Consider a full developed film of water of constant thickness $\backslash$delta flowing steadily under the action of gravity

over an inclined plate. At some location along the plate, the liquid film is exposed to a mixture of air and

ammonia $($species A$)$ vapor over a length L$,$ as sketched below. The objective is to absorb some ammonia

from the gas phase into water. At the inlet, the water film contains a very small amount of ammonia resulting

in a mass fraction of $\backslash$omega A$,$in$.$ On the liquid side of the gas$/$liquid interface, the mass fraction of ammonia is

$\backslash$omega A$,$s $>\backslash$omega A$,$in$.$ Use constant properties, and assume that the gas phase offers negligible resistance to the motion

of the liquid. The entire system is essentially isothermal.

$($a$)$ Keeping in mind that mass diffusion in liquids is very slow; determine the concentration profile of

ammonia in the liquid sheet.

$($b$)$ Determine the mass flux of ammonia at the interface, and then the total amount of ammonia

absorbed into water over a length L for a film width of W$.$