中文摘要：

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。

英文摘要：

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 de- duced. Different coefficients and source terms have been discussed under different boundary conditions, which in- clude 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 expres- sion. Feasibility and stability of numerical method have been demonstrated by running result.