Closed form solutions of cross flows of Casson fluid over a stretching surface

Abstract

The boundary layer flow for the Casson fluid generated by a stretching sheet with cross flows is studied. In this paper we analyzed three different cases of cross flow with streamwise flow. The cross flow in the first case, is generated due to uniform transverse free stream while the stretching surface is at rest. In second case the cross flow is caused by the motion of stretching surface with uniform transverse velocity and the cross flow in third case deals with the transverse shearing motion of the stretching surface. In all the case, possible one parameter solutions appear namely material parameter. The similarity solution for the present model is obtained from the Weidman solution by using some proper transformation. The velocity profiles and the wall shearing parameters for all type of flows are displayed in graphical form. It is depicted that Casson fluid material parameter β causes reduction in stream wise flow, uniform transverse plate motion and transverse shearing motion. Moreover, it is found that the magnitude of longitudinal wall shear stress parameter is greater than or equal to transverse wall shear stress for β.