The wedge-shaped cavity shown in the accompanying sketch consists of two long strips joined along one edge. Surface 1 is 1-m-wide, has an emittance of 0.4, and has a temperature of 1000 K. The other wall has a temperature of 600 K. Assuming gray diffuse processes and uniform flux distribution, calculate the rate of energy loss from surface 1 and 2 per meter length.

Question

GIVEN

• The wedge shaped cavity shown above

• Width of A1 (W1) = 1 m

• Emittance of A1 (?1) = 0.4

• Temperature of A1 (T1) = 1000 K

• Temperature of A2 (T2) = 600 K

• A2 is black

FIND

• The rate of energy loss from A1 and A2 per meter length (q1/L and q2/L)

ASSUMPTIONS

• Enclosure temperature (Te) = 0 K

• Gray diffuse processes

• Uniform flux distribution

PROPERTIES AND CONSTANTS

the Stephan-Boltzmann constant (?) = 5.67 × 10–8 W/(m2 K4)

Answer 1

Width of A3 (W3) = 1 m

Width of A2 (W2) =

The crossed-string methods can be used to calculate F12.





Since neither A1 nor A2 can see itself, F11 = F22 = 0

Since A2 is black: ?2 = 0 and ?2 = 1



for A1



Solving for G1







for A2





Since ?1 = 1 – ?1