Two parameter scaling group for unsteady convective magnetohydrodynamic flow

A mathematical model for two dimensional unsteady magneto-convective flows with heat and mass transfer in the presence of a time dependent magnetic field is presented. The system of partial differential equations governing the transport problem is converted to a system of ordinary differential equations via two parameter scaling group transformations, before being solved using an implicit finite difference method. Computed results for non-dimensional velocity, temperature and concentration distributions as well as skin friction factor, local Nusselt number and Sherwood number are discussed for various values of the controlling parameters (Prandtl number, Schmidt number, Richardson number, magnetic field and buoyancy ratio). It is found that the magnetic field causes an increase in the rate of the heat and mass transfers. The buoyancy ratio increases the heat transfer rates and decreases the mass transfer rates.