Porous and Magnetic Effects on Modified Stokes’ Problems for Generalized Burgers’ Fluids

Abstract

In this paper, exact analytical expressions are derived for dimensionless steady-state solutions corresponding to the modified Stokes’ problems for incompressible generalized Burgers’ fluids, considering the influence of porous and magnetic effects. Actually, these are the first exact solutions for such motions of these fluids. They can easily be particularized to give similar solutions for Newtonian, second-grade, Maxwell, Oldroyd-B and Burgers’ fluids. It is also proven that MHD motion problems of such fluids between infinite parallel plates can be investigated when shear stress is applied at the boundary. To validate the obtained results, the velocity fields are presented in two distinct forms, and their equivalence is proven through graphical representations. The obtained outcomes are utilized to determine the time required to reach a steady state and to elucidate the impacts of porous and magnetic parameters on the fluid motion. This investigation reveals that the attainment of a steady state occurs later when a porous medium or magnetic field is present. Additionally, the fluid’s flow resistance is augmented in the presence of a magnetic field or through a porous medium. Thus, as was expected, the fluid moves slower through porous media or in the presence of a magnetic field.