“Volume-Point” heat conduction constructal optimization with entransy dissipation minimization objective based on rectangular element

By taking equivalent thermal resistance, which reflects the average heat conduction effect and is defined based on entransy dissipation, as optimization objective, the “volume to point” constructal problem of how to discharge the heat generated in a fixed volume to a heat sink on the border through relatively high conductive link is re-analyzed and re-optimized in this paper. The constructal shape of the control volume with the best average heat conduction effect is deduced. For the elemental area and the first order construct assembly, when the thermal current density in the high conductive link is linear with the length, the optimized shapes of assemble based on the minimization of entransy dissipation are the same as those based on minimization of maximum temperature difference, and the mean temperature difference is 2/3 of the maximum temperature difference. For the second and higher order construct assemblies, the thermal current densities in the high conductive link are not linear with the length, and the optimized shapes of assemble based on the minimization of entransy dissipation are different from those based on minimization of maximum temperature difference. For the same parameters, the constructs based on minimization of entransy dissipation and the constructs based on minimization of maximum temperature difference are compared, and the results show that the constructs based on entransy dissipation can decrease the mean temperature difference better than the constructs based on minimization of maximum temperature difference. But with the increase of the number of the order, the mean temperature difference does not always decrease, and there exist some fluctuations. Because the idea of entransy describes the heat transfer ability more suitably, all of the heat conduction constructal problems may be re-optimized based on it. Supported by the Program for New Century Excellent Talents in University of China and the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200136)     

火积耗散理论在平行流热管换热器性能评价中的应用

火积耗散作为传热过程可逆性判断依据,可应用于换热器优化. 分析探究了热管换热器的温差、充液率、倾角及迎面风速对火积耗散的影响,利用焓差实验室进行平行流热管换热器性能试验. 随温差增大,火积耗散增大. 随充液率增大,火积耗散先增大后减小,温差越大,火积耗散变化幅度随充液率增大而增大. 增加倾角,火积耗散比未倾斜时小. 随迎面风速增大,火积耗散减小,且减小幅度随温差增大而增大. 相同传热量,火积耗散值最小时,为系统最优工况.     

对流换热可控温差场分布原则

应用火积概念导出了对流换热过程的火积耗散表达式,进一步基于火积耗散极值原理讨论了换热器N股冷、热流在不同情况下参与换热的优化。研究表明,若参与换热的任何冷、热流之间的温差可以独立调控,在总换热量一定寻求火积耗散最小或在总火积耗散一定的条件下寻求换热量最大,则整个换热系统冷、热流之间的温差分布均匀时换热最优;若参与换热的任何冷、热流体之间的换热量或火积损耗可独立确定,则换热冷热流之间的温差分别保持各自的均匀温差分布时换热最优;若在任何冷、热流之间存在可能换热的情况下,无论是总换热量一定时寻求火积耗散最小,还是总火积耗散一定时寻求换热量最大,整个换热系统不同的冷热流换热的优化温差并不是同一个常数。     

Application of entransy dissipation extremum principle in radiative heat transfer optimization

The concepts of entransy flux and entransy dissipation in radiative heat transfer were introduced based on the analogy with heat conduction and heat convection processes. Entransy will be partially dissipated during the radiative heat transfer processes due to the irreversibility. The extremum principle of entransy dissipation was developed for optimizing radiative heat transfer processes. This principle states that for a fixed boundary temperature the radiative heat transfer is optimized when the entransy dissipation is maximized, while for a fixed boundary heat flux the radiative heat transfer process is optimized when the entransy dissipation is minimized. Finally, examples for the application of the entransy dissipation extremum principle are presented. Supported by the National Basic Research Program of China (“973” Project) (Grant No. 2007CB206901)     

Constructal optimization for geometry of cavity by taking entransy dissipation minimization as objective

The entransy dissipation extremum principle provides new warranty and criterion for optimization of heat transfer. For two cases (body with heat generation and body heated externally) of a solid conducting wall with an open cavity, a dimensionless equivalent thermal resistance based on entransy dissipation definition was taken as the optimization objective to optimize the model constructal geometry. Numerical results validated the necessity and feasibility of the presented method. Comparisons of the numerical results based on minimization of dimensionless maximum thermal resistance and minimization of dimensionless equivalent thermal resistance, respectively, showed that there was no obvious difference between the two results when the volume fraction Φ occupied by cavity was small, but the difference between the two results increased with the increases of Φ and the body aspect ratio H/L for any model. The optimal cavities for bodies heated externally were more slender than those for bodies with heat generation. Heat origin had obvious effect on the global performance of heat transfer. The entransy dissipation of body heated externally increased 2–3 times than that of body with heat generation, indicating that the global performance of heat transfer weakened. The method presented herein provides some guidelines for some relevant thermal design problems.     

