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

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.