Time-Dependent MHD Flow of Non-Newtonian Generalized Burgers' Fluid (GBF) Over a Suddenly Moved Plate With Generalized Darcy's Law

Aisha M Alqahtani,Ilyas Khan

doi:10.3389/fphy.2019.00214

Abstract

Time dependent magnetohydrodynamic (MHD) motion of a generalized Burger's fluid (GBF) is investigated in this article. GBF is a highly complicated non-Newtonian fluid and is of highest degree in the class of rate type fluids. GBF is taken electrically conducting by using the restriction of small magnetic Reynolds' number. The Darcy’s law has been used here in its generalized form using the GBF constitutive relation, hence the medium is made porous. The impulsive motion in the fluid is induced due to sudden jerk of the plate. Exact expressions for velocity and as well as for shear stress fields are obtained using the Laplace transform method. The solutions for hydrodynamic fluid (absence of MHD) in a non-porous medium, as well as those for a Newtonian fluid (NF) executing a similar motion are also recovered. Results are sketched in terms of several plots and discussed for embedded parameters. It is found that the Hartmann number and porosity of the medium have strong influence on the velocity and shear stress fields.

Highlights

Most of the fluid problems, or fluid problems with heat transfer or heat and mass transfer together, are computed numerically due to the difficult nature of these problems
Exact analytic solutions are obtained for the dimensionless fluid velocity and non-trivial shear stress exerted by the fluid on the plate
The problem formulation states that an incompressible flow strongly depends on time of a highly non-Newtonian fluid known as generalized Burgers’ fluid (GBF) lies in a semi-infinite porous space y > 0 ; i.e., the fluid is over a rigid plate kept at y = 0

Summary

Introduction

Most of the fluid problems (published literature), or fluid problems with heat transfer or heat and mass transfer together, are computed numerically due to the difficult nature of these problems. Exact analytic solutions are obtained for the dimensionless fluid velocity and non-trivial shear stress exerted by the fluid on the plate.

Objectives

Results

Conclusion