IJPAM: Volume 99, No. 2 (2015)

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 exponentially decaying pressure gradient. A uniform magnetic field that is perpendicular 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 temperature distributions. The effects of suction parameter S, radiation parameter $R_{d}$, Grashof number Gr, magnetic parameter H, Prandtl number Pr and Eckert number $E_{c}$ on the velocity and temperature distributions are investigated.

Received: May 15, 2014

AMS Subject Classification: 76R10, 76W05

Key Words and Phrases: MHD, natural convection, thermal radiation, couette flow, permeable plates, finite element method

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DOI: 10.12732/ijpam.v99i2.1 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 99
Issue: 2
Pages: 123 - 143


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