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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 675287, 17 pages
http://dx.doi.org/10.1155/2012/675287
Research Article

Lie Group Analysis of Unsteady Flow and Heat Transfer over a Porous Surface for a Viscous Fluid

1Department of Mechanical Engineering, Celal Bayar University, Muradiye, 45140 Manisa, Turkey
2Applied Mathematics and Computation Center, Celal Bayar University, Muradiye, 45140 Manisa, Turkey

Received 27 September 2012; Accepted 27 October 2012

Academic Editor: Fazal M. Mahomed

Copyright © 2012 M. B. Akgül 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.

Abstract

The problem of a two-dimensional, unsteady flow and a heat transfer of a viscous fluid past a surface in the presence of variable suction/injection is analyzed. The unsteadiness is due to the time dependent free stream flow. The governing equations are derived with the usual boundary layer approximation. Using Lie group theory, a group classification of the equations with respect to the variable free stream flow and suction/injection velocity is performed. Restrictions imposed by the boundary conditions on the symmetries are discussed. Adopting the obtained symmetry groups, governing partial differential equations are converted into ordinary differential equations and then solved numerically. Effects of the dimensionless problem parameters on the velocity and temperature profiles are outlined in the figures.