Chapter 13, Problem 13.86P

Consider two very large metal parallel plates. The top plate is at a temperature $T_t=400\text{K}$ while the bottom plate is at $T_b=300\text{K}$ . The desired net radiation heat flux between the two plates is $q^{″}=300{\text{W/m}}^2$ .

(a) If the two surfaces have the same radiative properties, show that the required surface emissivity is $\epsilon =0.5$ .
(b) Meal surfaces at relatively low temperatures tend to have emissivities much less than 0.5 (see Table A.11). An engineer proposes to apply a checker pattern, similar to that of Problem 12.132, onto each of the metal surfaces so that half of each surface is characterized by the low emissivity of the bare metal and the other half is covered with the high-emissivity paint. If the average of the high and low emissivities is 0.5, will the net radiative heat flux between the surfaces be the desired value?