Remarks on some unidirectional flows of Maxwell fluids through a rectangular channel filled with porous medium

Abstract

AbstractExact solutions for the dynamics of incompressible fluids showing rate‐type behavior have mostly been found in circumstances where the boundary velocities are given in the body of existing research. This phenomenon results from the constitutive equation of the corresponding extra‐stress tensor, which specifies the natural relationship between velocity and shear stress. In this paper, we focus on a unique observation of the magnetohydrodynamic (MHD) movements of incompressible Maxwell fluids, and the governing equations regulating velocity and shear stress. We focus our analysis on the case of an infinite plate submerged in a porous substance. Within this framework, we do an analytical analysis of a motion issue with a boundary that has a predetermined shear stress. We can easily ascertain the shear stress associated with the motion brought on by a flat plate in order to be more exact. The fluid is subjected to a shear stress by this plate that changes over time. The velocity field from a boundary motion with a predetermined velocity is used to achieve this. We give two graphical representations of individual solutions for the sake of clarity and result verification. Last but not least, we use graphical depiction to highlight how a magnetic field and a porous media affect the fluid's flow resistance. The results show that the flow resistance of the fluid increases in the presence of a porous media and decreases when a magnetic field is present.