Please answer a - d, Thanks in advance

3. (30 points) To humidify air before it is fed into a reactor, air is bubbled through a column of water. Assume the air bubbles are spherical with a 1.0 mm radius. Assume the medium is stationary, and diffusion is 1-D radially. The properties and total molar concentration are constant. The diffusion coefficient of water vapor (species A) in air is 0.26 x 10+ m/s at the operating temperature. The air is initially dry when it enters the column. Once the air bubbles enter the column, they are at equilibrium and have a constant surface concentration of water vapor equal to 1.280 mol/m. The residence time (contact time) is designed such that the water vapor concentration at the center of the bubble is 1.260 mol/m?. (a) Start from the governing mass diffusion and write the simplified mass diffusion equation for CA(t,r). (b) What is the mass transfer Biot number if the convection mass transfer coefficient is 3.4 x 10 m/s? (c) Using dimensionless variables (r*, r* and Fom), what are the dimensionless initial and boundary conditions to solve for Ca(t,r) in terms of y*? (d) Use the first term approximation of the exact infinite series solution for this PDE to calculate the column contact time (te) in seconds. (e) What is the mass transfer Fourier number? Was this an appropriate approximation to use