Exact Solutions for an MHD Generalized Burgers fluid: Stokes' Second Problem

TL;DR

This paper derives exact analytical solutions for the MHD flow of a generalized Burgers fluid under Stokes' second problem, analyzing magnetic field effects on velocity and boundary layer thickness.

Contribution

It provides the first exact solutions for MHD generalized Burgers fluid flow in the Stokes' second problem with modified Darcy's law.

Findings

Magnetic field reduces velocity magnitude.

Magnetic field decreases boundary layer thickness.

Velocity and stress depend on multiple parameters.

Abstract

This paper offers the exact analytical solutions for the magnetohydrodynamic (MHD) flow of an incompressible generalized Burgers fluid corresponding to the second problem of Stokes in the presence of the transverse magnetic field. Modified Darcy's law has been taken into account. The expression for the velocity field and associated tangential stress, presented as a sum of the steady-state and transient solutions, are obtained by means of the integral transforms. Moreover, several figures are plotted to investigate the effects of various emerging parameters on the velocity field. The obtained results show that the magnitude of the velocity and boundary layer thickness significantly reduce in the presence of magnetic field.