Effects of the heating process and body dimensions on the estimation of the thermal conductivity components of orthotropic solids

Abstract

In this article, we design the experiment for estimating the thermal conductivity components of an orthotropic medium, with respect to the solid dimensions and to the magnitude of the fluxes that are used to heat the solid. The D-optimum approach is used in the experimental design. By using a transformation that maps the heat conduction equation for an orthotropic medium into the heat conduction equation for an isotropic medium, we show that thermal conductivity components with identical relative accuracies can be estimated by appropriately selecting the experimental variables under picture. The Levenberg-Marquardt method is applied for the solution of the present parameter estimation problem by using simulated temperature measurements.