On the Momentum-Integral Method of Solution for the Laminar Entrance-Flow Problems

抄録

For the laminar entrance-flow problem, the present author developed previously a new momentum-integral method of solution in which the independent parameter [numerical formula], where h is the half gap width and U=[u]_y=h, was introduced together with the usual Pohlhausen's parameter [numerical formula]. The method was applied to solve the problem of the radially outward entrance-flow between two parallel discs, and it was confirmed that the theory might describe satisfactorily the complicated characteristics of the fluid flow which involved separation and reattachment phenomena. In the present paper, the author's method is further applied to analyze the most fundamental case, the two-dimensional flow between flat plates, and is compared with prior methods of solution. The result of the author's analysis agrees very well throughout the whole flow field with the exact solution given by a difference method : faults inherent in many other momentum-integral methods proposed to date are eliminated from the present method. It can be emphasized from the present research that, in order to describe satisfactorily the laminar entrance-flow phenomenon in terms of a momentum-integral method, it is most indispensable to introduce Γ as an unknown variable to be solved.