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Advances in Mathematical Physics
Volume 2017, Article ID 1658305, 20 pages
Research Article

Heat Transfer in a Porous Radial Fin: Analysis of Numerically Obtained Solutions

DST/NRF Centre of Excellence in the Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg, Wits 2050, South Africa

Correspondence should be addressed to C. Harley;

Received 23 January 2017; Revised 4 May 2017; Accepted 24 May 2017; Published 27 June 2017

Academic Editor: Igor L. Freire

Copyright © 2017 R. Jooma and C. Harley. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A time dependent nonlinear partial differential equation modelling heat transfer in a porous radial fin is considered. The Differential Transformation Method is employed in order to account for the steady state case. These solutions are then used as a means of assessing the validity of the numerical solutions obtained via the Crank-Nicolson finite difference method. In order to engage in the stability of this scheme we conduct a stability and dynamical systems analysis. These provide us with an assessment of the impact of the nonlinear sink terms on the stability of the numerical scheme employed and on the dynamics of the solutions.