Identification of the Thermal Conductivity and Heat Capacity in Unsteady Nonlinear Heat Conduction Problems Using the Boundary Element Method

Abstract

In this study the inverse problem of the identification of temperature dependent thermal properties of a heat conducting body is investigated. The solution of the corresponding direct problem is obtained using a time marching boundary element method (BEM), which allows, without any need of interpolation and solution domain discretisation, efficient and accurate evaluation of the temperature everywhere inside the space–time dependent domain. Since the inverse problem, which requires the determination of the thermal conductivity and heat capacity from a finite set of temperature measurements taken inside the body, possesses poor uniqueness features, additional information is achieved by assuming that the thermal properties belong to a set of polynomials. Thus the inverse problem reduces to a parameter system estimation problem which is solved using the nonlinear least-squares method. Convergent and stable numerical results are obtained for the finite set of parameters which characterise the thermal properties for various test examples. Once the thermal properties are accurately obtained then the BEM determines automatically the temperature inside the solution domain and the remaining unspecified boundary values and the numerically obtained results show good agreement with the corresponding analytical solutions.