Analyses of thermodynamic performance for the endoreversible Otto cycle with the concepts of entropy generation and entransy

In this paper,power the the and endoreversible the Otto cycle is analyzed with the entropy generation minimization objectives,and the the entransy theory.of The output power,the heat-work conversion efficiency are taken as the optimization rate,and relationships the output heat-work conversion efficiency,entransy the entropy generation and the entropy generation rate numbers,the work entransy are loss rate,The entransy loss of coefficient,the dissipation rate the entransy variation associated with discussed.applicability entropy the entropy generation minimization and the entransy theory while to the analyses is also analyzed.It is found do that smaller generation rate does not always lead to larger output our power,smaller entropy entransy generation loss numbers and not always lead to larger heat-work conversion efficiency,either.larger the In calculations,power,both larger larger rate larger entransy variation heat-work rate associated with work correspond also to that output while entransy is loss coefficient suitable results the in larger conversion developed efficiency.It is found concept of entransy dissipation not always for analyses because it was for heat transfer.     

Entransy functions for steady heat transfer

In this paper, the entransy functions for steady heat transfer are summarized and discussed based on the variational theory and the entransy theory. The entransy functions for steady convective heat transfer are derived for the first time. In steady heat transfer processes, it is shown that the steady distributions of heat flux and temperature(radiative thermal potential) should make the corresponding entransy functions reach their minimum values when the temperature(radiative thermal potential) or the heat flux of the boundary is given. The extremum entransy dissipation principles and the minimum entransy-dissipation-based thermal resistance principles are compared with the entransy functions. It is shown that the entransy functions can describe a steady state,but cannot directly give a way to optimize heat transfer processes, while the extremum entransy dissipation principles and the minimum entransy-dissipation-based thermal resistance principles act in an opposite way.     

基于理论的相变储能换热器传热性能分析

在理论成功应用于常规换热器的基础上,将传递效率、耗散数及基于耗散的换热器热阻应用于相变储能换热器的传热性能分析中。定义广义耗散率并由此推导出相变储能换热器蓄热、放热及总过程的传递效率及其瞬时值。确定耗散数及基于耗散的换热器热阻计算中换热量的取法。选取一种相变储能装置作为分析对象,通过理论分析绘制各主要部分温度变化趋势,进一步简化得到硅油、水的出口温度表达式,作为算例分析基础。结果表明, 传递效率的应用范围最广,可用于计算相变储能换热器蓄热、放热及总过程的(瞬时)不可逆热损失,且评价结果与传热性能相符,瞬时传递效率随蓄热时间的增加先增大后不变再增大,随放热时间的增加先减小后不变再减小; 耗散数在蓄热过程和总过程中的评价结果与传递效率一致,瞬时耗散数随蓄热时间的增加先减小后不变再减小,然而在放热过程中的应用受限。基于耗散的换热器热阻的部分评价结果与实际不符,应用限制较大。蓄热过程及总过程中,当蓄热量、取热量与蓄、放热阶段时长同步变化时, 传递效率、耗散数与基于耗散的换热器热阻几乎无变化;当装置传热性能提高时, 传递效率增大, 耗散数减小,基于耗散的换热器热阻减小;放热过程中,设置参数的变化不影响装置传热性能, 传递效率基本无变化。     

Heat transfer performance evaluation of one-stream heat exchangers and one-stream heat exchanger networks

One-stream heat exchangers and one-stream heat exchanger networks are widely used in engineering. In this paper, the heat transfer performance evaluation of one-stream heat exchangers and one-stream heat exchanger networks is analyzed with the concepts of entropy generation rate, entropy generation number, revised entropy generation number, entropy resistance, entransy dissipation rate, entransy dissipation number and generalized thermal resistance. For the analyzed one-stream heat exchangers, our numerical results show that the extremum value of the entransy dissipation rate and the minimum values of the entropy resistance and the generalized thermal resistance always lead to the largest heat transfer rate or the lowest temperature of the cooled object,while the minimum values of the other parameters do not always. For the analyzed one-stream heat exchanger networks, the minimizations of entransy dissipation rate, entransy dissipation number and generalized thermal resistance always correspond to the lowest average temperature of the cooled objects, while the minimizations of the other parameters do not. Therefore, only the extremum entransy dissipation principle and the minimum generalized thermal resistance principle are always applicable for the heat transfer performance evaluation of the systems in this paper, while the applicability of the other parameters is conditional.     

