Project ForgeA vertically falling water film (height 1.0m, thickness 10⁻⁴m, average velocity 0.01 m/s) absorbs a non-reactive gas over its entire height. The film-thickness-averaged gas concentration is C̄Ay=CAt(1−e^(−30y)), y in meters from the top (pure water enters at y=0). The liquid-side mass transfer coefficient (mm/s), averaged over the height, is (round off to 3 decimal places)
Explanation
A differential mass balance gives d/dy[v̄δ·C̄Ay]=NA(y)=kL(y)(CAt−C̄Ay). Differentiating the given profile: v̄δ·CAt·30e^(−30y)=kL(y)·CAt·e^(−30y), so kL(y)=30v̄δ — a CONSTANT, independent of y. kL=30×0.01×10⁻⁴=3×10⁻⁵ m/s=0.030 mm/s.
Source: GATE CH 2020 (2020)
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