二维热传导方程有限容积法的MATLAB实现

摘要

通过偏微分方程描述了二维无扩散热传导现象.基于有限容积法推导了该方程的离散代数方程组,针对恒定热流强度、恒定温度、对流换热和绝热这四种不同边界条件,分别讨论了热传导代数方程的离散系数和源项.通过MATLAB编程,分析了一维具有均匀厚度无限大板和二维矩形区域的瞬态传热现象.采用图形显示方式使得偏微分方程求解更为直观和容易理解,计算结果证明了有限容积求解方法是可行、稳定的.%Two dimensional diffusionless heat conduction phenomenon has been described on partial differential equation. Based on finite volume method, discretized algebraic equation of partial differential equation has been deduced. Different coefficients and source terms have been discussed under different boundary conditions, which include prescribed heat flux, prescribed temperature, convection and insulation. Transient heat conduction analysis of infinite plate with uniform thickness and two dimensional rectangle region is realized by programming using MAT-LAB. It is useful to make the heat conduction equation more understandable by its solution with graphical expression. Feasibility and stability of numerical method have been demonstrated by running result.