Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 347568, 9 pages
doi:10.1155/2008/347568
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.