Upper Boundary

The upper boundary B5 in Fig 25.1 is having the usual no-slip and impervious conditions for velocity components. i.e., For vorticity (25.2) will apply.

But how to evaluate at the upper wall?

The value of at the upper wall is constant and may be evaluated by integrating the velocity profile at the inlet. Integration may be performed through Simpson's rule to get

(25.3)

If we want to model the condition of no boundary at B5, or, in other words, in y-direction, fluid at infinite extent is assumed, the problem is little more difficult. However, Thoman and Szewczyk (1966) used a treatment which specifies this far-field condition of with and Thus was applied through a Neumann condition at the boundary along B5 as

(25.4)

where B5 is considered at