Vol. 7, No. 3, 2012

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ISSN: 1559-3959
Analytical-numerical solution of the inverse problem for the heat conduction equation

Michał Ciałkowski, Andrzej Maćkiewicz, Jan Adam Kołodziej, Uwe Gampe and Andrzej Frąckowiak

Vol. 7 (2012), No. 3, 239–253
Abstract

The solution of the inverse problem for the transient heat transfer equation is considered. The partial differential equation was discretized with respect to the space variable, and a system of ordinary differential equations of first order was obtained. The solution of the system of equations has a wave form. The numerical results obtained from the solution of the inverse problem confirm the effectiveness of the proposed method.

Keywords
inverse problems, stability, matrix exponential, sensitivity analysis, transient heat transfer equation
Milestones
Received: 14 October 2010
Revised: 16 January 2012
Accepted: 3 April 2012
Published: 6 May 2012
Authors
Michał Ciałkowski
Chair of Thermal Engineering
Poznan University of Technology
ul. Jana Pawla II 24
60-965 Poznan
Poland
Andrzej Maćkiewicz
Institute of Mathematics
Poznan University of Technology
ul. Jana Pawla II 24
60-965 Poznan
Poland
Jan Adam Kołodziej
Institute of Applied Mechanics
Poznan University of Technology
ul. Jana Pawla II 24
60-965 Poznan
Poland
Uwe Gampe
Institut für Energietechnik
Technische Universität Dresden
Helmholtzstraße 14
01069 Dresden
Germany
Andrzej Frąckowiak
Chair of Thermal Engineering
Poznan University of Technology
60-965 Poznan
Poland