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Journal of Porous Media
Facteur d'impact: 1.49 Facteur d'impact sur 5 ans: 1.159 SJR: 0.43 SNIP: 0.671 CiteScore™: 1.58

ISSN Imprimer: 1091-028X
ISSN En ligne: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v12.i8.70
pages 811-819

Solutions Using Symmetry Methods and Conservation Laws for Viscous Flow Through a Porous Medium Inside a Deformable Channel

Saleem Ashgar
Department of Mathematical Sciences, COMSATS Institute of Information Technology, Islamabad, Pakistan
M. Mahmood
Department of Mathematics, COMSATS Institute of Information, Technology, H-8, Islamabad, Pakistan; and School of Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa
A. H. Kara
School of Mathematics and Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa


We present here some definitions and methods for dealing with the reduction of a system of partial differential equations (p.d.e.'s) to a system of ordinary differential equations (o.d.e.'s) on the basis of the underlying symmetry structure, conservation laws, and a combination of these. The method is used to reduce a complex system to an easy-to-handle, second-order o.d.e., independent of restrictions of any physical parameter. As a particular example, we construct a solution of system modeling a viscous flow through a porous medium inside a deformable porous channel.