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 extre- mum principle are presented.

Constructal design for a steam generator based on entransy dissipation extremum principle

Steam generator is optimized by applying entransy dissipation extremum principle and constructal theory and adopting analyti-cal method.The obtained results show that the optimal spacing between adjacent tubes,the mass flow rate of gas and the maximum entransy dissipation rate all depend on the dimensionless diameter of one tube,the dimensionless pressure difference number and the dimensionless length of flow channel of gas.Besides the three dimensionless groups,the optimal numbers of riser tubes and downcomer tubes and their summation all depend on the dimensionless height of one tube.The maximum entransy dissipation rate increases as the pressure difference that drives the gas flowing increases,and as the diameter of one tube and the length of flow channel both decrease.The mean heat flux in the heat transfer process of hot gas grows greatly,and the performance of the system is improved.Compared with the optimal construct with heat transfer rate maximization,the optimal construct with entransy dissipation rate maximization can improved the heat transfer effect of the steam generator more.

Thermal insulation constructal optimization for steel rolling reheating furnace wall based on entransy dissipation extremum principle

Analogizing with the heat conduction process, the entransy dissipation extremum principle for thermal insulation process can be described as: for a fixed boundary heat flux (heat loss) with certain constraints, the thermal insulation process is optimized when the entransy dissipation is maximized (maximum average temperature difference), while for a fixed boundary temperature, the thermal insulation process is optimized when the entransy dissipation is minimized (minimum average heat loss rate). Based on the constructal theory, the constructal optimizations of a single plane and cylindrical insulation layers as well as multi-layer insulation layers of the steel rolling reheating furnace walls are carried out for the fixed boundary temperatures and by taking the minimization of entransy dissipation rate as optimization objective. The optimal constructs of these three kinds of insulation structures with distributed thicknesses are obtained. The results show that compared with the insulation layers with uniform thicknesses and the optimal constructs of the insulation layers obtained by minimum heat loss rate, the optimal constructs of the insulation layers obtained by minimum entransy dissipation rate are obviously different from those of the former two insulation layers; the optimal constructs of the insulation layers obtained by minimum entransy dissipation rate can effectively reduce the average heat loss rates of the insulation layers, and can help to improve their global thermal insulation performances. The entransy dissipation extremum principle is applied to the constructal optimizations of insulation systems, which will help to extend the application range of the entransy dissipation extremum principle.

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 ge- ometry.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 fractionΦoccupied by cavity was small, but the difference between the two results increased with the increases ofΦand 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.

Comparative study on constructal optimizations of T-shaped fin based on entransy dissipation rate minimization and maximum thermal resistance minimization

The constructal optimizations of T-shaped fin with two-dimensional heat transfer model are carried out by finite element method and taking the minimization of equivalent thermal resistance based on entransy dissipation and the minimization of maximum thermal resistance as optimization objectives, respectively. The effects of the global parameter a (integrating the coefficient of convective heat transfer, the overall area occupied by fin and its thermal conductivity) and the volume fraction ? of fin on the minimums of equivalent thermal resistance and maximum thermal resistance as well as their corresponding optimal configurations are analyzed. The comparison of the results based on the above two optimization objectives is conducted. The results show that the optimal structures based on the two optimization objectives are obviously different from each other. Compared with the optimization result by taking the minimization of maximum thermal resistance as the objective, the optimization result by taking the equivalent thermal resistance minimization as the objective can reduce the average temperature difference in the fin obviously. The increases of a and ? can all improve the working status of local hot spot and the global heat transfer performance of the system. But the improvement effects of the increases of a and ? on the minimization of equivalent thermal resistance are different from those on the minimization of maximum thermal resistance. For either objective, the effect of a is different from that of ?. The T-shaped fin with minimum equivalent thermal resistance is much taller than that with minimum maximum thermal resistance; for either optimization objective, the stem of fin is thicker than the branches of fin, and the stem thickness is relatively close to branch thickness when the minimization of equivalent thermal resistance is taken as the optimization objective. The T-shaped fin with flat stem and slender branches can benefit the reduction of the maximum thermal resistance.

一维换热器中温差场均匀性原则的证明

The uniformity principle of temperature difference field is a phenomenological principle,which has not been theoretically proved.For one-dimensional two-and three-stream heat exchangers,the extremum principle of entransy dissipation was used to optimize the heat transfer process by variational calculus.It was indicated that the temperature difference field between the hot and cold fluids should be completely uniform if the entransy dissipation reached a minimum for a given heat duty,or if the heat duty reached a maximum for a given entransy dissipation.So,the uniformity principle of temperature difference field of heat exchangers was primarily proved.

