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. 541