$5-$ In using the von K$$rm$$n approximate method for analyzing the boundary layer over a flat plate,

the following velocity and concentration profiles were assumed: $(20$ points$)$

$V_x=a+b{y}^{\frac{1}{7}}$ and $C_A-C_{As}=A+B{y}^{\frac{1}{7}}$

a$.$ Determine $a,b,A,$ and $B,$ and provide the resulting equations for velocity and concentration

profiles.

b$.$ Obtain the hydrodynamic and concentration boundary layer thicknesses as a function of $x,$

$Re,$ Sc etc.

c$.$ Obtain the expression for local convective mass transfer coefficient.