Slip Effect on Free Convection Flow of Second Grade Fluids With Ramped Wall Temperature

The unsteady free convection flow of an incompressible second-grade fluid near a vertical plate is considered on the assumption that the fluid moves with a slip at the heated wall. The relative velocity of the fluid is assumed to be proportional to the shear rate at the wall. The exact expressions for temperature and velocity are determined by means of the Laplace transform with respect to the temporal variable t. The velocity fields corresponding to both the slip and no-slip conditions for second-grade and Newtonian fluids are obtained in the general case where the vertical plate is moved with the velocity Uof(t). Two particular cases, namely translation with a constant velocity and sinusoidal oscillations of the wall are discussed. Some physical aspects of the two flows are illustrated graphically. The influence of the slip coefficient on the velocity is also studied.