STUDY OF STEADY AND UNSTEADY VISCOUS INCOMPRESSIBLE MHD FLUID FLOW

Abstract

An analytical study of laminar steady, viscous, incompressible Couette fluid flow between two infinite parallel plates under the influence of transverse magnetic field is studied. The resulting governing partial differential equation was solved analytically by Sumudu Transform for the linear differential equation with constant coefficients. The Couette flow velocity profiles for various Hartmann number and various angles of inclinations were presented graphically. The results showed that, increase in magnetic field strength and magnetic inclinations resulted into decrease in velocity profiles. The motion of two dimensional steady laminar Poiseuille flow of a viscous MHD incompressible fluid between two parallel porous plates under the influence of uniform transverse magnetic field was also examined. The resulting coupled differential equations were solved numerically using finite difference approach. The numerical computation of the generated linearized system of equations was achieved with the aid of MATLAB application software. The results depicted graphically showed that, an increase in Hartmann number led to decrease in Poiseuille flow velocity distribution which was as a result of Lorentz force which offered resistance opposing the fluid motion. Unsteady MHD Couette laminar flow of viscous incompressible fluid between two parallel porous plates in presence of uniform magnetic field was also investigated. The upper and lower plates were maintained at two different but constant temperatures. A sudden uniform and a constant pressure gradient, an external uniform magnetic field was applied in the positive y - direction. The flow was subjected to a uniform suction from above and uniform injection from below at t ≥ 0. The resulting linear differential equations were solved numerically using finite difference approach. The Crank-Nicolson implicit method was used at two successive time levels so as to determine the velocity and temperature distributions for different values of the parameters M ,S and α. The results showed that, when suction was suppressed, increasing the porosity parameter had no marked effect on velocity distribution but increasing the suction resulted into a decrease in the velocity which reached the steady state monotonically with time due to convection of the fluid from regions in the lower half of the centre of channel. It was also reported that, increasing suction decreased the temperature at the centre of the channel for all values of t due to influence of convection in the pumping of the fluid from the lower cold region of the channel towards the centre.