Dissertation (MSc Mathematics)This dissertation investigates the magnetic field and Soret influence on MHD unsteady free convection radiating and reacting fluid past an exponentially accelerated inclined infinite porous plate of uniform permeability with variable temperature and concentration numerically. In this model the fluid is considered a gray, emitting absorbing radiation but a non-scattering medium and a magnetic field of intensity B0 is imposed in the perpendicular direction to the plate. The governing equations of the model are transformed into dimensionless form by adopting suitable non-dimensional variables and parameters, then the resulting coupled non-linear PDE´s are solved by the finite difference method. The influence of flow control parameters on the velocity, concentration and temperature fields are illustrated graphically whilst numerical results of the skin friction, Sherwood and Nusselt numbers are displayed in Tables. It is found that permeability of the medium, thermal and mass buoyancy force improve the fluid velocity whilst the magnetic field and inclination angle have reverse effect. The fluid velocity and temperature tends to decrease with an increment in radiation parameter whilst reverse trend is noticed in case of Nusselt number. The Soret effect is to elevate the fluid velocity and concentration whilst chemical reaction rate has reverse impact,and these parameters have opposite effect on the Sherwood number. The progression of time escalates the fluid velocity, temperature and concentration whilst it has a reverse effect on the skin friction, Sherwood and Nusselt numbers. This flow model has various industrial applications in the field of food processing, polymer production, design of fins, steel rolling, etc.