Calculate the net radiant-heat-transfer rate if the two surfaces in Problem 11.18 are black and are connected by a refractory surface with an area of 500 m2. A1 is at 555 K and A2 is at 278 K. What is the refractory surface temperature?
GIVEN
• Rectangular surfaces A1 and A2 connected by a refractory surface A3
• A1 is parallel to and centered 5 m above A2
• Dimensions of A1 = 1 m × 20 m
• A2 is 20 m2
• A3 is 500 m2
• Temperature of A1 (T1) = 555 K
• Temperature of A2 (T2) = 278 K
• A1 and A2 are black
FIND
(a) The net radiating heat transfer rate (q1)
(b) The refractory surface temperature (T3)
SKETCH
PROPERTIES AND CONSTANTS
the Stephan-Boltzmann constant (?) = 5.67 × 10–8 W/(m2 K4)
F12 = 0.427
For the black surfaces A1 and A2
?1 = ?2 = 0 and ?1 = ?2 = 1
J1 = Eb1 and J2 = Eb2 Since q3 = 0
Since q3 = 0, J3 = G3
Since neither A1 nor A2 can see themselves, F11 = F22 = 0
With these simplifications reduces to
The shape factors are calculated below
Solving part (b) first
(a) The rate of heat loss from A1 is
As a check
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