Eur. Phys. J. Plus (2016) 131: 140
https://doi.org/10.1140/epjp/i2016-16140-5

Regular Article

Analytical solutions for wall slip effects on magnetohydrodynamic oscillatory rotating plate and channel flows in porous media using a fractional Burgers viscoelastic model

¹ Department of Mathematics & Statistics, FBAS, IIU, 44000, Islamabad, Pakistan
² Fluid Mechanics, Spray Research Group, Mechanical and Petroleum Engineering, School of Computing, Science and Engineering, G77, Newton Building, University of Salford, M54WT, Manchester, UK
³ Department of Mathematics, Comsats Institute of Information Technology, 54000, Lahore, Pakistan

^* e-mail: O.A.Beg@salford.ac.uk

Received: 11 February 2016
Accepted: 14 March 2016
Published online: 10 May 2016

Abstract

The theoretical analysis of magnetohydrodynamic (MHD) incompressible flows of a Burgers fluid through a porous medium in a rotating frame of reference is presented. The constitutive model of a Burgers fluid is used based on a fractional calculus formulation. Hydrodynamic slip at the wall (plate) is incorporated and the fractional generalized Darcy model deployed to simulate porous medium drag force effects. Three different cases are considered: namely, the flow induced by a general periodic oscillation at a rigid plate, the periodic flow in a parallel plate channel and, finally, the Poiseuille flow. In all cases the plate(s) boundary(ies) are electrically non-conducting and a small magnetic Reynolds number is assumed, negating magnetic induction effects. The well-posed boundary value problems associated with each case are solved via Fourier transforms. Comparisons are made between the results derived with and without slip conditions. Four special cases are retrieved from the general fractional Burgers model, viz. Newtonian fluid, general Maxwell viscoelastic fluid, generalized Oldroyd-B fluid and the conventional Burgers viscoelastic model. Extensive interpretation of graphical plots is included. We study explicitly the influence of the wall slip on primary and secondary velocity evolution. The model is relevant to MHD rotating energy generators employing rheological working fluids.