Consider a vertically falling film of water over an impermeable wall. The film is in contact with a static pool of an non-reactive pure gas. The gas diffuses into the water film over the entire height of the falling film. The height of the film is $1.0 \: m$, and its thickness is $10^{-4} \:m$. The velocity of water, averaged over the film thickness, is $0.01 \: m \: s^{-1}$. The gas concentration (in $kg \: m^{-3}$), averaged over the film thickness is $$\overline{C_{A_y}}=C_{A_i}(1-e^{-30y})$$ where $y$ is the vertical position in meters measured from the top of the wall.
In addition, use the following data and assumptions
- The flow is fully developed
- The width of the film is much larger than the thickness of the film, and the dissolved gas concentration is invariant over this width.
- The solubility of the gas in water, $C_{A_i}$, is constant
- pure water enters at $y=0$
- The evaporation of water is negligible.
The mass transfer coefficient on the liquid side (in $mm \: s^{-1}$), averaged over the entire height of the falling film is __________ (round off to $3$ decimal places)