Meccanica 39: 345–355, 2004. © 2004 Kluwer Academic Publishers. Printed in the Netherlands. Some Steady MHD Flows of the Second Order Fluid T. HAYAT ∗ , M. I. HAMEED, S. ASGHAR 1 and A. M. SIDDIQUI 2 Department of Mathematics, Quaid-i-Azam University 45320, Islamabad, Pakistan; 1 COMSATS Institute of Information Technology, Abbottabad, Pakistan; 2 Department of Mathematics, Pennsylvania State University, York Campus, 1031 Edgecomb Avenue, York,PA 17403, USA (Received: 29 November 1999; accepted in revised form: 31 October 2003) Abstract. The exact analytic solutions of two problems of a second order fluid in presence of a uniform transverse magnetic field are investigated. The governing equation is of fourth order ordinary differential equation and is solved using perturbation method. In the first problem we discuss the flow of a second order fluid due to non- coaxial rotations of a porous disk and a fluid at infinity. In second problem the flow of a second order conducting fluid between two infinite plates rotating about the same axis is investigated, with suction or blowing along the axial direction. For second order conducting fluid it is observed that asymptotic solution exists for the velocity both in the case of suction and blowing. Key words: Suction flow, Second order fluids, Perturbation method, Non-coaxial rotation, Steady MHD flows. 1. Introduction The flow due to a rotating disk in a fluid which at infinity is rotating rigidly has been con- sidered by a number of workers [1]. The possibility of an exact solution of the Navier– Stokes equations for this type of flow has been implied by Berker [2]. He considered the flow between two disks rotating with the same angular velocity. Later on, Coirier [3] discussed the flow due to the disk and a fluid at infinity rotating non-coaxially at slightly different angular velocities. Exact solutions of the three dimensional Navier–Stokes equations are ob- tained by Erdogan [4, 5]. Murthy and Ram [6] have considered the magnetohydrodynamic flow and heat transfer due to eccentric rotations of a porous disk and the fluid at infinity. Sarpkaya [7] discussed the steady laminar flow of a uniformly conducting non-Newtonian fluid between two parallel planes. The flows of Newtonian and non-Newtonian fluids between parallel disks rotating about a common axis has been reviewed by Rajagopal [8]. In another paper, Rajagopal [9] studied the flow of a Newtonian fluid between two porous parallel plates rotating about the same axis. The classical problem of flow due to a rotating disk has been generalized in several manners to include diverse effects. Thus the heat transfer aspects have been considered by Millsaps and Polhausen [10], Sparrow and Grag [11] and others. Recently the effect of a magnetic field, when the fluid is electrically conducting, has been taken into account in two separate investigations by Kumar et al. [12] and Watanabe and Oyana [13]. There is yet another area in which the flow due to a rotating porous disk and a fluid a infinity has specially drawn the attention of the researchers. It is the fluid dynamics of the so called non-Newtonian fluids: the fluids for which the commonly accepted assumption of a ∗ Author for correspondence: Fax: +92-51-2275341; e-mail: l_pensy@hotmail.com