Some aspects of free convection in electrically conducting fluids: Flow near vertical plates

Free convection in incompressible, electrically conducting fluids in the presence of applied magnetic field has been a subject of active research due to numerous applications. Both numerical and analytical methods have been widely used in the literature to solve the equations governing such convective flows. Among the physically important hydromagnetic flows, there are special types of flows for which the nonlinear magnetofluiddynamical equations simplify to linear ones whose solutions can be obtained in closed form. In this work, we have analysed a specific facet of the transient free convection when the flow of an electrically conducting viscous fluid takes place near a moving vertical surface. It is assumed that this bounding surface is subjected to uniform heat flux. Analytical solutions of the energy and momentum equations, under Boussinesq approximation and an applied magnetic field - either fixed relative to the fluid or to the bounding surface - have been presented for two types of boundary motion. There arises a number of nondimensional parameters characterising various magneto-thermo-fluiddynamical features. The composite effects of these parameters, especially on the developing velocity profiles, have been discussed.