Effects of Thermal Radiation and Free Convection Currents on the Unsteady Couette Flow Between Two Vertical Parallel Plates with Constant Heat Flux at one Boundary

An exact analysis of the natural convection in unsteady Couette flow of a viscous incompressible
fluid confined between two vertical parallel plates in the presence of thermal radiation is performed. The flow
is induced by means of Couette motion and free convection currents occurring as a result of application of
constant heat flux on the wall with a uniform vertical motion in its own plane while constant temperature on the
stationary wall. The fluid considered here is a gray, absorbing-emitting but non-scattering medium, and the
Rosseland approximation is used to describe the radiative heat flux in the analysis. The dimensionless
governing partial differential equations are solved using Laplace transform technique. Numerical results for the
velocity, the temperature, the skin-friction, the Nusselt number, the volume flow rate and the vertical heat flux
are shown graphically. The effect of different parameters like thermal radiation parameter, Grashof number,
Prandtl number and time are discussed. It is observed that the momentum and thermal boundary layer thickness
decreases owing to an increase in the value of the radiation parameter. An increase in the Grashof number is
found to increase the velocity of air and water and to decrease the skin-friction at the moving plate.