three-dimensional unsteady stagnation-point flow andheat transfer impinging obliquely on a flat platewith transpiration

In this study, an exact solution of the navier-stokes and energy equations is obtained for the problem ofunsteady three-dimensional stagnation point flow and heat transfer of viscous, incompressible fluid on a flatplate. an external flow with strain rate a / (1- at) impinges obliquely on the flat plate when the plate isassumed to be with transpiration. this flow consists of an irrotational stagnation-point flow (hiemenz) and atangential component. the relative importance of these two flows is measured by a parameter y. appropriatesimilarity 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 characterizingthe problem. the results achieved reveal that the transpiration rate has a considerable effect on thedistributions of velocity components, temperature and pressure. moreover, it is shown that the mainconsequence of the free stream obliqueness is to move the stagnation point away from the origin of thecoordinate system.