层流对流换热中的势容耗散极值与最小熵产

在一定的约束条件下,存在一个最优的速度场,它能够使得温度场和速度场的协同程度最好,从而使得对流换热的整体传热性能达到最优。目前对传热效果的评价存在熵产最小化和势容耗散取得极值两种不同的准测。分别根据这两种优化准则,用变分方法推导了在粘性耗散一定的条件下,稳态无内热源的层流对流换热的场协同方程,并对方腔内对流换热问题进行了优化。数值计算结果表明,势容耗散取得极值时的换热效果优于熵产最小的结果,因此势容耗散极值原理更适合做为对流换热的优化准则。     

基于最小热量传递势容耗散原理的导热优化

导热是一个不可逆过程,它的优化遵循最小热量传递势容耗散原理。本文根据该原理,对体点问题中的高导热材料布置进行了优化。当域内导热系数的积分为定值时,最小热量传递势容耗散对应于导热系数与当地热流成正比,即全场的温度梯度均匀。以温度梯度均匀化为准则,利用仿生优化方法得到了域内有均匀和非均匀热源时高导热材料的最优布置。     

不同目的热优化目标函数:热量传递势容损耗与熵产

热量传递势容(势容)反映了物体的导热能力,在导热过程中势容有损耗,对应于势容损耗最小的导热过程效率最高,传热速率最大。熵反映了过程的不可逆性,在导热过程中熵有增加(熵产),对应于熵产最小的过程是系统做有用功的能力((?))损失最小的过程。以势容损耗和熵产为目标函数,分别对导热平板和圆形导热管进行了导热优化计算。以势容损耗作为目标函数的优化,要求沿传热方向温度的梯度为常数,结果是系统具有最大的导热能力。以熵产作为目标函数的优化,要求沿传热方向温度的自然对数的梯度为常数,结果是系统具有最小的(?)损耗。     

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.     

热传导中的变分原理

采用力学中建立最小势能原理和最小余能原理的加权余量法,分别得到了热传导中势能型与余能型的变分原理。通过对势能型变分原理的分析发现,对于可逆的导热过程,“力”(热流)在“位移”(温度)上做的“功”完全转换为物体的“势能”,即热量传递势容。而在不可逆的稳态导热过程中,这个势能完全被耗散掉了,成为传递势容耗散。对于非稳态导热过程,则类似于粘弹性物体,热流在温度位移上做的“功”一部分转换为物体的传递势容,而另外一部分成为传递势容的耗散。     

熵产最小化理论在传热和热功转换优化中的应用探讨

针对传热和热功转换系统的优化设计,分析了熵产最小化理论的优化方向和适用条件.熵产直接度量系统可用能或做功能力的损失,因此熵产最小化理论的优化方向为将系统可用能或做功能力的损失降到最低,从而使系统保有最大的做功能力.然而,在工程应用中,设计目标各有不同.因此,并非所有设计目标均能与熵产最小化的设计方向一致,这就使得熵产最小化并不总是与优化目标相关联.针对传热速率、输出功率等可与熵产建立关联的优化目标,讨论了熵产最小化理论的适用条件.当这些条件不能得到满足时,最小熵产并不一定对应最优性能.对一维传热过程、换热器等传热系统和以输出功率、热功转换效率、热经济性能等为优化目标的热功转换过程进行了分析,结果验证了理论分析所得的结论.     

具体热源的湍流对流中热量传递势容耗散的界

本文从数学上确定了具体热源的湍流对流中时均热量传递势容耗散的上界和下界,该上界和下界反映了体热源对湍流对流中热量传递势容耗散的影响.其上界表明具体热源的湍流对流中时均热最传递势容耗散不会大于导热情况下时均热量传递势容耗散;其下界表明,给定湍流流场的统计特性,即在某种意义上,粘性耗散一定,这时时均热量传递势容耗散可能达到的下界依赖于体热源和速度的时均值.     

板翅式换热器传热、阻力多目标权衡优化

本文利用NSGA-Ⅱ算法对板翅式换热器中流体的传热和阻力分别引起的熵产数和(?)耗散数进行了多目标权衡优化。使传热和压降这两个相互矛盾的目标函数同时达到最优,并对帕累托前沿解域进行了LINMAP(多维偏好分析的线性规划)决策,最后对比了两种适值函数的优化结果。结果显示:换热器结构在11个自由度,并满足较小的熵产数或■耗散数的条件下,相比单一目标函数压降最大减少73.65%,成本最多节省1.61%;在相同换热效率下,煨耗散法优化得出的总成本比熵产法减少0.01%。     

层流场协同方程的验证及其性质

在粘性耗散一定的条件下,以热量传递势容耗散取得极值为优化目标,利用变分方法可以导出稳态层流对流换热的场协同方程。场协同方程的意义在于能够求解一定边界条件所对应的最佳速度场,从而实现最优的传热效果。本文采用二维方腔内空气的层流对流换热模型,通过将最佳速度场与其它流场的换热结果进行比较,初步验证了场协同方程的正确性,并对场协同方程的优化过程和原理进行了深入的分析。     

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.     

