Unsteady MHD flow of a Brinkman type fluid between two side walls perpendicular to an infinite plate

Abstract

In this paper, we calculated the velocity of the unsteady flow of a Brinkman MHD type viscous fluid which is enclosed between two parallel side walls perpendicular to a plate by applying the Fourier transformation. The movement of the fluid is caused by the plate which at time t=0+, exerts shear stress to the fluid. We presented the solutions into two categories i.e. steady state and transient state, which satisfy the given equation as well as boundary and initial conditions. Furthermore, by making h→∞, we recover the solutions obtained in the literature corresponding to the motion over an infinite plate. The effect of the side walls and the time required to reach the steady state are discussed through graphs. Also we checked the effect of different parameters by graphical representations. When Keff and Reynolds number become zero and one respectively, the general solution obtained in this manuscript reduce to special cases in the literature. Keywords: MHD, Brinkman type fluid, Shear stress, Side walls, Exact solution, Fourier transformation