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 nonscattering 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 Rd, Received: May 15, 2014 c © 2015 Academic Publications, Ltd. url: www.acadpubl.eu Correspondence author 124 V.M. Job, S.R. Gunakala Grashof number Gr, magnetic parameter H, Prandtl number Pr and Eckert number Ec on the velocity and temperature distributions are investigated. AMS Subject Classification: 76R10, 76W05
Highlights
Magnetohydrodynamics (MHD) is the study of electrically conducting fluids in the presence of an imposed magnetic field
The approximate solutions for the fluid velocity and temperature were computed for different values of the suction parameter, radiation parameter, Grashof number, magnetic parameter, Prandtl number and Eckert number in the cases of impulsive (c = 0) and uniformly accelerated (c = 1) movement of the plate at y = 0
The following values of the above parameters were used in the analysis of the numerical results: suction parameter S = 1, 3, 5; radiation parameter Rd = 0.1, 1, 10; Grashof number Gr = 1, 5, 10; magnetic parameter H = 2, 4, 6; Prandtl number Pr=0.71, 3, 7 and Eckert number Ec = 0.2, 1, 2
Summary
Magnetohydrodynamics (MHD) is the study of electrically conducting fluids in the presence of an imposed magnetic field. The steady flow of an electrically conducting fluid between two infinite parallel stationary plates in the presence of a transverse uniform magnetic field was first studied by Hartmann and Lazarus in 1937 ([1], [18]). Rossow [18] considered the flow of an electrically conducting fluid over a flat plate in the presence of a transverse magnetic field in the cases where the magnetic field is fixed relative to the plate and fixed relative to the fluid. In the case where the magnetic field is fixed relative to the fluid, the fluid flow is retarded by the magnetic field
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