Flow Analysis of Third Order Fluid in a Helical Pipe with Circular Cross- Section

Abstract

In this paper, we studied viscous non –Newtonian fluid of third order flowing in a helical pipe with circular cross-section under action of the pressure gradient. Particular consideration is given to fluid flow which can be represented by the equation of state of the form: T=〖μA_1+α〗_1 A_2+α_2 〖A_1〗^2+β_1 A_3+β_2 (A_1 A_2+A_2 A_1 )+β_3 (tr〖A_1〗^2 ) A_1. where α_i (i=1,2),β_i (i=1,2,3) are material moduli and〖 A〗_i(i =1-3) are the first three Rivlin-Ericksen tenser. The cylindrical coordinates have been used to describe the fluid motion. It is found that motion equations are controlled by the dimensionless numbers namely Dean number L, non-Newtonian parameter β, and material moduli (γ_1,γ_3). The motion equations are solved analytically. The analytic solutions of the secondary velocity and the axial velocity are obtained. The effects of each of the dimensionless numbers upon the components of the secondary and the axial velocity are analyzed.