UNSTEADY FREE CONVECTIVE COUETTE FLOW OF HEAT

Abstract

The exact solution of unsteady free convective Couette flow of a viscous incompressible heat generating/ absorbing fluid confined between two vertical parallel plates in a porous medium is performed in this paper. The flow is set up by the buoyancy force arising from the temperature gradient occurring as a result of asymmetric heating of the parallel plates as well as constant motion of one of the plates. The non-dimensional governing equations are solved in closed form by using Laplace-transform technique. Numerical results for velocity, temperature, skin-friction, and Nusselt numbers are presented graphically. The effect of different parameters like Prandtl number (Pr), Grashof number (Gr), heat generation/ absorption parameter (S) and Darcy number (Da) on the flow situations are discussed. The steady state solution of the flow field is derived separately. It is observed that the transient solutions at large time coincides with the steady-state solutions.