Question 12.119: KNOWN: Dimensions and construction of truck roof. Roof inter......

ANALYSIS: (a) To minimize heat transfer through the roof, minimize solar absorption relative to surface emission. Hence, use zinc oxide white for which α_S = 0.16 and ε = 0.93.

(b) Performing an energy balance on the outer surface of the roof, \alpha_S G_S+q_{\text {conv}}^{\prime \prime}- E -q_{\text {cond}}^{\prime \prime}=0, it follows that

\alpha_{ S } G _{ S }+\overline{ h }\left( T _{\infty}- T _{ s , o }\right)=\varepsilon \sigma T _{ s , o }^4+( k / t )\left( T _{ s , o }- T _{ s , i }\right)

where it is assumed that convection is from the air to the roof. With

\operatorname{Re}_{ L }=\frac{ VL }{\nu}=\frac{30  m / s (5  m )}{15 \times 10^{-6}  m ^2 / s }=10^7

\overline{ Nu }_{ L }=0.037 \operatorname{Re}_{ L }^{4 / 5} \operatorname{Pr}^{1 / 3}=0.037\left(10^7\right)^{4 / 5}(0.71)^{1 / 3}=13,141

\overline{ h }=\overline{ Nu }_{ L }( k / L )=13,141\left(0.026  W / m \cdot K / 5  m =68.3  W / m ^2 \cdot K .\right.

Substituting numerical values in the energy balance and solving by trial-and-error, we obtain

T_{s,o} = 295.2 K.

(c) The heat load through the roof is

q =\left( kA _{ s } / t \right)\left( T _{ s , o }- T _{ s , i }\right)=\left(0.05  W / m \cdot K \times 10  m ^2 / 0.025  m \right) 35.2  K =704  W .

(d) Using the IHT First Law Model with the Correlations and Properties Toolpads, the following results are obtained.

The surface temperature and heat load decrease with decreasing V due to a reduction in the convection heat transfer coefficient and hence convection heat transfer from the air.

COMMENTS: The heat load would increase with increasing α_S/ε.