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

Abstract

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Time-dependent magnetohydrodynamic (MHD) motion of a generalized Burgers' 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. 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 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.

Keywords

• time-dependent flow
• MHD
• generalized Burgers' fluid
• generalized Darcy's law
• Laplace transform