Analytical solutions of Poiseuille flow of second-grade fluid

Abstract

Poiseuille flow are considered as flows of Newtonian fluids through stationary pipes, with applications ranging from the pharmaceutical industries to manufacturing companies. These flows have been extensively studied in several works of literature due their relevance in many spheres of life. However, the Poiseuille flow for non-Newtonian flows have not gained much attention, despite the fact that most fluids are non-Newtonian. Based on this, this study investigates the Poiseuille flow of the second-grade fluid. Second-grade fluid are viscoelastic non-Newtonian fluids that exhibit both shear-thinning and shear-thickening with applications found in several industrial applications such as pharmaceutical, cosmetics and polymer processing. The Poiseuille flow of second-grade fluid is formulated from the underlying Navier-Stokes’ equations and the general assumptions of Poiseuille flow are invoked to reduce the equations to the regular ordinary differential equations. Analytical solution for the flow problem is sought using the method of separation of variables and the results are graphed to show the response of velocity and flow rate to the parameters of the flow. The outcomes show that velocity distribution reduces as the pipe radius increases and second-grade fluid have lower velocity than the Newtonian fluid.

Journal of Naval Architecture and Marine Engineering, 21(1), 2024, P: 67-77