Species b cannot be absorbed in liquid a and the boundary

Question

1) For the forced convection mass transfer example given in class, begin with the simplified governing equation derived in class along with the boundary conditions, and derive the solution given for this problem

The problem can be approximated as: V_max (∂C_A/∂Z) = D_AB(∂C_A/∂x₂)

Boundary conditions:

At  z=0, C_{A= 0}

At x=0, C_A = C_AB

At x →∞ C_A = 0

This problem becomes a semi-infinite problem that can be solved with the similarity variable.

The solution is:

Which is the complimentary function.

Now please show step by step how to get the above solutions.

Consider the evaporation of liquid A into a column containing a binary gas mixture of A and B. Species B cannot be absorbed in liquid A and the boundary conditions. Show how the ratio of the molar-average velocity to the species velocity of A. click,, varies with the mole fraction of species A.