大平板瞬态热传导问题的一种新的近似解法

１引言大平板瞬态热传导问题有着广泛的工程应用背景。对于复杂的初边值条件或含内热源问题，以及工程上常见的多层复合平壁对象，分析求解难度很大甚至无法求解。在此类情况下往往采用数值方法。但是单纯的数值解不便于理解影响该问题的各种参数的物理意义。因此，各种近似分析方法得到了发展［１，２］。但在近似精度上，往往难以对整个时间坐标范围都达到较高的精度，这就使得近似解更多地局限于定性分析。此外，对于不同的初边值条件或含内热源问题，近似解的形式相异，降低了解的通用性。增加了求解的工作量。本文提出一种基于矩阵理论…

A NEW APPROXIMATE ANALYTIC METHOD FOR TRANSIENT HEAT-CONDUCTION PROBLEMS IN AN INFINITE PLANE WALL

Approximate analytic solutions are useful when exact analytic solutions are too difficultor impossible to obtain or when the numerical solution of the problem can not be justified. Furthermore, an analytic solution provides a better insight to the physical significanceof various parameters effecting a given problem than a purely nuxnerical solution. Therefore, various approximate methods of analysis have been developed to solve heat-conduction problems, such as the integral method, the Ritz method, the Galerkin method, and so on.However, high accurate approximate solution in large scale is hardly obtained. In this paper a new approximate analytic method for transient heat--conduction problems in an infiniteplane wall was preseoted on the. basis of matrix theory and spline interpolation theory. Casesunder different boundary and initial conditions or heat generation can be conveniently dealtwith in a uniform way with this method. Compared with the exact solutions, this methodcan warrant high accuracy.