Numerical General Solution for Identifying the Position of Point Heat Source for Steady Inverse Heat Conduction Problems

Abstract

Abstract This paper constructs an explicit formula for numerical general solution with position parameters of heat source as variables based on the heat conduction finite element numerical solution in order to convert inverse heat conduction problem with position identification of heat source to multi-variables limit problem. And it establishes linear equations with variables of position parameters of heat source by derivation, and gets the position parameters of heat source. The paper gives out the detailed procedure and formula for numerical general solution method, which includes describing position of point heat source, calculating numerical solutions for homogeneous solution and particular solution of the governing equation for heat conduction problem, constructing numerical general solution, solving the linear equations and getting the position parameters. The paper gives an example of identifying position parameters of heat source for inverse heat conduction problem.