Numerical study of Magneto-Hydrodynamic Three-Dimensional couette flow through a medium in the presence of heat source

In the present article numerical simulation is made using an implicit finite difference scheme on Couette flow of a viscous incompressible electrically conducting fluid between two horizontal parallel porous flat plates in the presence of heat source. A magnetic field is applied normal to the fluid flow. The plate in uniform motion and stationary plate are subjected to constant suction and the transverse sinusoidal injection of the fluid respectively. This type of sinusoidal injection velocity makes the flowthree-dimensional. Obtaining exact solution of thisproblem is very difficult, so the governing non-linear equations with boundary conditions are transformed to ordinary and partial differential equations of zeroth and first order respectively, using perturbation method. Exact solutions correspondingto the zeroth order differential equations are obtained in the case of Thefirst order differential equations in the case of are reduced to ordinary differential equationsusing appropriate substitutions. Then, these resultant equations are transformed to system of equations using implicit-finite difference method, for which simulation is carried out by coding in C-Program. The results obtained for Nusselt number are discussed graphically and compared with previously published work in the absence of heat source parameter. These comparisons have shown a good agreement between the results. From this study, it is observed that the temperature and Nusselt number increasein the presence of heat source parameter.