SOME MATHEMATICAL INVESTIGATIONS INTO BOUNDARY LAYER FLOW OVER FLAT SURFACES

Abstract

The thesis presents a theoretical investigation into the combined effects of transverse magnetic field and chemical reaction on boundary layer flow contro l. The conservation laws of nature have been emplo yed to derive the basic fluid dynamic equations of continuity, momentum , energy and concentration . The equations modeling the flow problems were expressed in partial derivatives and transformed to ordinary differential equations using similarity variable s. A numerical method based on the fourth order Runge-Kutta integration scheme and the modified version of the Newton-Raphson shooting techniques were used to solve the boundary layer problems. The first problem analyzed the effects of chemical reaction on the magnetoh ydrodynamic (MHD) boundary layer flow over a stretching sheet. The second analyzed the MHD boundary layer flow past a vertical porous plate with Arrhenius chemical reaction and Ohmic heating , whilst the third exam ined the chemically reacting MHD boundary layer flow across a low-heat-resistant sheet moving vertically downwards. The higher order ordinary differential equations were reduced to first order equations and a program written in maple computer software package. Results for skin friction coefficient , heat and mass transfer rates at the surface were obtained . Graphical results were obtained for the velocity, temperature and concentration profiles . The results revealed that the effect of transverse magnetic field in the boundary layer increases the skin friction coefficient which reduces the velocity profiles. Furthermore , the rate of heat and mass transfers in the boundary layer was significantly influenced by the transverse magnetic field and chemical reactions.