Non-Darcy unsteady MHD Hartmann flow in a porous medium with heat transfer

¹ Department of Engineering Mathematics and Physics, Faculty of Engineering, El-Fayoum University, 63514 El-Fayoum, Egypt
² Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, 12211 Giza, Egypt

^a Corresponding author: mostafaamabdeen@hotmail.com

Received: 17 October 2013
Accepted: 26 June 2015

Abstract

The time varying magneto-hydrodynamic (MHD) Hartmann non-Darcy flow with heat transfer through a porous medium of an electrically conducting, viscous, incompressible fluid between two infinite parallel insulating porous plates is studied. A non-Darcy model that obeys the Forchheimer extension is assumed for the characteristics of the porous medium. A uniform suction and injection as well as an externally applied uniform magnetic field are applied in the direction normal to the plates where a uniform and constant pressure gradient is imposed in the axial direction. The two plates are kept at different but constant temperatures while the Joule and viscous dissipations are considered in the energy equation. The effect of the magnetic field, the Hall current, the porosity of the medium, and the uniform suction and injection on both the velocity and temperature distributions are studied and interesting results are presented for various values of the existing parameters.