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The numerical solution of natural convection in unsteady hydromagneticCouette flow of a viscous incompressible electrically conducting fluid between two vertical parallel plates in the presence of thermal radiation is obtained here. The fluid is considered to be a gray, absorbing â€“ emitting but non â€“ scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The dimensionless governing coupled, non â€“ linear boundary layer partial differential equations are solved by an efficient, accurate, and extensively validated and unconditionally stable finite difference scheme of the Crank â€“ Nicolson method. Computations are performed for a wide range of the governing flow parameters, viz., the thermal Grashof number, SolutalGrashof number, Magnetic field parameter (Hartmann number), Prandtl number, Thermal radiation parameter and Schmidt number. The effects of these flow parameters on the velocity and temperatureare shown graphically. Finally, the effects of various parameters on the on the skin â€“ friction coefficient and Rate of heat and mass transferat the wall are prepared with various values of the parameters.These findings are in quantitative agreement with earlier reported studies.

Thermal radiation effect on an unsteady MHD natural convection Couette flow with Heat and mass transfer