Couette and Poiseuille flows of an Oldroyd 6-constant fluid with magnetic field

Abstract

In this paper, we develop a set of differential equations describing the steady flow of an Oldroyd 6-constant magnetohydrodynamic fluid. The fluid is electrically conducting in the presence of a uniform transverse magnetic field. The developed non-linear differential equation takes into account the effect of the material constants and the applied magnetic field. We presented the solution for three types of steady flows, namely, (i) Couette flow (ii) Poiseuille flow and (iii) generalized Couette flow.Homotopy analysis method (HAM) is used to solve the non-linear differential equation analytically. It is found from the present analysis that for steady flow the obtained solutions are strongly dependent on the material constants (non-Newtonian parameters) which is different from the model of Oldroyd 3-constant fluid. Numerical solutions are also given and compared with the solutions by HAM.  2004 Elsevier Inc. All rights reserved.

Numerical treatment and Global Error Estimation of a MHD Flows of an Oldroyd 6-Constant Nano-Fluid through a non-Darcy Porous medium with Heat and Mass Transfer

“…Baris [21] investigated the steady flow of an Oldroyd 6-constant fluid between intersecting planes using the series expansion method. Hayat et al [23] studied the Couette and Poiseuille flows of an Oldroyd 6-constant fluid with magnetic field by using the Homotopy analysis method. Hayat et al [25] studied the steady flow of a magneto-hydrodynamic Oldroyd 6-constant fluid by the motion of an infinite plate using the Homotopy analysis method.…”

Thin film flow of an Oldroyd 6-constant fluid over a moving belt: an analytic approximate solution

“…The MHD solutions for a Newtonian fluid as well as those corresponding to the Oldroyd 3 and 6-constant fluids, a Maxwell fluid and a second grade one, appear as limiting cases of the obtained solutions. Hayat et al [7] and Wang et al [8] considered Couette and Poiseuille flows of an Oldroyd 6-constant fluid with magnetic field. Sajid et al [9] investigated the problem of wire coating by withdrawal from a bath of MHD Oldroyd 8-constant fluid, using homotopy analysis method, and Khan et al [10] also discussed an Oldroyd 8-constant MHD fluid but between coaxial cylinders subject to partial slip at the boundaries.…”

Thin film flow of non‐Newtonian MHD fluid on a vertically moving belt

“…Baris [5] considered the steady flow of an Oldroyd 6-constant fluid between intersecting planes and studied the problem using 1410 M. HAMEED AND R. ELLAHI the series expansion method. Hayat et al [6] used Oldroyd 6-constant fluid model and investigated the effect of magnetic field on the Couette and the Poiseuille flows of a visco-elastic fluid. Rana et al [7] investigated Hall effects for an Oldroyd 6-constant fluid between concentric cylinders.…”