Pergamon
Energy Convers. Mgmt Vol. 39, No. 5/6, pp. 541-548, 1998
© 1997ElsevierScienceLtd. All rights reserved
Printed in Great Britain
PII: S0196-8904(96)00107-0 0196-8904/98 $19.00+ 0.00
MHD STOKES PROBLEM FOR A VERTICAL INFINITE
PLATE IN A DISSIPATIVE ROTATING FLUID WITH HALL
CURRENT
M. KINYANJUI, N. CHATURVEDIt and S. M. UPPAL
Department of Mathematics, Jkuat, P.O. Box 62000, Nairobi
(Received 19 December 1995)
Abstract--Natural convectionin the hydromagneticflowof a viscousincompressiblerotating fluid system,
taking into account viscous dissipative heat and Hall current, has been studied. The coupled nonlinear
equations are solved by a finite differencemethod. Velocityand temperature profilesare shown graphically
and the results discussed in terms of the Hall parameter m, rotation parameter E and Gr (Grashof number,
Gr > 0 cooling of the plate by free convection currents). © 1997 Elsevier Science Ltd.
Hall effects Rotation effect Free convection Magnetic field Dissipative heat
INTRODUCTION
The study of the general theory of rotating fluids has an important application in comic and
geophysical sciences [1]. The steady and unsteady Ekman layers of an incompressible fluid have
been investigated as basic boundary layers in a rotating fluid appearing in oceanic, atmospheric
and cosmic fluid dynamics and solar physics or geophysical problems. The Ekman layer on a
horizontal plate has been studied by Batchelor [2]. Gupta [3] solved the Stokes problem for a
rotating porous flat plate in the presence of a uniform transverse magnetic field. Mazumder [4]
studied the flow and heat transfer in the hydromagnetic Ekman layer on a porous plate with Hall
current. A similar problem without Hall current has been solved by Gupta and Soundalgekar [5].
Stokes[6] and Chaturvedi[13] studied the flow of an incompressible viscous fluid past an
impulsively started infinite horizontal plate, and MHD flow past an infinite plate with constant
and variable suction. Stewartson [7] studied analytically the flow of an incompressible viscous fluid
past an impulsively started semi-infinite horizontal plate. The Stokes problem, taking into account
the free convection current was solved by Soundalgekar [8].
Rossow [9] studied the same problem under a transversely applied magnetic field, whereas
Soundalgekar et al. [10] solved the corresponding problem for a vertical impulsively started infinite
plate. The same problem was solved by Kinyanjui et al. [12], taking into account the effect of Hall
current. However, in practical applications, another situation arises where the Hall current (in the
presence of a strong magnetic field) and viscous dissipative heat play an important role.
Hence, the main objective of the present investigation is to study the effects of Hall current in
the Stokes problem for a vertical infinite plate in a rotating fluid system, taking into account viscous
dissipative heat.
MATHEMATICAL ANALYSIS
The flow of a viscous incompressible MHD free-convection heat generating fluid past an
impulsively started infinite plate has been considered. Assume that a strong magnetic field of
tDepartment of Mathematics, University of Nairobi, P.O. Box 30197, Nairobi, Kenya.
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