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

摘要

A theoretical analysis of magnetohydrodynamic (MHD) incompressible flows of Burger's fluid through a porous medium in a rotating frame of reference is presented. The constitutive model of a Burger's fluid is used based on a fractional calculus formulation. Hydrodynamic slip at the wall (plate) is incorporated and a fractional generalized Darcy model deployed to simulate porous medium drag force effects. Three different cases are considered- namely, flow induced by a general periodic oscillation at a rigid plate, periodic flow in a parallel plate channel and finally Poiseuille flow. In all cases the plate (s) boundary (ies) are electrically-non-conducting and small magnetic Reynolds 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. 4 special cases are retrieved from the general fractional Burgers model, viz Newtonian fluid, general Maxwell viscoelastic fluid, generalized Oldroyd-B fluid and the conventional Burger’s viscoelastic model. Extensive interpretation of graphical plots is included. We study explicitly the influence on wall slip on primary and secondary velocity evolution. The model is relevant to MHD rotating energy generators employing rheological working fluids.