UNSTEADY MHD FLOW WITH HEAT TRANSFER IN A DIVERGING CHANNEL P. Y. MHONE, O. D. MAKINDE 1 Applied Mathematics Department, University of Limpopo, Private Bag X1106, Sovenga 0727, South Africa Received April 12, 2006 In this paper, we investigate the combined effects of unsteadiness and a transversely imposed magnetic field on viscous incompressible fluid flow and heat transfer in a slowly varying exponentially diverging symmetrical channel. The nonlinear governing equations are obtained and solved analytically using a petubation technique. Graphical results are presented and discussed quantitatively for various flow characte- ristics like axial velocity, temperature, axial pressure gradient, wall shear stress and Nusselt number. Key words: Flow unsteadiness, diverging channel, magnetic field, conducting fluid. 1. INTRODUCTION MHD flow in diverging channels/ducts has important applications in MHD pumps and generators, liquid metal magnetohydrodynamics and physiological fluid flow. In liquid metal magnetohydrodynamics, magnetic fields are used to levitate samples of liquid metal, to control their shape and to induce internal stirring for the purpose of homogenisation of the final product [6]. Magnetic fields are also used to control the natural convection of semiconductor melts such as silicon or gallium arsenide to improve crystal quality [7]. In physiological fluid flow, Barnothy has reported experiments [4] where the heart rate decreased by exposing biological systems to an external magnetic field. In this line of application is magnetic resonance imaging (MRI), a technique for obtaining high resolution images of various organs within the human body in the presence of a magnetic field. In 1937, Hartmann and Lazarus [11] studied the influence of a transverse uniform magnetic field on the flow of a viscous incompressible electrically conducting fluid between two infinite parallel stationary and insulating plates. Since then, this pioneering work in MHD flow has received much attention and has been extended in numerous ways. Closed form solutions for the velocity fields under different physical effects have been studied in [8] and [16]. A heat 1 Corresponding author: makindeo@ul.ac.za Rom. Journ. Phys., Vol. 51, Nos. 9–10, P. 967–979, Bucharest, 2006