A modified method for determining the surface heat flux of IHCP

作者：Qian Z^*; Fu C L; Xiong X T

来源：Inverse Problems in Science and Engineering, 2007, 15(3): 249-265.

DOI：10.1080/17415970600725128

• ill-posed problem
• inverse heat conduction
• regularization

We consider the determination of the surface heat flux of a body from a measured temperature history at a fixed location inside the body. Mathematically, it is formulated as a problem for the one-dimensional heat equation in a quarter plane with data given along the line x = 1, and the gradient of the solution is determined for 0 <= x < 1. This problem is of practical interest in some engineering contexts and it is severely ill-posed, in the sense that the solution (if it exists) does not depend continuously on the data. In this article, we employ a fourth-order modified method to solve the problem. Some stability estimates are given. Numerical examples show that the modified method works very well.

• 单位
  兰州大学