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Journal of Applied Mathematics
Volume 2012, Article ID 648675, 18 pages
Research Article

Lie Group Analysis of Natural Convective Flow from a Convectively Heated Upward Facing Radiating Permeable Horizontal Plate in Porous Media Filled with Nanofluid

1School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia
2Department of Engineering Sciences, Pakistan Navy Engineering College, National University of Sciences and Technology, Karachi 75350, Pakistan

Received 9 February 2012; Revised 19 March 2012; Accepted 20 March 2012

Academic Editor: Srinivasan Natesan

Copyright © 2012 Md. Jashim Uddin et al. 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.


Two-dimensional, steady, laminar and incompressible natural convective flow of a nanofluid over a connectively heated permeable upward facing radiating horizontal plate in porous medium is studied numerically. The present model incorporates Brownian motion and thermophoresis effects. The similarity transformations for the governing equations are developed by Lie group analysis. The transformed equations are solved numerically by Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. Effects of the governing parameters on the dimensionless velocity, temperature and nanoparticle volume fraction as well as on the dimensionless rate of heat and mass transfer are presented graphically and the results are compared with the published data for special cases. Good agreement is found between numerical results of the present paper and published results. It is found that Lewis number, Brownian motion and convective heat transfer parameters increase the heat and mass transfer rates whilst thermophoresis decreases both heat and mass transfer rates.