利用内部温度史重构表面未知热通量

doi:10.6040/j.issn.1671-9352.0.2019.010

摘要/Abstract

摘要： 讨论了一类利用内部某点不同时刻的温度观测值重构加热器壁表面热通量的热传导反问题。利用分离变量法求解出正问题的解析解,然后将原问题转化为第二类Volterra积分方程,并证明了积分方程解的唯一性。利用一种直接求解法进行数值模拟,数值结果验证了所提出方法的可行性与有效性,且表面热通量的重构效果很好。

关键词: 热通量, 反问题, Volterra积分方程, 唯一性, 数值模拟

Abstract: An inverse heat conduction problem is discussed by using the temperature observed at a certain point in the interior of the heater to recover the surface heat flux of heater wall. The forward problem is solved with the method of variable separation, then the original problem is transformed into Volterra integral equation of the second kind and the uniqueness of the solution of integral equation is proved. Numerical simulation is conducted with the direct solving method. The numerical results are carried out to confirm the feasible and effective of the aforementioned method,and the heat flux is recovered very well.

Key words: heat flux, inverse problem, Volterra integral equation, uniqueness, numerical simulation

中图分类号:

O175.26

任建龙. 利用内部温度史重构表面未知热通量[J]. 《山东大学学报(理学版)》, 2019, 54(9): 83-90.

REN Jian-long. Reconstruction of unknown surface heat flux from an internal temperature history[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(9): 83-90.

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