Author(s)

A. Kassab, E.Divo, M. Chyu & F. Cunha

Abstract

The purpose of the inverse problem considered in this study is to solve a steadystate 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. Temperaturemeasurements 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. 1 Introduction In this paper, we consider the reconstruction of temperature distribution at inaccessible surfaces subjected to convection. An inverse problem method that relies on internal temperature measurements taken close to that surface is formulated in order to resolve the unknown surface temperature distribution using a steady-state approach. A regularized quadratic functional is defined to measure the deviation of computed temperatures at the measuring points from their measured values under

Keywords