Generalization of the Thwaites integral method for laminar boundary-layers due to moving continuous surfaces

In this study, attention has been given towards the development of an approximate method for the boundary-layer flows involving no pressure gradient (the flows due to moving continuous surfaces in a still fluid). The integral method devised in this study is an extension of the existing Thwaites integral method; applicable to boundary-layer flows over the stationary surfaces of finite length (which, in general, involve the pressure gradient because of the presence of external potential flow, except for the case of uniform external flow). The existing Thwaites integral method does not give an acceptable approximation for the flows over moving continuous surfaces in a quiescent fluid, involving no pressure gradient. Therefore, the extension of the existing Thwaites integral method, proposed in this study, will make it applicable to the flows due to moving continuous surfaces in a stationary fluid (involving no pressure gradient), also. With the combination of the two, the existing, and the extended Thwaites integral method, the generalized Thwaites integral method is proposed, applicable to the boundary-layer flows whether involving a pressure gradient or not.