离散发热器件基于(火积)耗散率最小和最高温度最小的构形优化比较

建立了导热基座上圆柱体离散发热器件的三维湍流散热模型,基于构形理论,考虑空气变物性及可压缩性和黏性耗散,研究了器件材料的热导率、热源强度和流体流速对器件最高温度、基于(火积)耗散定义的当量热阻和平均Nu数的影响.结果表明:在总发热功率一定的条件下,以器件最高温度和当量热阻为性能指标进行热设计,均存在最优热源强度分布使得散热性能最优.当各热源强度相同且热源热导率小于基座热导率时,提高热源热导率可明显改善散热性能;将热源热导率沿流动方向从低到高布置可降低器件最高温度,而将热源热导率均匀布置可使当量热阻最小.所得结果可为实际热设计中不同材质和不同发热率的电子器件最优布置提供理论支撑.

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,(?)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、(?)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(?)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(?)耗散极值原理进行分析。

矩形肋片热沉(火积)耗散率最小与最大热阻最小构形优化的比较研究

针对矩形肋片热沉,分别以最大热阻最小化和基于(火积)耗散定义的当量热阻最小化为优化目标,采用二维传热模型并结合有限元数值仿真对其进行构形优化,比较了两种目标下的热沉最优构形,并分析了全局参数(综合了对流换热系数、肋片占据的总面积及其热导率的函数)和材料占比对两种目标(最大热阻、当量热阻)及其对应最优构形的影响.结果表明:热沉外形固定时,两种目标下均不存在最优的肋片厚度;热沉外形自由变化时,两种目标下的最优构形存在一定的差异.此外,全局参数对两种目标下的最优构形均没有影响,而材料占比对两种目标下的最优构形均有较大影响.提高全局参数和材料占比均可以减小最大热阻最小值和当量热阻最小值,但对两种目标的减小程度不同.总体上,调节热沉结构参数使当量热阻最小,可以同时获得很好的局部极限性能;而调节热沉结构参数使最大热阻最小,获得的整体平均散热性能却较差.因此,对本文热沉模型进行优化时,以当量热阻最小化为优化目标更合理.

(火积)理论及其在化工过程节能中的应用进展

(火积)和(火积)耗散极值原理的提出,为化工过程系统节能开辟了新的方向。阐述了(火积)的物理意义、(火积)是过程量等(火积)理论的最新研究成果,从(火积)在换热器设计、热力学过程中的不可逆性、换热网络综合等方面的应用情况综述了(火积)理论在化工过程系统节能中的最新应用进展。重点围绕(火积)耗散率与熵产率的异同点比较分析、(火积)耗散极值原理与换热网络综合结合等方面,阐述了(火积)理论的科学性。

Application of entransy to optimization design of parallel thermal network of thermal control system in spacecraft

For distribution optimization of the flow rate of cold fluid and heat transfer area in the parallel thermal network of the thermal control system in spacecraft,a physical and mathematical model is set up,analyzed and discussed with the entransy theory.It is found that the optimization objective of this problem and the optimization direction of the extremum entransy dissipation principle are consistent in theory.For a two-branch thermal network system,the distributions of the flow rate of the cold fluid and the heat transfer area are optimized by calculating the extremum entransy dissipation with the Newton method.The influential factors of the optimized distributions are also analyzed and discussed.The results show that the main influence factors are the heat transfer rate of the branches and the total heat transfer area.The total flow rate of the cold fluid has a threshold,beyond which further increasing its value brings very little influence on the optimization results.Moreover,the difference between the extremum entransy dissipation principle and the minimum entropy generation principle is also discussed when they are used to analyze the problem in this paper,and the extremum entransy dissipation principle is found to be more suitable.In addition,the Newton method is mathematically efficient to solve the problem,which could accomplish the optimized distribution in a very short time for a ten-branch thermal network system.

Constructal entransy dissipation rate minimization for a heat generating volume cooled by forced convection

The geometry of a heat generating volume cooled by forced convection is optimized by applying the entransy dissipation extremum principle and constructal theory, while the optimal spacing between the adjacent tubes and the optimal diameter of each tube are obtained based on entransy dissipation rate minimization. The results of this work show that the optimal constructs based on entransy dissipation rate minimization and maximum temperature difference minimization, respectively, are clearly different. For the former, the porosity of the volume of channels allocated to the heat generating volume is 1/2; while for the latter, the larger the porosity is, the better the performance will be. The optimal construct of the former greatly decreases the mean thermal resistance and improves the global heat transfer performance of the system compared with the optimal construct of the latter. This is identical to the essential requirement of the entransy dissipation extremum principle that the required heat transfer temperature difference is minimal with the same heat transfer rate (the given amount of heat generated in the heat generating volume) based on the entransy dissipation extremum principle.

