稳态热传导线源识别反问题的数值通解方法

提出了一种稳态热传导源项识别反问题的求解方法.构造了基于有限元数值解,满足热传导控制方程和边界条件、离散形式、以热源强度为变量的数值通解显式表达,从而将热传导源项识别反问题转化为多元极值问题,能够方便地反演出热源强度.推导了基本计算公式,讨论了热传导源项识别中热源强度的数学建模问题,进行了算法的误差分析.并以模具加热板的热源设计为算例,验证了算法的正确性与实用性.这对进一步研究热源空间分布识别和多维源项识别反问题具有重要意义.

Method of Numerical General Solution for Inverse Line Heat Source Problem in Steady State

A method for identification of source terms for inverse heat conduction problems in steady state was presented. Based on finite element numerical solution, an explicit formula for numerical general solution was constructed, which satisfied the heat conduction governing equations and boundary condition, taking the intensity of heat source as the variable with discrete form. The method converted the heat conduction inverse problem to multi variables limit problem, which made the identification of intensity of heat source easy. The basic computational formula was derived, the mathematics modeling problem of identification of intensity of heat source for inverse heat conduction problems was discussed and error analysis was conducted. Taking the heat source design of mould heating plate as an example, the correctness and practicability of the algorithm was validated, which is of importance for further investigation of identification of space of heat source and multi dimensional source terms for inverse heat conduction problems.