Two parallel, aligned, black, rectangular plates $(1m2m)$ spaced $0\mathrm{.}5$ m apart, are located in a large room whose walls are maintained at $300$ K $.$ One of the plates $($node $1)$ is maintained at a uniform temperature of $800$ K $,$ while the backside of the second plate $($node $2)$ is well insulated

$($a$)$ Compute the view factors $F_{12}$ and $F_{13}?[4$ points$]F_{12}=\mathrm{.}51$

$F_{13}=\mathrm{.}49$

$($b$)$ Draw the radiation network for this problem $[3$ points$]$

$($c$)$ What is the temperature of the insulated plate, $($surface $2)?[3$ points$]676$ K

$($d$)$ What is the net heat transfer from surface $1?[3$ points$]33894$

$($c$)$ What is the net heat transfer to the environment? $33488$

Correct answers are given, please provide the work and network