A flat steel plate of 2.0 m length and 2.0 m width initially contains a very thin coating of light hydrocarbon lubricating oil (species A) 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 of the surface. In the present process, air at 400 K (127°C) and 1.0 atm is blown parallel to the surface at a brisk velocity of 50 m/s. The initial thickness of the liquid lubricating oil coating the surface is 100 microns (0.10 mm). At the steady-state surface temperature of the plate, the lubricating oil is very slightly volatile with a vapor pressure (P_A) of 20 Pa. The liquid density of the lubricating oil (ρ_A.liq) is 900 kg/m³, the latent heat of vaporization of the lubricating oil (∆H_v,A) is 200 J/g, and the average molecular weight of the lubricating oil is 300 g/gmole. At 400 K and 1.0 atm, the molecular diffusion coefficient of the lubricating oil vapor (A) in air (B) is D_AB = 0.065 cm²/s, as estimated by the Fuller–Schettler–Giddings correlation. 

a. At what position down the length of the plate is the flow no longer laminar? Based on the value of the Reynolds number, can the contribution of the laminar boundary layer to the overall mass-transfer rate be neglected? 

b. What is the average mass-transfer coefficient (k_c) over the entire length of the plate? 

c. How long will it take for the lubricating oil to locally evaporate at a distance of at least 1.2 m from the leading edge of the plate? 

d. What is the average heat-transfer coefficient (h) by the Chilton–Colburn analogy? What is the surface temperature (T_s) of the plate? Is it safe to assume that the steady-state temperature of the plate is sufficiently close to the gas stream temperature?