AN INVESTIGATION ON MAGNETOHYDRODYNAMICS FLUID FLOW BETWEEN TWO PARALLEL INFINITE PLATES SUBJECTED TO AN INCLINED MAGNETIC FIELD AND VARYING TEMPERATURES

Abstract

Magnetohydrodynamics (MHD) is the study of electrically conducting fluids in the presence of magnetic fields. This study examined the motion of a viscous, electrically conducting and incompressible fluid flowing steadily between two infinite parallel horizontal plates along one dimension. The plates were subjected to an inclined magnetic field and heated at varying temperatures. The objectives of the study were to determine the effects of variation of temperature of the plates, angle of inclination of magnetic field, Reynold’s number, Hartmann number Prandtl number and pressure gradient on the velocity of the flow of the fluid. The equations governing the fluid motion were used to develop the model; these are a combination of Maxwell’s equation of magnetism and Navier-Strokes equation of fluid dynamics, continuity equation, momentum equation and energy equation. The model governing the flow was developed with appropriate boundary conditions imposed, simplified using the boundary layer approximations, non-dimensionalized and solved analytically. The solutions were simulated and with the use of mathematical software MATLAB; the results for various values of varying temperatures (from 200C to 500C), the angle of inclination of magnetic field (from 6 c  to 2 c  ), Reynolds number (from 0.2 to 0.8), Hartmann number (from 2.4 to 3.0), Pressure gradient (from 2.0 to 8.0) and Prandtl number (from 0.07 to 0.22) were obtained and presented graphically. The objectives of the study were to determine the effect of the following variables on the flow velocity: the angle of inclination of magnetic field, change in temperature, Prandtl number and Reynold’s number. The results obtained from the study showed that when the angle of inclination of magnetic field is reduced, the flow velocity increases; increase in velocity of the fluid also results from increase in temperature of the fluid when the plates are heated; increase in Hartmann number retards the velocity of the flow; the velocity will increase when the pressure gradient increases; increase in Reynolds number leads to increase in velocity while increase in Prandtl number reduces the temperature of the fluid and as a result retards the velocity of the flow.