A Boundary Element Inverse Formulation for Multiple Point Heat Sources Estimation in a Diffusive System: Application to A 2D Experiment

Abstract

This paper deals with an inverse problem that consists of the location estimation of multiple line heat sources placed in a homogeneous diffusive system. In the inverse problem under investigation, the location and strength of the line heat sources are unknown. The estimation procedure is based on a boundary integral formulation using Green functions as weighting functions. The discretized problem is non-linear if the location of the line heat sources is unknown and an iterative procedure has to be applied to find out the location of the sources. The proposed approach is based on the minimization of the distance between the vector of the modeled point heat sources and the vector of the boundary variables. The proposed method is valid for steady and transient case. Some numerical and experimental results are given for a 2D domain.

Keywords:

• Homogeneous Diffusive System
• Green Functions
• 2d Experiment