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.     

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.     

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.     

微、纳米尺度下圆盘(火积)耗散率最小构形优化

基于构形理论, 以(火积)耗散率最小为优化目标, 在微、纳米尺度下对圆盘导热问题进行构形优化, 得到尺寸效应影响下的无量纲当量热阻最小的圆盘构造体最优构形. 结果表明: 在微、纳米尺度下, 尺寸效应影响下的圆盘构造体最优构形与无尺寸效应影响时的圆盘构造体最优构形有明显区别. 存在最佳无量纲高导热材料通道长度使无量纲当量热阻取得最小值; 随着扇形单元体数目的增大, 最小无量纲当量热阻先减小后增大, 存在最佳的扇形单元体数目使得无量纲当量热阻取得双重最小值, 这与常规尺度下圆盘构造体相应的性能特性明显不同. (火积)耗散率最小的圆盘构造体(火积)耗散率比最大温差最小的构造体(火积)耗散率降低了7.31%, 也即圆盘构造体的平均传热温差降低了7.31%. 微、纳米尺度下基于(火积)耗散率最小的圆盘构造体最优构形能够降低圆盘构造体的平均传热温差, 同时有助于提高其整体传热性能. 本文工作有助于进一步拓展(火积)耗散极值原理的应用范围. 关键词： 构形理论 (火积)耗散率最小 微、纳米尺度 广义热力学优化     

Constructal Optimizations of Line-to-Line Vascular Channels with Turbulent Convection Heat Transfer

The multi-scale line-to-line vascular channels (LVCs) widely exist in nature because of their excellent transmission characteristics. In this paper, models of LVCs with turbulent convection heat transfer are established. Based on constructal theory and the entropy generation minimization principle, the constructal optimizations of LVCs with any order are conducted by taking the angles at bifurcations as the optimization variables. The heat flux on the channel wall per unit length is fixed and uniform. The areas occupied by vasculature and the total volumes of channels are fixed. The analytical expressions of the optimal angles, dimensionless total entropy generation rate and entropy generation number (EGN) of LVCs with any order versus dimensionless mass flow rate are obtained, respectively. The results indicate that the dimensionless total entropy generation rate of LVCs with any order can be significantly decreased by optimizing the angles of LVCs, which is significantly more when the order of LVCs is higher. As the dimensionless mass flow rate increases, the optimal angles of LVCs with any order remain unchanged first, then the optimal angles at the entrance (root) increase, and the other optimal angles decrease continuously and finally tend to the respective stable values. The optimal angles of LVCs continue to increase from the entrance to the outlet (crown), i.e., the LVCs with a certain order gradually spread out from the root to the crown. The dimensionless total entropy generation rate and EGN of LVCs first decrease and then increase with the growth of the dimensionless mass flow rate. There is optimal dimensionless mass flow rate, making the dimensionless total entropy generation rate and the EGN reach their respective minimums. The results obtained herein can provide some new theoretical guidelines of thermal design and management for the practical applications of LVCs.     

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.     

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.     

Electroosmosis-Optimized Thermal Model for Peristaltic Transportation of Thermally Radiative Magnetized Liquid with Nonlinear Convection

The present study addresses the heat transfer efficiency and entropy production of electrically conducting kerosene-based liquid led by the combined impact of electroosmosis and peristalsis mechanisms. Effects of nonlinear mixed convection heat transfer, temperature-dependent viscosity, radiative heat flux, electric and magnetic fields, porous medium, heat sink/source, viscous dissipation, and Joule heating are presented. The Debye–Huckel linearization approximation is employed in the electrohydrodynamic problem. Mathematical modeling is conducted within the limitations of δ << 1 and Re → 0. Coupled differential equations after implementing a lubrication approach are numerically solved. The essential characteristics of the production of entropy, the factors influencing it, and the characteristics of heat and fluid in relation to various physical parameters are graphically evaluated by assigning them a growing list of numeric values. This analysis reveals that heat transfer enhances by enhancing nonlinear convection and Joule heating parameters. The irreversibility analysis ensures that the minimization of entropy generation is observed when the parameters of viscosity and radiation are held under control. Fluid velocity can be regulated by adjusting the Helmholtz–Smoluchowski velocity and magnetic field strength.