Open Access Research

Dual solutions in MHD flow on a nonlinear porous shrinking sheet in a viscous fluid

Fadzilah M Ali1*, Roslinda Nazar2, Norihan M Arifin1 and Ioan Pop3

Author Affiliations

1 Department of Mathematics & Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Selangor, 43400 UPM, Malaysia

2 School of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, Bangi, Selangor, 43600 UKM, Malaysia

3 Department of Mathematics, Babeş-Bolyai University, Cluj-Napoca, 400084, Romania

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Boundary Value Problems 2013, 2013:32 doi:10.1186/1687-2770-2013-32

Published: 18 February 2013

Abstract

In this paper, the problem of magnetohydrodynamic (MHD) flow of a viscous fluid on a nonlinear porous shrinking sheet is studied. The boundary layer partial differential equations are first transformed into an ordinary differential equation, which is then solved numerically by the shooting method. The features of the flow for various governing parameters are presented and discussed in detail. It is found that dual solutions only exist for positive values of the controlling parameter.

MSC: 34B15, 76D10.

Keywords:
boundary layer; dual solutions; magnetohydrodynamic; shrinking sheet; numerical solution