Answer to Question #256762 in Mechanical Engineering for Jnl

Question

A 6-in bare oxidized steel pipe (6.625 in O.D) carries steam at a temperature of 540°F and is loacted in a large room having wall temperatures of 80 °F. Determine the net radiant-heat exchange in BTU/(hr)(ft) between the pipe and the room, (a) if the surface temperature of the pipe is assumed to be the same as the steam temperature; (b) if the pipe is covered with a single layer of asbestos paper and the temperature of the outer surface of the paper is 530 °F; (c) if the asbestos paper painted with aluminum paint containing 26 percent aluminum and the surface temperature is 530 °F.

Answer 1

a)

$T_1=540$

$T_2=80$

$\epsilon_1=0.9$

$\epsilon_2=0.4$

$\sigma=5.67*10^{-8}$

$Q_{net}=\frac{\sigma(T_1^4-T_2^4)}{\frac{1}{\epsilon_1}+\frac{1}{\epsilon_2}-1}$

$Q_{net}=\frac{5.67*10^{-8}(540^4-80^4)}{\frac{1}{0.9}+\frac{1}{0.4}-1}$

$=1845.54 BTU/hr ft$

b)

$T_1=530$

$T_2=80$

$\epsilon_1=0.9$

$\epsilon_2=0.4$

$\sigma=5.67*10^{-8}$

$Q_{net}=\frac{\sigma(T_1^4-T_2^4)}{\frac{1}{\epsilon_1}+\frac{1}{\epsilon_2}-1}$

$Q_{net}=\frac{5.67*10^{-8}(530^4-80^4)}{\frac{1}{0.9}+\frac{1}{0.4}-1}$

=$1712.52$ BTU/hr ft

c)$T_1=530$

$T_2=80$

$\epsilon_1=0.67$

$\epsilon_2=0.4$

$\sigma=5.67*10^{-8}$

$Q_{net}=\frac{\sigma(T_1^4-T_2^4)}{\frac{1}{\epsilon_1}+\frac{1}{\epsilon_2}-1}$

$Q_{net}=\frac{5.67*10^{-8}(530^4-80^4)}{\frac{1}{0.67}+\frac{1}{0.4}-1}$

$=1494.24$ BTU/hr ft