Stagnation point flow—a free boundary value problem formulation

Abstract

The two dimensional laminar flow of a visous, incompressible fluid near a stagnation point is considered. The equations of motion governing the flow are reformulated as a free boundary value problem. The latter is solved numerically using the shooting method with the invocation of Newton's iterative scheme for finding the missing initial condition and the location of the free boundary. Much improved values of the skin-friction at the plate are obtained. Further it is shown that the improvement of the accuracy is dependent on the value of the free boundary. The formulation also eliminates the possibility of obtaining the extraneous solutions which do not satisfy the asymptotic boundary condition.

Keywords:

• Stagnation point flow
• free boundary value problem
• shooting method
• Runge-Kutla method
• Adam-Moulton method

C.R. Categories:

• 65L10