Open Access Research

Lie group analysis and similarity solutions for hydro-magnetic Maxwell fluid through a porous medium

Khaled S Mekheimer1*, Mostafa F El-Sabbagh2 and Rabea E Abo-Elkhair1

Author Affiliations

1 Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City 11448, Cairo, Egypt

2 Mathematics Department, Faculty of Science, Minia University, Minia 61111, Egypt

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Boundary Value Problems 2012, 2012:15 doi:10.1186/1687-2770-2012-15

Published: 13 February 2012

Abstract

The equations of two dimensional incompressible fluid flow for hydro-magnetic Maxwell fluid through a porous medium have been studied. Lie group analysis has been employed and the group invariant solutions are obtained. Solutions corresponding to translational and rotational symmetries are obtained. A boundary value problem for the translational symmetry is investigated and the results are also sketched graphically. The effects of physical parameters have been noticed.

MSC 2011: 53C11; 76S05.

Keywords:
lie point symmetries; similarity solutions; Maxwell fluid; porous medium; MHD