Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 347568, 9 pages
doi:10.1155/2008/347568
Research Article
Transient Heat Diffusion with Temperature-Dependent Conductivity
and Time-Dependent Heat Transfer Coefficient
School of Computational and Applied Mathematics, University of the Witwatersrand, Private bag 3, Wits 2050, South Africa
Received 8 April 2008; Revised 5 June 2008; Accepted 18 July 2008
Academic Editor: Yuri V. Mikhlin
Copyright © 2008 Raseelo J. Moitsheki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Lie point symmetry analysis is performed for an unsteady nonlinear heat
diffusion problem modeling thermal energy storage in a medium with a
temperature-dependent power law thermal conductivity and subjected to a
convective heat transfer to the surrounding environment at the boundary
through a variable heat transfer coefficient. Large symmetry groups are admitted
even for special choices of the constants appearing in the governing
equation. We construct one-dimensional optimal systems for the admitted
Lie algebras. Following symmetry reductions, we construct invariant solutions.