You are tasked with designing the cooling system for a refrigerated tractor trailer. The walls and roof of the trailer have a layer of insulation (???????????????? = 0.025 ????⁄???????? ,????ℎ???????????? = 50 ????????) sandwiched between two metal panels (???????? = 100 ????⁄???????? ,????ℎ???? = 5 ????????). The length and width of the roof are L = 10 m and W = 3.5 m, respectively, and the temperature of the inner surface is ????????,???????? = −10℃. Consider conditions for which the truck is moving at a speed of ???? = 100 ????????/ℎ????, the air temperature is ????∞ = 32℃, and the solar irradiation on the roof is ???????? = 750 ????/????2 . (50 points)

a. At what position will the flow transition from laminar to turbulent? Based on this result, what assumptions can you make?

b. You want to calculate the heat loss through the roof of the trailer. For equivalent values of the solar absorptivity and the emissivity of the outer surface (???????? = ???? = 0.5) estimate the average temperature of the outer surface of the trailer roof. What is the corresponding heat load imposed on the refrigeration system due to heat gain through the roof?

c. A special finish (???????????????????????? = 0.15, ???? = 0.85) is applied to the outer surface of the roof. What effect does such an application have on the surface temperature and heat gain through the roof?