Progress of entransy analysis on the air-conditioning system in buildings

It is of great importance to improve the energy performance of the air-conditioning system for building energy conversation. Entransy provides a novel perspective to investigate the losses existing in the air-conditioning system. The progress of entransy analysis in the air-conditioning system is comprehensively investigated in the present study. Firstly missions and characteristics of the air-conditioning system are analyzed with emphasis on heat or mass transfer process. It is found that reducing the temperature difference, i.e. reducing the entransy dissipation helps to improve the performance. Entransy dissipations and thermal resistances of typical transfer processes in the air-conditioning system are presented. Characteristics of sensible heat transfer process and coupled heat and mass transfer processes are researched in terms of entransy dissipation analysis. Reasons leading to entransy dissipation are also clarified with the help of unmatched coefficient ξ. Principles for reducing the entransy dissipation and constructing a high temperature cooling system are summarized on the basis of case studies in typical handling processes. It's recommended that reducing mixing process, improving match properties are main approaches to reduce the entransy dissipation. The present analysis is beneficial to casting light on the essence of the air-conditioning system and proposing novel approaches for performance optimization.     

Constructal entransy dissipation rate minimization for X-shaped vascular networks

Combining with entransy theory, constructal designs of the X-shaped vascular networks(XSVNs) are implemented with fixed total tube volumes of the XSVNs. The entransy dissipation rates(EDRs) of the XSVNs are minimized, and the optimal constructs of the XSVNs are derived. Comparison of the optimal constructs of the XSVNs with two optimization objectives(EDR minimization and entropy generation rate(EGR) minimization) is conducted. It is found that when the dimensionless mass flow rate(DMFR) is small, the optimal diameter ratio of the elemental XSVN derived by EDR minimization is different from that derived by EGR minimization. For the multilevel XSVN, when the DMFR is 100, compared the XSVN with the corresponding H-shaped vascular network(HSVN), the dimensionless EDRs of the elemental, second and fourth order XSVNs are reduced by 26.39%, 15.34% and 9.81%, respectively. Compared with the entransy dissipation number(EDN) of the second order XSVN before angle optimization, the EDN after optimization is reduced by 26.15%, which illustrates that it is significant to conduct angle optimization of the XSVN. Entransy theory is applied into the constructal design of the vasculature with heat transfer and fluid flow in this paper, which provides new directions for the vasculature designs.     

Application of entransy dissipation based thermal resistance to design optimization of a novel finless evaporator

Entransy has been applied and studied in a broad range of heat transfer optimizations recently. Current study proposes the entransy of evaporators to conduct the optimization of heat exchangers in heating, ventilation, air conditioning and refrigeration systems. A novel finless bare tube heat exchanger was studied using a validated heat exchanger modeling tool. The capacity based optimization and entransy dissipation based thermal resistance were used and compared. The applicability of using entransy dissipation based thermal resistance in this type of heat exchanger optimization has been discussed. It has been demonstrated that minimizing entransy dissipation and maximizing capacity are equivalent to optimizing evaporators with fixed flow rates and different when optimizing evaporators with variable flow rates and the deviation is negligible when heat exchanger capacity is small (～1 kW) and more obvious as heat exchanger capacity increases. Thus entransy dissipation based thermal resistance could be used as an alternative optimization index to capacity for evaporators with fixed flow rate and small capacity evaporators with variable flow rates and should be used individually with capacity as an optimization index for evaporators with large capacity and variable flow rates.     

