二维热传导方程有限容积法MATLAB实现_薛琼.pdf

Computer Engineering and Applications 计算机工程与应用 2012 ，48 （24 ） 197 二维热传导方程有限容积法的MATLAB 实现 1 2 薛 琼 ，肖小峰 1 2 XUE Qiong , XIAO Xiaofeng 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 1.School of Science ，Wuhan University of Technology ，Wuhan 430070 ，China 2.College of Mechanical Engineering and Automation ，Wuhan Textile University ，Wuhan 430073 ，China XUE Qiong, XIAO Xiaofeng. Two dimensional heat conduction equation finite volume method to achieve on MATLAB. Computer Engineering and Applications, 2012, 48 （24 ）：197-200. Abstract ：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. Key words ：heat conduction equation; finite volume method; MATLAB 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。 关键词：热传导方程；有限容积法；MATLAB 文章编号：1002-8331（2012 ）24-0197-04 文献标识码：A 中图分类号：O551 1 引言 文章介绍用MATLAB 实现有限差分方法求解传热问 [6] 热传导广泛存在于各种材料成型过程中，多晶 题 ，本文主要讨论一、二维热传导方程有限容