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圆柱坐标系下非稳态导热问题改进数值求解方法
作者：任玉鸿
来源：《当代化工》2015年第07期
摘要：针对圆柱坐标系下的非稳态导热问题，通常采用集总参数法和格林函数法，但其
具有一定的局限性。为提高求解精度和广度，将圆柱坐标系下的导热方程转化为类直角坐标系下的导热方程，采用有限容积法（FVM）求解计算区域内的温度场，通过加密网格确定网格
无关解，并与两种坐标系下求出的温度对比。计算结果表明，类直角坐标系下得出的温度分布更符合实际情况。
关键词：有限容积法；非稳态导热；类直角坐标；网格无关解
中图分类号：TK 123 文献标识码： A 文章编号： 1671-0460（2015）07-1634-04
Improved Numerical Solving Method of Unsteady
Heat Conduction Problem Under Cylindrical Coordinate System
REN Yu-hong
（China University of Petroleum， Beijing 102249，China）
Abstract： In view of the unsteady heat conduction problem under cylindrical coordinate system， the lumped parameter method and green function method are usually used， but they have some limitations. In this paper，to improve the precision and width， the heat conduction equation under cylindrical coordinate system was turned to that under the approximate rectangular coordinate system， the finite volume method （FVM） was used to solve the temperature field in computing area， grid independent solution was determined by subdividing the mesh， and it was compared with the temperature obtained under two coordinates. The results show that the temperature distribution under the approximate rectangular coordinate system is more in line with the actual situation.
Key words： Finite volume method；Unsteady heat conduction；Approximate rectangular coordinates；Grid independent solution
流动与热现象大量地存在于自然界及各个工程领域中，通过大量阅读近年来流体力学和传热学方面的文献，不难发现，针对描述非稳态导热问题的偏微分方程求解，可分为求解解析解和数值解两种，求解解析解的方法主要有集总参数法、分离变量法、格林函数法和拉普拉斯变