Abstract

An analysis is performed for an unsteady nonlinear heat diffusion problems modeling thermal energy storage in a medium with power law temperature-dependent heat capacity, thermal conductivity and heat source term and subjected to a convective heat transfer to the surrounding environment at the boundary through a variable heat transfer coefficient. Lie group theory is applied to determine symmetry reductions of the governing nonlinear partial differential equation (PDE) with the boundary conditions. The resulting nonlinear ordinary differential equation (ODE) with appropriate corresponding boundary conditions is solved using Adomian decomposition method (ADM) coupled with Padé approximation technique. The effects of material parameters on the thermal decay in the system are shown graphically and discussed quantitatively.

Key words: Unsteady heat diffusion, thermal energy storage, group method, decomposition method, nonlinear problem.