Rotating Disk in a Finite Gap

Notice that a choice was made to scale the circumferential velocity using the inlet velocity U. The rotation-rate scale is used in the boundary-condition specification. With these variables the nondimensional equations are 

In these equations, as in the finite-gap stagnation flow, the Reynolds number is based on the gap distance and the inlet velocity, Rcy = p aUL/n, the Prandtl number is evaluated at the inlet conditions, and the nondimensional eigenvalue is given as Ar = ArL2 / pmU2. 

The boundary conditions required to solve the system of equations are 

The surface rotation rate comes into the boundary condition for W at z = 0, 

The eigenvalue Ar must be determined to satisfy the velocity boundary conditions. 

---