热声热机换热器性能的分析

热声换热器热量传递的速率与效率直接影响着热声热机的性能. 　　耗散理论能更好地揭示换热器的传热优化特性,在热声换热器研究中引入　　耗散理论,针对顺流和逆流两种情况,计算了热声换热器的　　耗散热阻,并和最小熵产原理的结果进行了对比分析. 结果表明,在一定条件下,顺流比逆流情况下的不可逆损失要大;当换热器低温端流体的热容量小于高温端流体热容量时不可逆损失较小,结果最优.     

An area method for visualizing heat-transfer imperfection of a heat exchanger network in terms of temperature–heat-flow-rate diagrams

The identification of the imperfection originating from finite-temperature-difference heat transfer is an indispensable step for both the performance analysis and the better design of a heat exchanger network(HEN) with the aim of energy saving. This study develops a convenient area method for visualizing the heat-transfer imperfection of a HEN in terms of temperature–heat flow diagrams( T-Q diagrams) by combining the composite curves that have already been used in pinch analysis and the recently developed entransy analysis. It is shown that the area between the hot and cold composite curves and the hot and cold utility lines on a T-Q diagram is just equal to the total entransy dissipation rate during the multi-stream heat transfer process occurred in a HEN, and this area can be used to graphically represent the total heat-transfer imperfection of the HEN. The increase in heat recovery or decrease in energy requirements with decreasing the minimum temperature difference, ΔT_(min), of a HEN can then be attributed to a lower entransy dissipation rate, quantitatively represented by the decrease of the area between the composite curves and the utility lines. In addition, the differences between the T-Q diagram and the pre-existing energy level–enthalpy flow diagram(Ω-H diagram) in the roles of visualizing process imperfection and designing HENs are discussed.     

An entransy dissipation-based optimization principle for solar power tower plants

The entransy theory,which can be used to optimize the heat transfer network of a solar power tower system(SPTS)and improve its energy efficiency,was introduced in this paper.Firstly,the irreversibility of the heat transfer processes in a SPTS was analyzed and the total entransy dissipation equation of a SPTS was derived.Then,two types of optimization problems(reducing the total circulating flow rate or the total heat-exchanging area)of a SPTS were solved with conditional extremum model based on the formulas of total entransy dissipation.Finally,the entransy dissipation-based optimization principle was applied to a simple SPTS without re-heater and a complex SPTS with a re-heater.The results showed that under the chosen calculation conditions the minimum total thermal conductance was 19306.03 W K?1 for a SPTS without re-heater when the total heat capacity rate of heat transfer fluid(HTF)was 3200 W K?1.The minimum total thermal conductance was about 7.9%lower than the value predicted based on the typical outlet temperature of a receiver.This meant that the total heat exchange area or initial investment could be effectively reduced under the prescribed total HTF circulating flow rate.We also studied the variation trends of the two optimized results including minimum total HTF heat capacity rate and minimum total thermal conductance.The minimum total HTF heat capacity rate decreased with the given total thermal conductance,the minimum total thermal conductance decreased first and then increased with the given total HTF heat capacity rate.We also found that for a SPTS with a re-heater,the mixing temperature and the mixing position of HTF had significant effects on the two types of optimization problems.     

基于“火积”的喷淋室内气-水热湿交换性能分析

为研究空气饱和程度对换热效果的影响,采用数值模拟方法,计算气体沿等温线、等焓线、等含湿量线向饱和线靠近的过程中全热交换量、"火积"耗散、"火积"耗散热阻、全热交换效率的变化情况。研究发现:气体沿着这三条线逐渐向饱和线靠近时其"火积"耗散热阻始终在减小,全热交换效率在增大。     

Distribution optimization of circulating water in air-cooled heat exchangers for a typical indirect dry cooling system on the basis of entransy dissipation

The flow and heat transfer of air-cooled heat exchangers play important roles in the performance of indirect dry cooling systems in power plants,so it is of benefit to the design and operation of a typical indirect dry cooling system to optimize the thermo-flow characteristics of air-cooled heat exchangers.The entransy dissipation method is applied to the performance optimization of air-cooled heat exchangers in this paper.Two irreversible heat transfer processes in air-cooled heat exchangers,the heat transfer between circulating water and cooling air and the mixing of circulating water,are taken into account and analyzed by means of the entransy dissipation method.The total entransy dissipation rate,which connects the geometrical parameters of air-cooled heat exchanger sectors and the heat capacity rates of the fluids to the heat flow rate in every sector,is obtained.Based on the mathematical relation and the conditional extremum method,an optimization equation group is derived,by which the air-cooled heat exchanger with known air-side parameters is optimized,showing that the entransy dissipation based optimization approach can contribute to the distribution optimization of circulating water in air-cooled heat exchangers of a typical indirect dry cooling system.     

