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.
Funding
This study was financed in part by CAPES—Coordenaçäo de Aperfeiçoamento de Pessoal de Nível Superior—Brasil, Finance Code 001. The authors would also like to thank the other sponsoring agencies, CNPq—Conselho Nacional de Desenvolvimento Científico e Tecnológico, and FAPERJ—Fundaçäo Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro.