二维热传导方程有限容积法的MATLAB实现  

Two dimensional heat conduction equation finite volume method to achieve on MATLAB

作　　者：薛琼[1] 肖小峰[2] 

机构地区：[1]武汉理工大学理学院,武汉430070 [2]武汉纺织大学机械工程与自动化学院,武汉430073

出　　处：《计算机工程与应用》2012年第24期197-200,221,共5页Computer Engineering and Applications

基　　金：国家自然科学基金(No.10901067);中央高校基本科研业务费专项资金(No.2011-1a-023)

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 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.

关 键 词：热传导方程 有限容积法 MATLAB 

分 类 号：O551[理学—热学与物质分子运动论]