Fitted numerical methods to solve di erential models describing unsteady magneto-hydrodynamic ow

Abstract

In this thesis, we consider some nonlinear di erential models that govern unsteady magneto-hydrodynamic convective ow and mass transfer of viscous, incompressible, electrically conducting uid past a porous plate with/without heat sources. The study focusses on the e ect of a combination of a number of physical parameters (e.g., chem- ical reaction, suction, radiation, soret e ect, thermophoresis and radiation absorption) which play vital role in these models. Non-dimensionalization of these models gives us sets of di erential equations. Reliable solutions of such di erential equations can- not be obtained by standard numerical techniques. We therefore resorted to the use of the singular perturbation approaches. To proceed, each of these model problems is discretized in time by using a suitable time-stepping method and then by using a tted operator nite di erence method in spatial direction. The combined methods are then analyzed for stability and convergence. Aiming to study the robustness of the proposed numerical schemes with respect to change in the values of the key parame-ters, we present extensive numerical simulations for each of these models. Finally, we con rm theoretical results through a set of speci c numerical experiments.