Entransy dissipation/loss-based optimization of two-stage organic Rankine cycle (TSORC) with R245fa for geothermal power generation

Based on organic Rankine cycle (ORC), the two-stage evaporation strategy is adopted to replace the single-stage evaporation to improve the system performance. In order to evaluate the temperature matching of the two-stage evaporation, a theoretical optimization model was established to optimize the two stage organic Rankine cycle (TSORC) based on the entransy theory and thermodynamics, with the ratio of the entransy dissipation rate of the TSORC to that of the ORC as the objective function. This paper aims to illuminate the improving degree of the system performance of the TSORC. The results show that the TSORC enhances the average evaporating temperature, thereby reducing the entransy dissipation rate in the evaporator and the total entransy dissipation rate. The maximal net power output is proportional to the entransy loss rate and inversely proportional to the entransy dissipation rate. However, compared with the ORC, the TSORC can output more power but requires a higher total thermal conductance. Moreover, there exists an optimal intermediate geothermal water temperature (IGWT) to maximize the net power output of the TSORC. The TSORC can be considered in engineering applications.     

Constructal design progress for eight types of heat sinks

This review paper summarizes constructal design progress performed by the authors for eight types of heat sinks with ten performance indexes being taken as the optimization objectives, respectively, by combining the methods of theoretical analysis and numerical calculation. The eight types of heat sinks are uniform height rectangular fin heat sink, non-uniform height rectangular fin heat sink, inline cylindrical pin-fin heat sink(ICPHS), plate single-row pin fin heat sink(PSRPHS), plate inline pin fin heat sink(PIPHS), plate staggered pin fin heat sink(PSPHS), single-layered microchannel heat sink(SLMCHS) with rectangular cross sections and double-layered microchannel heat sink(DLMCHS) with rectangular cross sections, respectively.And the ten performance indexes are heat transfer rate maximization, maximum thermal resistance minimization, minimization of equivalent thermal resistance which is defined based on the entransy dissipation rate(equivalent thermal resistance for short),field synergy number maximization, entropy generation rate minimization, operation cost minimization, thermo-economic function value minimization, pressure drop minimization, enhanced heat transfer factor maximization and efficiency evaluation criterion number maximization, respectively. The optimal constructs of the eight types of heat sinks with different constraints and based on the different optimization objectives are compared with each other. The results indicated that the optimal constructs mostly are different based on different optimization objectives under the same boundary condition. The optimization objective should be suitable chosen based on the focus when the constructal design for one heat sink is performed. The results obtained herein have some important theoretical significances and application values, and can provide scientific bases and theoretical guidelines for the thermal design of real heat sinks and their applications.     

Generalized constructal optimization for the secondary cooling process of slab continuous casting based on entransy theory

Based on constructal theory and entransy theory,a generalized constructal optimization of a solidification heat transfer process of slab continuous casting for a specified total water flow rate in the secondary cooling zone was carried out.A complex function was taken as the optimization objective to perform the casting.The complex function was composed of the functions of the entransy dissipation and surface temperature gradient of the slab.The optimal water distribution at the sections of the secondary cooling zone were obtained.The effects of the total water flow rate in the secondary cooling zone,casting speed,superheat and water distribution on the generalized constructal optimizations of the secondary cooling process were analyzed.The results show that on comparing the optimization results obtained based on the optimal water distributions of the 8 sections in the secondary cooling zone with those based on the initial ones,the complex function and the functions of the entransy dissipation and surface temperature gradient after optimization decreased by 43.25%,5.90%and 80.60%,respectively.The quality and energy storage of the slab had obviously improved in this case.The complex function,composed of the functions of the entransy dissipation and surface temperature gradient of the slab,was a compromise between the internal and surface temperature gradients of the slab.Essentially,it is also the compromise between energy storage and quality of the slab.The"generalized constructal optimization"based on the minimum complex function can provide an optimal alternative scheme from the point of view of improving energy storage and quality for the parameter design and dynamic operation of the solidification heat transfer process of slab continuous casting.