Question 11.21: A bare steel pipe of outside diameter 3.50 in. runs through ...
A bare steel pipe of outside diameter 3.50 in. runs through a room whose walls are at 70°F. Determine the heat loss by radiation from 5 ft. of the pipe if its outside temperature is 120°F.
From Table 11.4, case 2,F_{A} = 1, A is the area of the pipe, and F_{e} is the emissivity of the steel pipe.
Table 11.4, case 2:
| Surfaces between Which Radiation Is Being Interchanged | Area, A | F_{A} | F_{e} |
| Completely enclosed body, small compared with enclosing body. (Subscript 1 refers to enclosed body.) | A_{1} | 1 | ε_{1} |
From Appendix 2, for oxidized steel, ε = 0.79. Therefore,
\begin{aligned}\dot{Q}=0.173 \times 10^{-8} \times 0.79 \times 1 \times \frac{\pi(3.5)}{12} & \times5\left[(120+460)^{4}\right.\\&\left.-(70+460)^{4}\right]=214.5 Btu / h\end{aligned}
It should be noted that Equation 11.31 contains a T_{1}^{4}-T_{2}^{4} term, not a \left(T_{1}-T_{2}\right)^{4} term, a very common mistake.
\dot{Q}_{r}=\sigma F_{e} F_{A} A\left(T_{1}^{4}-T_{2}^{4}\right) (11.31)
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