Constructal optimization on T-shaped cavity based on entransy dissipation minimization

The entransy dissipation extremum principle provides new warranty and criterion for optimization of heat transfer. For a heat transfer model of a rectangular solid wall with an open T-shaped cavity, a dimensionless equivalent thermal resistance based on entransy dissipation is taken as optimization objective, and constructal optimization for the model is carried out when the system volume, the cavity volume and the volume of rectangle occupied by T-shaped cavity are fixed. Numerical results indicate that the optimal geometry construct of cavity can be schemed out based on entransy dissipation extremum principle. The formulation of dimensionless global (maximum) thermal resistance presented in a literature is modified; some new rules which are different from those reported in the literature are obtained based on the minimization of the modified objective. Comparisons of the numerical results show that the optimal system constructs deduced respectively from the two thermal resistance objectives are very different. The optimization by taking equivalent thermal resistance minimization as objective can more effectively reduce mean temperature difference of heat transfer than the optimization by taking maximum thermal resistance minimization as objective, so that the performance of heat transfer for the total system can be improved. The more freedom the cavity has, the better the total system performance is. The correlations of the equivalent thermal resistance and the maximum thermal resistance of the system and three geometric degrees of freedom are found by using function fitting.

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.

Equivalent thermal resistance minimization for a circular disc heat sink with reverting microchannels based on constructal theory and entransy theory

Thermal designs for microchannel heat sinks with laminar flow are conducted numerically by combining constructal theory and entransy theory. Three types of 3-D circular disc heat sink models, i.e. without collection microchannels, with center collection microchannels, and with edge collection microchannels, are established respectively. Compared with the entransy equivalent thermal resistances of circular disc heat sink without collection microchannels and circular disc heat sink with edge collection microchannels, that of circular disc heat sink with center collection microchannels is the minimum, so the overall heat transfer performance of circular disc heat sink with center collection microchannels has obvious advantages. Furthermore, the effects of microchannel branch number on maximum thermal resistance and entransy equivalent thermal resistance of circular disc heat sink with center collection microchannels are investigated under different mass flow rates and heat fluxes. With the mass flow rate increasing, both the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number all gradually decrease. With the heat flux increasing, the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number remain almost unchanged. With the same mass flow rate and heat flux, the larger the microchannel branch number, the smaller the maximum thermal resistance. While the optimal microchannel branch number corresponding to minimum entransy equivalent thermal resistance is 6.

广义流动中的积原理

自然界发生的热量传递、分子扩散、导电等现象具有一定的相似性,它们均可被称为广义流动.文章基于这种相似性,对过增元等针对传热过程提出的理论进行了推广,定义了积、积流、积耗散等概念.针对只有一种广义流动和存在两种广义流动的系统,指出了在该类系统中可以发展积原理的条件,并在满足相应条件的系统中得到了积损失极小值原理、积耗散极值原理和最小广义流阻原理.

矩形通道内层流对流换热的最优速度场

针对矩形通道内的层流对流换热问题,通过数值求解速度场协同方程,得到了给定黏性耗散条件下通道内的最优速度场为多纵向涡的流动结构,表明多纵向涡流型可在流阻增加不多的情况下使换热显著强化。通过在通道壁面布置不连续双斜肋,在通道内产生了接近于最优速度场的多纵向涡流动,数值计算结果表明,在Re=1000时,与光滑通道相比,不连续双斜肋通道的平均努谢尔数增加61.3%,阻力系数增加79.2%。

基于多物理场耦合计算的正六边形微通道热沉构形研究

提出了新的微通道正六边形热沉分别在无回流、边缘回流和中心回流3种回流方式下4种通道结构的设计原型,基于热-流-力-应变的多物理场耦合计算,研究了回流方式、微通道分支数和微通道分布演化对正六边形热沉的最大热阻和基于耗散的当量热阻的影响,并进行了热应力和形变分析.数值计算结果表明:以最大热阻最小化和当量热阻最小化为目标, 3种回流方式中的中心回流式为最佳回流方式,中心回流式六分支微通道正六边形热沉按上层微通道沿六边形内切圆半径分布、下层微通道沿六边形外接圆半径分布为最优构形,可使传热性能最优,且最大热应力为0.28 GPa,比硅的屈服强度小1个数量级以上,最大形变为1.4μm.所得结果可为实际微通道热沉提供多学科设计的理论支撑.

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。

自然对流条件下椭圆柱发热器件的构形设计

在自然对流条件下,基于构形理论和理论,建立了导热基座上椭圆柱离散热源的散热模型,分别在给定热源热导率总和与热源总发热强度的约束条件下,以热导率分布与热源强度分布为设计变量,以系统最高温度和基于耗散的当量热阻为性能指标,进行构形设计,得到了对应的热源散热最优构形,可为实际发热器件的热设计和热管理提供理论支撑。