In using the von Kármán approximate method for analyzing the turbulent boundary layer over a flat plate, the following velocity and concentration profiles were assumed:

and

The four constants€“α, β, η, and ζ €“ are determined by the appropriate boundary conditions at the surface and at the outer edge of the hydrodynamic and concentration layers. 

a. Determine α, β, η, and ζ, and provide the resulting equations for velocity and concentration profiles. 

b. Upon the application of the von Kármán momentum integral equation, the thickness of the turbulent boundary layer is given by 

Use this relationship, and the solution to von Kármán concentration integral equation for Sc = 1.0, to obtain the following equation for the local mass-transfer coefficient:

k_c = 0.0289 v_ˆž (Re_x) ^-1/5

|Vx a+/ CA-CAs + y7) . 1/7