General Solutions for Hydromagnetic Flow of Viscous Fluids between Horizontal Parallel Plates through Porous Medium

Abstract

Analytical solutions for the hydromagnetic flow of incompressible viscous fluids between two infinite horizontal parallel plates, with the lower plate moving in its plane with an arbitrary velocity, are established in the presence of porous effects. For illustration, different motions with technical relevance are examined, and combined magnetic and porous effects, as well as the influence of Reynolds number on the dimensionless velocity and shear stress fields, are graphically depicted and discussed for motions persuaded by a suddenly moved or constantly accelerating plate. The solutions for oscillatory motions are expressed as the sum of permanent (steady state) and transient components, and the necessary time to attain the steady state is established graphically. It was found that this time is lower for motions due to cosine oscillations of the plate. Moreover, the steady state is rather obtained under the effect of a magnetic field or for flows through a porous medium.