International Journal of Pure and Applied Mathematics Volume 99 No. 2 2015, 123-143 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v99i2.1 P A ijpam.eu FINITE ELEMENT ANALYSIS OF UNSTEADY RADIATIVE MHD NATURAL CONVECTION COUETTE FLOW BETWEEN PERMEABLE PLATES WITH VISCOUS AND JOULE DISSIPATION Victor M. Job 1 , Sreedhara Rao Gunakala 2 § 1,2 Department of Mathematics and Statistics The University of West Indies St. Augustine, TRINIDAD AND TOBAGO Abstract: This paper discusses the unsteady magnetohydrodynamic free convection Couette flow of an incompressible viscous fluid between two infinite vertical permeable plates in the presence of thermal radiation with an expo- nentially decaying pressure gradient. A uniform magnetic field that is perpen- dicular to the plates, and uniform suction and injection through the plates are applied. The magnetic field lines are assumed to be fixed relative to the moving plate. The momentum equation takes buoyancy forces into consideration, while the energy equation considers thermal radiation effects and viscous and Joule dissipations. The fluid is considered to be a gray absorbing-emitting but non- scattering medium in the optically thick limit. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The coupled pair of non-linear partial differential equations is discretized using the Galerkin finite element method. This yields a system of non-linear algebraic equations which is solved using an iterative method to obtain the velocity and tempera- ture distributions. The effects of suction parameter S, radiation parameter R d , Received: May 15, 2014 c  2015 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author