Exact solutions for incompressible couette flow with constant temperature and constant heat flux on walls in the presence of radiation

The present paper investigates a closed form solution for the transient free convection flow of a viscous incompressible fluid between two infinite vertical paranel plates in the presence of radiation. The flow is set up due to free convective currents occurring as a result of application of a constant heat flux (CHF) at one wall and a constant temperature on the other wall. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The goveming coupled non-linear partial differential equations have been solved exactly using the Laplace-transform technique. The numerical values obtained from analytical expressions of velocity, temperature, skin-mction and the Nusselt number have been presented graphically to study the behaviour of flow on the momentum and thermal boundary layer.