Chapter 7, Problem 7.20P

The roof of a refrigerated truck compartment is of composite construction, consisting of a layer of foamed urethane insulation $\left(t_2=50\text{mm,}{k}_i=0.026\text{W/m}\cdot \text{K}\right)$ sandwiched between aluminum alloy panels $\left(t_1=5\text{mm,}{k}_p=180\text{W/m}\cdot \text{K}\right).$ The length and width of the roof are $L=10\text{m}$ and $W=-3.5\text{m,}$ respectively, and the temperature of the inner surface is $T_{s,i}=-10°\text{C}\text{.}$ Consider conditions for which the truck is moving at a speed of V = 105 km/h, the air temperature is $T_{\infty }=32°\text{C,}$ and the solar irradiation is $G_S=750{\text{W/m}}^{\text{2}}.$ Turbulent flow may be assumed over the entire length of the roof.

1. For equivalent values of the solar absorptivity and the emissivity of the outer surface $\left({\alpha }_s=\epsilon =0.5\right),$ estimate the average temperature $T_{s,o}$ of the outer surface. What is the corresponding heat load impused on the refrigeration system?
2. A special finish $\left({\alpha }_s=0.15,\epsilon =0.8\right)$ may be applied to the outer surface. What effect would such an application have on the surface temperature and the heat load?
3. If, with ${\alpha }_s=\epsilon =0.5,$ the roof is not insulated $\left(t_2=0\right),$ what are the corresponding values of the surface temperature and the heat load?