The problem of unsteady, incompressible, laminar electrically conducting flow part a continuously stretching surface is investigated based on a time depended length scale. Similarity conditions for the stretching surface flow velocity and induced magnetic field functions are denied. The governing partial differential equations are first transformed to ordinary ones using similarity transformation. The governing system of equation includes the continuity equation, magnetic continuity equation, Maxwell’s equation, momentum equation and magnetic equations. The resulting similarity equation is then obtained through the use of Maple software. Effects of the unsteadiness parameter A, magnetic force parameter β and the reciprocal of the magnetic prandtl number ë on the velocity and magnetic induction functions are displayed graphically.
The problem of exponential law of steady, incompressible fluid flow in boundary layer and heat transfer are studied in an electrically conducting fluid over a semi-infinite vertical plate assuming the variable thermal conductivity in the presence of a uniform magnetic field. The governing system of equations including the continuity equation, momentum equation and energy equation have been transformed into nonlinear coupled ordinary differential equations using appropriate similarity variables. All the numerical and graphical solutions are obtained through the use of Maple software. The solutions are found to be dependent on three dimensionless parameters including the magnetic field parameter M, thermal conductivity parameter β and Prandtl number Pr. Representative velocity and temperature profiles are presented at various values of the governing parameters. The skin-friction coefficient and the rate of heat transfer are also calculated for different values of the parameters.