A thin (1.0-mm-thick) coat of fresh paint has just been sprayed over a 1.5-m by 1.5-m square steel body part, which approximates a flat surface. The paint contains a volatile solvent that initially constitutes 30 wt% of the wet paint. The initial density of the wet paint is 1.5 g/cm³. The freshly painted part is introduced into a drying chamber. Air is blown into the rectangular drying chamber at a volumetric flow rate of 60 m³/min, as shown in the figure below, which has dimensions L = 1.5 m, H = 1.0 m, W = 1.5 m). The temperature of the air stream and the steel body part are both maintained at 27°C, and the total system pressure is 1.0 atm. The molecular weight of the solvent is 78 g/ gmole, the vapor pressure exerted by the solvent at 27°C is 105 mm Hg, and the molecular diffusion coefficient of the solvent vapor in air at 27°C and 1.0 atm is 0.097 cm²/s. 

a. What is the Schmidt number and the average Sherwood number (Sh_L) for the mass-transfer process?

b. What is the estimated solvent evaporation rate from the surface of the whole body part in units of g/min? It may be assumed that convection mass-transfer limits the evaporation rate, and that the concentration of solvent vapor in the bulk gas is finite, but can be approximated as c_A,ˆž ‰ˆ 0.

c. Using the results from part (a), how long will it take for the paint to completely dry? 

d. What are the hydrodynamic (δ) and concentration boundary layer (δ_c) thicknesses at x = L = 1.5 m? How does this compare to H, the height of the drying chamber? 

e. What is the new required air flow rate (m³/min) if the desired solvent mass-transfer rate is 150 g/min?

Transcribed Image Text:

Drying Chamber CA, 000 H = 1.0 m 27°C, 1.0 atm (W = 1.5 m) 60 m³/min air painted steel plate L = 1.5 m heated surface (27°C) gas distributor