Three-Dimensional Unsteady Stagnation-Point Flow and Heat Transfer Impinging Obliquely on a Flat Plate with Transpiration

In this study, an exact solution of the Navier-Stokes and energy equations is obtained for the problem of unsteady three-dimensional stagnation point flow and heat transfer of viscous, incompressible fluid on a flat plate. An external flow with strain rate a / (1- at) impinges obliquely on the flat plate when the plate is assumed to be with transpiration. This flow consists of an irrotational stagnation-point flow (Hiemenz) and a tangential component. The relative importance of these two flows is measured by a parameter y. Appropriate similarity transformations are introduced, for the first time, to reduce the governing Navier-Stokes and energy equations to a coupled system of ordinary differential equations. The fourth-order Runge-Kutta method along with a shooting technique is applied to numerically solve the ordinary differential equations. The results obtained from numerical procedure are presented and discussed for a wide range of parameters characterizing the problem. The results achieved reveal that the transpiration rate has a considerable effect on the distributions of velocity components, temperature and pressure. Moreover, it is shown that the main consequence of the free stream obliqueness is to move the stagnation point away from the origin of the coordinate system.