Homotopy Perturbation Method for Flow of a Third-grade Fluid Through a Vertical Concentric Annulus

Abstract

Abstract This paper considers a theoretical study on steady incompressible flow of third grade fluid in helical screw rheometer (HSR) with zero flight angles (a vertical concentric annulus). The developed second order non linear coupled differential equations are solved by homotopy perturbation method. Expressions for torsional and longitudinal velocity components are derived. The effects of non-Newtonian parameter β on the velocity profiles are also presented through graphs. It is observed that the velocity profiles are strongly depending upon the Non-Newtonian parameter β.