Dissertation (MSc Mathematics)The objective of this study is to investigate the effects of chemical reaction on an unsteady hydro - magnetic natural convection heat and mass transfer flow of incompressible, vis-cous, rotating and radiating fluid past an infinite vertical porous flat plate in the presence of heat sink. The Rosseland approximation is used to describe the radiative heat flux for optically thick fluid in the energy equation. The system of non - dimensional partial differential equations governing the flow has been solved numerically by applying the Ritz finite element method. The effects of the various physical parameters describing the flow transport are discussed for Grashof number (Gr > 0), corresponding to cooling of the plate, and Grashof number (Gr < 0), corresponding to heating of the plate. Numerical data for the skin - friction coefficient, Nusselt number and the Sherwood number presented in the tables and then discussed. Keywords: MHD, natural convection, magnetic field, rotating fluid, optically thick fluid.