A flat steel plate is 2.0 m length and 2.0 m width initially contains a very thin coating of lubricating oil used in a manufacturing process. An engineer is considering the feasibility of using hot forced air convection to remove the lubricating oil from the surface as an alternative to using harmful solvents to rinse the lubricating oil off the surface. In the present process, air at 386 K and 1.0 atm is blown parallel to the surface at a velocity of 50 m/s. At this velocity, the location on the plate where laminar flow ends is 0.097 m from the leading edge.
The initial thickness of the liquid lubricating oil coating the surface is 10:0mm (1 × 10-5 m). AT 386 K, the viscosity of air is 2:23 × 10-5kg/m s, and the mass density of air is 0.917 kg/m3. At 386 K, the lubricating oil is slightly volatile with a vapor pressure of 0.20 Pa, and the liquid density of the lubricating oil is 1900 kg/m3. At 386 K and 1.0 atm, the molecular diffusion coefficient of the lubricating oil vapor in air, DAB, is 0.040 cm2 /s.
(a) What is the Schmidt number for the mass transfer of lubricating oil vapor in air?
(b) What is the average mass-transfer coefficient over the entire length of the plate?
(c) Determine the mass-transfer coefficient at 1.2 m downstream from the leading edge of the plate.