Stagnation point flow

Stagnation point flow represents a fluid flow in the immediate neighborhood of solid surface at which fluid approaching the surface divides into different streams or a counterflowing fluid streams encountered in experiments. Although the fluid is stagnant everywhere on the solid surface due to no-slip condition, the name stagnation point refers to the stagnation points of inviscid Euler solutions.

Hiemenz formulated the problem and calculated the solution numerically in 1911 and subsequently by Leslie Howarth(1934). The flow in the neighborhood of the stagnation point can be modeled by a flow towards an infinite flat plate, even though the whole body is a curved one(locally curvature effects are negligible). Let the plate be in the ${\displaystyle xz}$ plane with ${\displaystyle (x,y)=(0,0)}$ representing the stagnation point. The inviscid stream function ${\displaystyle \psi }$ and velocity ${\displaystyle (u,v)}$ from Potential flow theory are

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