Consider coaxial, parallel, black disks separated a listance of $0\mathrm{.}20m.$ The upper disk of diameter $0\mathrm{.}2m$ is quipped with an electric heater on the back side while the ower disk of diameter $0\mathrm{.}40m$ is maintained at $500K$ and the surroundings are at $300K.$

a$)$ Determine the shape factors $F_{12}($between upper and lower disks$)$ and $F_{13}($between upper disk and the surrounding$)$ using the chart and the summation rule, ie $F_{11}+F_{12}+F_{13}=1.$

b$)$ What temperature will the upper disk attain in equilibrium if electrical power of $P_e=17\mathrm{.}5W$ is supplied to the heater on the back side of the disk

Note that radiation is exchanged between the upper disk and lower disk and surrounding so that the total radiation leaving the upper disk is $Q_{\text{r}\text{a}\text{d}}=Q_{\text{u}\text{p}\text{p}\text{e}\text{r}-\text{l}\text{o}\text{w}\text{e}\text{r}}+Q_{\text{u}\text{p}\text{p}\text{e}\text{r}-\text{s}\text{u}\text{r}\text{r}\text{o}\text{u}\text{n}\text{d}\text{i}\text{n}\text{g}}$

Also from $1$st law of thermodynamics:

$-Q_{\text{r}\text{a}\text{d}}+W_e=0so$ that $Q_{\text{r}\text{a}\text{d}}=P_e$