Question

Two large parallel planes having emissivities of 0.4 and 0.6 are maintained at temperatures of 846 K and 288 K, respectively. A radiation shield having an emissivity of 0.2 on both sides is placed between the two planes. Calculate (a) the heat-transfer rate per unit area if the shield were not present, (b) the heat-transfer rate per unit area with the shield present. If the emissivity of the shield is increased by 50%, how many shields are needed for the heat transfer rate per unit area as compared with the obtained results from (b)?

Answer 1

Solution;

(a)

$\frac{\dot{Q}_{12}}{A}=\frac{\sigma(T_1^4-T_2^4)}{\frac{1}{\epsilon_1}+\frac{1}{\epsilon_2}-1}$

$\frac{\dot{Q}_{12}}{A}=\frac{(5.67×10^{-8}×(846^4-288^4)}{\frac{1}{0.4}+\frac{1}{0.6}-1}$

$\frac{\dot Q_{12}}{A}=9048.78W/m^2$