International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2533

Full Length Research Paper

On solutions of nonlinear heat diffusion model for thermal energy storage problem

O. D. Makinde1 and R. J. Moitsheki2*
1Faculty of Engineering, Cape Peninsula University of Technology, P. O. Box 652, Cape Town 8000, South Africa. 2School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, WITS 2050, South Africa.
Email: [email protected]

  •  Accepted: 09 December 2009
  •  Published: 31 March 2010


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.