Chapter 13, Problem 13.118P

The lower side of a 400-mm-diameter disk is heated by an electric furnace, while the upper side is exposed to quiescent, ambient air and surroundings at 300 K. The radiant furnace (negligible convection) is of circular construction with the bottom surface $\left({\epsilon }_1=0.6\right)$ and cylindrical side surface $\left({\epsilon }_2=1.0\right)$ maintained at $T_1=T_2=500\text{K}$ . The surface of the disk facing the radiant furnace is black $\left({\epsilon }_{d,1}=1.0\right)$ while the upper surface has an emissivity of ${\epsilon }_{d,2}=0.8$ . Assume the plate and furnace surfaces to be diffuse and gray.

(a) Determine the net heat transfer rate to the disk, $q_{\text{net},d}$ when $T_d=400\text{K}$ .
(b) Plot $q_{\text{net},d}$ as a function of the disk temperature for $300\le T_d\le 500\text{K}$ , with all other conditions remaining the same. What is the steady−state temperature of the disk?