Numerical simulation of fractional Maxwell fluid flow through Forchheimer medium

Abstract

In this article we have studied the unsteady oscillatory flow of incompressible fluid with heat transfer in a horizontal channel. Maxwell fluid is flowing through a space filled by Forchheimer medium. The Caputo time derivative has been used in the formulation of governing flow problem. A numerical solution has been obtained using Finite Element Method for space variables and Finite Difference Method for fractional time derivatives. A small increase in α gives increase in velocity gradient and also thickness of the momentum boundary layer increases with the increase of α values. For α = 1 velocity boundary layer has a maximum peak. It means fractional parameter controls momentum boundary layer. A smooth profile of temperature gradient decreases with rise of temperature distribution and thickness of the thermal boundary layer rises when increase β values. It observe that β play an important rule in thermal boundary layer. The effects of pertinent physical parameters like Forchheimer parameter, Grashof number and Reynolds number on velocity and temperature distribution are considered and demonstrated through graphs.