On the Rayleigh problem for a Sisko fluid in a rotating frame S. Abelman a, * , T. Hayat b , E. Momoniat a a Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South Africa b Department of Mathematics, Quaid-i-Azam University, 45320 Islamabad, Pakistan article info Keywords: Sisko fluid Unsteady flow Rotating frame Time-dependent magnetic field abstract The unsteady rotating flow of a Sisko fluid bounded by a suddenly moved infinite flat plate is investigated. The fluid is electrically conducting in the presence of a transverse applied time-dependent magnetic field. A highly non-linear differential equation resulting from the balance of momentum and mass, coupled with appropriate boundary and initial conditions is solved numerically. The numerical solutions for different values of the parameters are compared and discussed. Ó 2009 Elsevier Inc. All rights reserved. 1. Introduction Nature is abundant with examples of flows involving non-Newtonian fluids. Being scientifically appealing and challeng- ing, the interest of the investigators in the flows of non-Newtonian fluids has grown considerably during the past few dec- ades. The Navier–Stokes equations are inadequate to describe the flow behavior of such fluids. Due to great diversity in the physical structure of non-Newtonian fluids, there is not a single constitutive equation available in the literature which can describe the properties of all non-Newtonian fluids. Therefore, several models of non-Newtonian fluids have been proposed. Amongst these a particularly simple model namely the Sisko fluid model exists. This fluid model is capable of describing shear thinning and shear thickening phenomena. In general, the governing equations of non-Newtonian fluids are more com- plicated, higher order and subtle in comparison to the Navier–Stokes equations. In many situations the constitutive equa- tions give rise to a flow problem in which the order of the differential equation(s) exceeds the number of available boundary or initial conditions. This issue has been discussed in detail by Rajagopal [1,2], Rajagopal et al. [3], Rajagopal and Kaloni [4] and Rajagopal [5]. The flow of a fluid induced by the sudden motion of a plate from rest, also referred to as the Rayleigh problem [6], is not of fundamental theoretical interest, but it occurs in many applied problems. This problem has been studied extensively for vis- cous fluids in a non-rotating frame. Singh and Sathi [7] studied the Rayleigh problem for rotating flow of a viscous fluid. Re- cently, Tan and Masuoka [8,9] analyzed the Rayleigh problem for second-grade and Oldroyd-B fluids in a non-rotating system. In the present paper, we present a mathematical model for the unsteady rotating flow of a Sisko fluid bounded by a sud- denly moved infinite flat plate. The fluid is electrically conducting and a transverse time-dependent magnetic field is present. Such unified analysis of rotation and magnetic field in fluid flows has promising applications in geophysics and technology. It is well known that a number of astronomical bodies (e.g. the Sun, Earth, Jupiter, magnetic stars, pulsars) possess fluid inte- riors and (at least surface) magnetic fields. Changes in the rotation rate of such objects suggest the possible importance of 0096-3003/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2009.08.060 * Corresponding author. E-mail address: Shirley.Abelman@wits.ac.za (S. Abelman). Applied Mathematics and Computation 215 (2009) 2515–2520 Contents lists available at ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc