Transient Heat Diffusion with Temperature-Dependent Conductivity and Time-Dependent Heat Transfer Coefficient

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. Copyright (C) 2008 Raseelo J. Moitsheki.