Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 689074, 11 pages
On Nonperturbative Techniques for Thermal Radiation Effect on Natural Convection past a Vertical Plate Embedded in a Saturated Porous Medium
1Faculty of Engineering, Cape Peninsula University of Technology, P.O. Box 1906, Bellville 7535, South Africa
2School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa
Received 16 March 2008; Revised 30 May 2008; Accepted 24 June 2008
Academic Editor: Carlo Cattani
Copyright © 2008 O. D. Makinde and R. J. Moitsheki. 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.
In this article, the heat transfer characteristics of natural convection about a vertical permeable flat surface embedded in a saturated porous medium are studied by taking into account the thermal radiation effect. The plate is assumed to have a power-law temperature distribution. Similarity variables are employed in order to transform the governing partial differential equations into a nonlinear ordinary differential equation. Both Adomian decomposition method (ADM) and He's variational iteration method (VIM) coupled with Padé approximation technique are implemented to solve the reduced system. Comparisons with previously published works are performed, and excellent agreement between the results is obtained.