Torsional flow of third grade fluid using modified homotopy perturbation method

This paper considers the steady flow of an incompressible third grade fluid between two vertical concentric rotating cylinders of infinite lengths. Modified Homotopy perturbation method is used to reduce the volume of tedious calculations involved to solve second order nonlinear differential equation. Special cases with one cylinder, inner or outer at rest (bounded domain case), and fluid flow at a rotating cylinder (unbounded domain case) are obtained. The effect of β, the non-dimensional number related to the material constants, ω, rotation of the cylinder and R, the ratio between radii of outer and inner cylinders, on the velocity profile are discussed and are shown graphically.