An inverse BEM-based heat conduction approach to identify surface temperatures

摘要

The purpose of the inverse problem considered in this study is to solve a steady-state two-dimensional heat conduction problem with ill-posed boundary conditions arising from the determination of unknown surface temperature distributions at an inaccessible surface exposed to convection. Temperature measurements supply the additional information that renders the problem solvable. The measurements are taken from thermocouples placed at the interior of a heat spreader whose backsurface is insulated. It is assumed that the contact resistance between the heater and the solid body is measured and known. A regularized quadratic functional is defined to measure the deviation of computed temperatures from the values under current estimates of the surface temperatures. The inverse problem is solved by minimizing this functional using a parallelized genetic algorithm (PGA) as the optimization algorithm and a two-dimensional multi-region boundary element method (BEM) heat conduction code as the field variable solver.