Incompressible Viscoelastic Flow of a Generalised Oldroyed-B Fluid through Porous Medium between Two Infinite Parallel Plates in a Rotating System

Abstract

ABSTRACT Incompressible viscous fluid flow through a porous medium between two infinite parallel plates with moving upper plate in a rotating system has been studied here. The exact solution of the governing equation for the velocity field has been obtained by using Laplace and finite Fourier sine transformations in series form in terms of Mittage-Leffler function. It can be found that the fluid velocity decreases with the increasing values of fractional calculus parameter α and the permeability of the porous medium K. It can be also observed that the fluid velocity increases with the higher values of the viscosity of the porous medium. The dependence of the velocity field on fractional calculus parameters as well as material parameters has been illustrated graphically. Keywords Caputo operator; Generalised Oldroyed-B fluid; Laplace transformation: Finite Fourier sine transformation; porous medium . 1. INTRODUCTION In fluid dynamics the study of non-Newtonian fluid flow through porous medium has applications in different fields such as purification of crude oil, petroleum industry, polymer technology, electrostatic precipitation, irrigation, sanitary engineering, food industry etc. The flow behavior of non-Newtonian fluids cannot be described by Newtonian fluid model. For this reason various types of constitutive equations have been proposed and Oldroyed-B fluid model is one of them that has some success in describing non-Newtonian fluids. In recent years fractional calculus approach is found to be quite flexible in describing the viscoelastic fluids. In the approach the time derivative of integer order in the constitutive equation is replaced by Caputo fractional calculus operator. Charyulu and Ram [1] have investigated laminar flow of an incompressible micro polar fluid between two parallel plates with porous lining. Fetecau