Determination Of The Effects Of Applying Variable Pressure Gradient To A Magnetohydrodynamic Fluid Flowing Between Plates With Inclined Magnetic Field

ABSTRACT

In this study the effects of applying variable pressure gradient to a MHD fluid flowing between two plates in an inclined magnetic field was carried out. It involved an unsteady hydromagnetic fluid flowing through two plates where the upper plate was porous and moving with a constant velocity in a direction that is contrary to fluid flow direction. The lower plate was non-porous and stationary. In the past years, research studies relating to MHD fluid flow through plates have been done. The information obtained from these studies have been implemented in various industrial systems for instance designing of electromagnetic meters and MHD pumps. However these research studies have been carried out when the pressure gradient was a constant and none when the pressure gradient was a variable, hence the reason why we carried out this investigation. The objective of this project was to determine the effect of applying variable pressure gradient to a MHD flow in inclined magnetic field. Also the outcome of varying Hartmann number, Suction number, Reynolds number and Eckert number on velocity and temperature profiles have been determined. The governing equations used to carry out analysis were continuity equation, Navier stokes equations, electromagnetic equations and energy equations. These equations were then non-dimensionalised. The resulting equations were non-linear thus were solved using the finite difference method. MATLAB software was then inculcated in the resulting equations which were expressed in finite difference form and resulting solutions illustrated graphically. The results obtained showed that the application of a variable pressure gradient in the presence of an inclined magnetic field resulted to an increase in velocity of the fluid and a decrease in the fluid temperature, increasing the suction number decreased the fluid velocity while the temperature increased; increasing Reynold’s number yielded to a reduction in both velocity and temperature profiles; increase in Hartmann number resulted to decrease in velocity and an increase in temperature. These velocity and thermal profiles are important in the dyeing industries and modelling of systems that help in cooling of automobile moving parts.