The roof of a parked refrigerated truck compartment is of composite construction, consisting of a layer of foamed urethane insulation ($$t_2 = 35$$ mm, $$k_i = 0.026$$ W/m $$ \cdot $$ K) sandwiched between aluminum alloy panels ($$t_1 = 5$$ mm, $$k_p = 180$$ W/m $$ \cdot $$ K). The length and width of the roof are $$L = 12$$ m and $$W = 3.5$$ m, respectively, and the temperature of the inner surface is $$T_{s,i} = -10^\circ C$$. Consider conditions for which the truck is not moving, the air temperature is $$T_\infty = 30^\circ C$$, and the solar irradiation is $$G_S = 900$$ W/m$$^2$$.
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For $$ \alpha_S = \varepsilon = 0.6$$, determine the outer surface temperature $$T_{s,o}$$, in $$^\circ C$$, and the heat load, in W, imposed on the refrigeration system. Evaluate air properties at 310 K.
Hint: Assume $$T_{s,o} > T_\infty$$ and $$Ra_L > 10^7$$.
$$T_{s,o}$$ = i 147.97 $$^\circ C$$
$$q$$ = i 4929.22 W
