Stokes Problem of a Convective Flow Past a Vertical Infinite Plate in a Rotating System in Presence of Variable Magnetic Field

Topics: Fluid dynamics, Magnetic field, Maxwell's equations Pages: 15 (3903 words) Published: August 24, 2013
International Journal of Applied Mathematical Research, 2 (3) (2013) 372-386 ©Science Publishing Corporation www.sciencepubco.com/index.php/IJAMR

Stokes problem of a convective flow past a vertical infinite plate in a rotating system in presence of variable magnetic field Mutua, N.M*, Kinyanjui, M.N, Kwanza, J.K
Taita Taveta University College Jomo Kenyatta University of Agriculture and Technology Jomo Kenyatta University of Agriculture and Technology *Corresponding author E-mail: nicholasmuthama@ttuc.ac.ke

Abstract In this paper, Stokes problem of a free convective flow past a vertical infinite plate in a rotating system in presence of variable magnetic field is investigated. The fluid considered is electrically conducting. The equations governing the flow in this case are non-linear, thus they cannot be solved analytically. The finite difference method (FDM) and computer will be employed in solving the non-linear equations. The effects of the various parameters entering into the problem are discussed extensively and are shown graphically. Discussion of results is done by investigating the parameters: m (the Hall parameter), E (rotational parameter) and M 2 (The Magnetic parameter). If Gr > 0 (=0.5) then this is plate cooling by free convection currents, while when Gr < 0 (=-0.5), this is plate heating by free convection currents. The effect of a variable magnetic field is to retard the fluid motion by affecting the velocity and temperature. Keywords: MHD Stokes problem, Finite difference method, variable magnetic field, Hall current, free convection.

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Introduction

The study of rotating fluids has had considerable progress in the last few decades. For instance, the effect of an applied variable magnetic field on unsteady free convection flow along a vertical plate has been given considerable interest because of its application in the cooling of nuclear reactors or in the study of the structures of stars and planets. Important engineering applications in which the study of MHD flows of rotating fluids with variable magnetic field poises includes: power generators, heat exchangers, reactors and MHD accelerators among other devices. As such, MHD is used to explain certain phenomena in the universe. A study on MHD free convective heat and mass transfer of a heat generating fluid past an impulsively started infinite vertical porous plate with Hall current and radiation absorptions was carried out [1]. [2] analyzed MHD stokes free convection flow past an infinite vertical porous plate subjected to constant heat flux with ion-slip current and radiation absorption. In 2006 [3] studied computational challenges in fluid flow problems, a MHD Stokes problem of convective flow from a vertical infinite plate in a rotating fluid. A study on Hall current effect on Magnetohydrodynamic free convection flow past a semi-infinite vertical plate with mass transfer was done [4]. They discussed the effects of magnetic parameter, Hall parameter and the relative buoyancy force effect between species and thermal diffusion on the velocity, temperature and concentration. The problem of combined heat and mass transfer of an electrically conducting fluid in MHD free convection adjacent to a vertical surface has been analyzed by [5] taking into account the effects of Ohmic heating and viscous dissipation. An investigation of MHD effect on the flow structure and heat transfer characteristics was carried out [6]. This was studied numerically for a liquid-gas annular flow under a transverse magnetic field. The results showed that temperature distribution in the liquid film and the Nusselt number distribution in the angular direction were influenced by the flow structures with the side walls. [7] studied the effects of Ohmic heating and viscous dissipation on unsteady MHD and slip flow over a porous rotating disk with variable properties in the presence of Hall and Ion-slip currents. In 2003 [8] studied the nonlinear dynamics of traveling...
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