热传导问题的MATLAB数值计算

分析了应用MATLAB中PDE工具箱解热传导问题的方法和步骤,编制了三个难以用解析方法求解的算例。采用有限元法求解导热偏微分方程,应用PDE工具箱得到数值解。对适合圆柱坐标描述的问题,通过公式变化将其转换为能用PDE工具箱求解的形式。算例表明,用MATLAB对复杂形状和有内热源的非稳态导热问题进行数值计算和图形处理是方便高效的。

Numerical simulation of problems in heat conduction using MATLAB

The method and steps for finding the solutions for problems in heat conduction with the PDE toolbox in MATLAB are described. Three examples difficult to resolve with the analytical method are given. The partial differential equation (PDE) for heat conduction is solved with the finite element method and the PDE toolbox is adopted to obtain the numerical simulation. Problems suitable for description with cylindrical coordinates are transformed into forms that are capable of solution with the PDE toolbox through formula variation. Examples of calculation show that MATLAB is convenient and highly efficient for numerical simulation and graphic processing of complex geometry and non steady state heat conduction problems with internal thermal source.