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

Raseelo J. Moitsheki

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

Recommended by Yuri V. Mikhlin

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.