Explicit reconstruction of space- and time-dependent heat sources with integral transforms

Abstract

This work addresses an explicit methodology based on integral transforms for the inverse problem of reconstructing space and time dependent heat sources. The basic idea is to perform an integral transformation of the heat conduction equation and obtain an explicit expression for the integral transformed heat source in terms of the integral transformed temperatures. Once temperature measurements within the medium are available, they are transformed with the same kernel and readily employed in the derived expressions for the representation of the sought heat source as an eigenfunction expansion. In order to critically illustrate the approach, one- and two-dimensional examples are considered, with different functional forms of the sought heat source and different noise levels in the simulated experimental data.