Unsteady MHD flow of a fractional second grade fluid in a channel passing through a porous medium subject to a time-dependent motion of the bottom plate

Abstract

The velocity of an unsteady flow of a viscous fluid of the second-grade MHD-type enclosed between two parallel side walls perpendicular to a plate was obtained by applying the integral transformation. The fluid is required to move by the plate, which over time [Formula: see text] subjected the fluid to shear stress. The solutions satisfy the given equation as well as the boundary and initial conditions, and they were separated into two types: steady state and transient state. Furthermore, through [Formula: see text], we are able to recover the results found in the literature for motion across an infinite plate. Graphs depict the effect of the side walls and the time it takes to reach the steady state. The solutions are shown in graphs and discussed physically to examine the impact of different flow parameters. It is found that the fluid velocity decreases with an increasing fractional parameter [Formula: see text] and second-grade parameter [Formula: see text]. Also, it is noticed that the fluid velocity decreases with increasing values of Reynolds number and effective permeability. Numerous industrial products, including honey, paints, varnishes, coffee, chocolate and jelly, use this type of fluid flow concept.