Inverse determination of heat generation sources in two-dimensional homogeneous solids: Application to orthotropic medium

An implementation of the Network Simulation Method for determining the time-dependent heat generation of a source in a 2-D heat conduction problem under first and second type boundary conditions is presented. The thermal properties of the orthotropic solid are temperature-dependent. No prior information of the functional dependence of the time-dependent source was required. Input data for this inverse problem comprise the temperature history (measurements) at a particular location of the boundary. The common iterative least-squares approach, typical for this kind of ill-posed problem, is used in the estimation, while a piecewise continuous function is proposed as an approximate solution for the estimations. An application to estimate the triangular time dependence of the heat source generation, with error-affected measurements, is shown.