一种新的变域传热问题的边界条件  

A Novel Boundary Condition of Heat Transfer Problems with Variable Domain

作　　者：朱聪超[1] 秦世引[1] 杨学实[1] 

机构地区：[1]北京航空航天大学自动化科学与电气工程学院,北京100083

出　　处：《数学的实践与认识》2007年第18期133-140,共8页Mathematics in Practice and Theory

摘　　要：回顾古典热传导方程建立的假设条件的基础上,分析了热层材料由于表面烧蚀而引起的传热区域内部的热漏现象.基于能量守恒原理,利用有限元分析法推导出变域热传导方程,并得到了热漏函数的表达式,提出了变域传热问题边界条件的改进形式.为了检验这种边界条件的合理性,利用Crank-Nicholson法对此数学模型进行空间和时间离散化,并进行了数值仿真求解.仿真结果证实,基于边界条件改进形式的数学模型使计算更方便,结果更符合实际,从而为工程应用提供理论分析的依据.同时,该数学模型也为研究动边界发汗冷却控制问题奠定了理论研究的基础.Heat leakage in the interior of thermal materials on account of ablation is firstly analyzed after reviewing the assumptions for establishing the classical heat transfer equation. Based on the energy conversation law, the heat transfer equation with variable domain is derived by making use of finite element analysis, and a heat leakage function is yielded, based on which an improved boundary condition is obtained. To justify the boundary condition, a series of numerical simulations are implemented employing Crank-Nicholson method to discretize the mathematical model along time and space. The simulation results indicate that the computation is easy and the model agrees with the real process exactly with this improved boundary condition. Meanwhile, this mathematical model provides a basis for the theoretical research on the problems of transpiration cooling control with moving boundary.

关 键 词：烧蚀 可变域 热传导 分布参数 Crank—Nicholson 

分 类 号：O411.1[理学—理论物理]