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.

Question

Accepted Answer

From Table 11.4, case 2,[latex]F_{A}[/latex] = 1, A is the area of the pipe, and [latex]F_{e}[/latex] is the emissivity of the steel pipe.

Table 11.4, case 2:

Surfaces between Which Radiation Is Being Interchanged	Area, A	[latex]F_{A}[/latex]	[latex]F_{e}[/latex]
Completely enclosed body, small compared with enclosing body. (Subscript 1 refers to enclosed body.)	[latex]A_{1}[/latex]	1	[latex]ε_{1}[/latex]

From Appendix 2, for oxidized steel, ε = 0.79. Therefore,

[latex]\begin{aligned}\dot{Q}=0.173 imes 10^{-8} imes 0.79 imes 1 imes \frac{\pi(3.5)}{12} & imes5\left[(120+460)^{4} ight.\&\left.-(70+460)^{4} ight]=214.5 Btu / h\end{aligned}[/latex]

It should be noted that Equation 11.31 contains a [latex]T_{1}^{4}-T_{2}^{4}[/latex] term, not a [latex]\left(T_{1}-T_{2} ight)^{4}[/latex] term, a very common mistake.

[latex]\dot{Q}_{r}=\sigma F_{e} F_{A} A\left(T_{1}^{4}-T_{2}^{4} ight)[/latex] (11.31)

Question 11.21: A bare steel pipe of outside diameter 3.50 in. runs through ...

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