main difference of them is the shape of high-conductivity path.     

A New Method for Analyzing Heat Exchangers- Matching of Temperature Field

In heat exchangers, the magnitude of Nu of each duct is influenced by the temperature field, since the ratio of heat capacity rate will influence the matching status of the temperature field between contacting ducts, the total heat transfer coefficient is related with the ratio of heat capacity rate. Considering this relationship, a new method for analyzing heat exchanger is proposed - matching of temperature field. First, for a single duct with the temperature field varying exponentially along the flow direction, its Nu is calculated. Then under the hypothesis that the thermal resistance of the wall is negligible, the matching condition was set like this: both the temperature and heat flux are equal for the hot and cold fluids at the wall, so the matching relationship of parameter that describes the temperature field of the hot and cold fluids, was obtained. Finally the relationship between the total Nu and the ratio of heat capacity rate along with the ratio of inherent thermal resistance is obtained. Compared with traditional analyzing methods, the temperature matching method can be used to get the total heat transfer coefficient directly, and also be used for optimization of heat exchanger design. For a parallel flow, the optimal ratio of heat capacity rate is reciprocal to the ratio of inherent thermal resistance, and for a counter flow, the optimal ratio of heat capacity rate is zero or infinity.     

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.     

Application of entransy dissipation theory in heat convection

In the present work, formulas for calculating the rates of the local thermodynamic entransy dissipation in convective heat transfer in general, and the internal and external flows in particular, are established. Practically, these results may facilitate the application of entransy dissipation theory in thermal engineering. Theoretically they shed light on solving the contradiction of the minimum entropy production principle with balance equations in continuum mechanics.     

Effect of nanoparticle shape on the heat transfer and thermodynamic performance of a shell and tube heat exchanger

Nanofluid is a heat transfer fluid that can improve the performance of heat exchanger systems. Different parameters such as particle size, shape, and volume concentration affect the performance of these systems. The objective of this paper is to study the effect of different nanoparticle shapes (such as cylindrical, bricks, blades, platelets, and spherical) on the performance of a shell and tube heat exchanger operating with nanofluid analytically. Boehmite alumina (γ-AlOOH) nanoparticles of different shapes were dispersed in a mixture of water/ethylene glycol as the nanofluid. The thermodynamic performance of the shell and tube heat exchanger that is used in a waste heat recovery system was analysed in terms of heat transfer rate and entropy generation. Established correlations were used to measure the thermal conductivity, heat transfer coefficient and rate and entropy generation of nanofluid. The results show an increase in both the heat transfer and thermodynamic performance of the system. However, among the five nanoparticle shapes, cylindrical shape exhibited better heat transfer characteristics and heat transfer rate. On the other hand, entropy generation for nanofluids containing cylindrical shaped nanoparticles was higher in comparison with the other nanoparticle shapes. However, the increased percentage of entropy was below 1%. Therefore, this greater entropy generation could be deemed negligible and cylindrical shaped nanoparticles are recommended to be utilized in heat exchanger systems working with nanofluids.     

Application of entransy dissipation theory in heat convection

In the present work, formulas for calculating the rates of the local thermodynamic entransy dissipation in convective heat transfer in general, and the internal and external flows in particular, are established. Practically, these results may facilitate the application of entransy dissipation theory in thermal engineering. Theoretically they shed light on solving the contradiction of the minimum entropy production principle with balance equations in continuum mechanics.     

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.