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GATE 2020 CH – Question 58

Mass Transfer · Fick's laws, molecular diffusion and mass transfer coefficients · 2 marks · Numerical answer

A fully developed falling water film on an impermeable wall is 1 m high and 10⁻⁴ m thick. Its thickness-averaged velocity is 0.01 m/s. Nonreactive gas is absorbed throughout; thickness-averaged concentration is $\overline C_A(y)=C_{Ai}(1-e^{-30y})$, with y in metres downward from the top. Cₐᵢ is constant solubility, inlet water is pure, width is much greater than thickness, concentration is width-independent and evaporation is negligible. Find height-averaged liquid-side mass-transfer coefficient in mm/s, to three decimal places.

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Correct answer: 0.025 to 0.035

Explanation

For a differential film strip, solute gain is $w\delta\bar v\,d\overline C_A=k_Lw(C_{Ai}-\overline C_A)dy$. The profile gives $d\overline C_A/dy=30C_{Ai}e^{-30y}$ and driving difference $C_{Ai}e^{-30y}$. Cancelling these factors yields constant $k_L=30\delta\bar v=30(10^{-4})(0.01)=3\times10^{-5}$ m/s. Its height average is the same, 0.030 mm/s.

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