试算迭代法在求解多层复合材料稳态导热问题中的应用

Application of Trial Iteration Algorithm in Steady-state Heat Conduction of Multilayer Composites

传热学是能源与动力工程专业类的主干专业基础课之一,在能源与动力工程专业的人才培养方案和课程体系中处于极为重要的地位。教学过程中往往会采用实际工程问题对传热学的知识点进行讲解,使学生对知识点的理解更深刻,而在工程实际问题的求解过程中,常常会用到试算法。本文以通过多层平壁及圆筒壁的稳态导热问题为例,在传热学稳态导热部分的教学中以下两种情况就必须采用试算法:(1)在计算多层平壁稳态导热过程中,各层之间的温度未知导致材料的导热系数无法确定时。(2)在求解通过多层筒壁的稳态导热过程中未知量出现在两个不同的对数中时。此外,在案例探讨的基础上,本文还对迭代过程的收敛性及收敛的加速进行了分析。

Heat transfer is one of the main professional basic courses of energy and power engineering specialty.It plays an extremely important role in the talent training program and curriculum system of energy and power engineering specialty.In the teaching process,practical engineering problems are often used to explain the knowledge points of heat transfer,so that students can understand the knowledge points more deeply.In the process of solving practical engineering problems,trial algorithm is often used.Taking the steady-state heat conduction through multi-layer flat wall and cylindrical wall as example,trial algorithm must be used in the following two situations:(1)when the thermal conductivity of materials cannot be determined due to the unknown temperature between layers in the calculation of steady-state heat conduction through multi-layer flat wall.(2)When the unknown quantity appears in two different logarithms in solving the steady-state heat conduction process through the multi-layer cylinder wall.In addition,based on the case study,this paper also analyzes the convergence of the iterative process and the acceleration of convergence.