孤立系内热传导过程(火积)耗散的解析解  

Analytical solution of the entransy dissipation of heat conduction process in isolated system

作　　者：王焕光[1] 吴迪[1] 饶中浩[1] 

机构地区：[1]中国矿业大学电力工程学院,徐州221116

出　　处：《物理学报》2015年第24期243-252,共10页Acta Physica Sinica

基　　金：中央高校基本科研业务费(批准号:2014QNB07)资助的课题~~

摘　　要：(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.Entransy dissipation and entropy generation both can be used as measures of the irreversibilities of heat transfer problems. Nowadays those who oppose the entransy theory insist that the entransy is needless. In order to illustrate the necessity of the entransy theory, demonstration is made from the viewpoint of effectiveness which is based on the fact that when describing the variation of the irreversibility in the process of heat transfer, the exact analytical solution of the entransy dissipation exists, but that of the entropy generation is difficult to obtain. In this paper, one-dimensional（1D） and multi-dimensional heat conduction models within isolated systems are constructed, among which, the former is to illustrate the deriving process concisely, and the latter is to verify the universal existence of the analytical solution of entransy dissipations. In the 1D model, two bodies with the same geometrical and thermophysical properties but different initial temperatures transfer heat through the contacting surfaces; while in the three-dimensional（3D） model, the initial condition is arbitrary. According to the literature, the primary expression of the total entransy dissipation is derived when substituting the series-typed expression of temperature gradient into the universal calculating equation, which is in the form of a multi integral of a multi series. To reduce such an expression to the simplest form without performing any integral calculation, the orders of the integral and the series are exchanged, and considering the independence between the concerning variables and functions, the multi integral calculation is simplified into the product of several1 D integrals, one relates to time and is easily solved, and the others are dependent on space, of which the dimension is reduced by using the inherent orthogonality of the characteristic functions. The ultimate solutions of the entransy dissipation for all the models are expressed as the summation of a stationary item and a transient item, and the fo

关 键 词：(火积)耗散 不可逆性 (火积)耗散率 解析解 

分 类 号：O551.3[理学—热学与物质分子运动论]