A segment of a tube with 2-cm inner diameter and a length of 10.00 m has its inner surface covered by a chemical that dissolves in water and releases CO 2 , resulting in a constant CO 2 mass fraction...

A segment of a tube with 2-cm inner diameter and a length of 10.00 m has its inner surface covered by a chemical that dissolves in water and releases CO₂, resulting in a constant CO₂
mass fraction at the wall surface. Pure water with fully developed velocity enters the tube segment with a mean velocity of 0.04 m/s. The mean mass fraction of CO₂
in water at the exit from the tube segment is 5 × 10⁻⁴. The entire system is at 300 K temperature.

(a) Find the mass fraction of CO₂
at the surface by using an appropriate mass transfer correlation. Note that you should search a standard heat transfer textbook, find an empirical correlation that accounts for the entrance effect, and develop its equivalent mass transfer version.

(b) If the boundary condition was a constant heat flux, what would be the required CO₂
mass flux at the surface?

(c) For part (b), calculate the mass transfer coefficient and the mass fraction of CO₂
at the wall in the middle of the tube.