Application of Lie point symmetry and Adomain decomposition techniques to thermal-storage nonlinear diffusion models

Abstract

Classical Lie point symmetry techniques are employed to time dependent nonlinear heat diffusion equations describing thermal energy storage in a medium subjected to a convective heat transfer to the surrounding environment at the boundary through a variable heat transfer coefficient. Exponential temperature-dependent thermal conductivity and heat capacity are assumed. Group classification for the source term is performed and some exciting large symmetry algebras are admitted. It turns out that the principal Lie algebra extends when the source term vanishes and when it is given as the exponential function of temperature. Reduction by one of the independent variables is performed for some realistic choices of the source term. In some case the resulting nonlinear ordinary differential equation with appropriate corresponding conditions are solved using Adomian decomposition method. © 2008 IOP Publishing Ltd.