Two thin radiation shields with different emissivities on their two surfaces are placed between two very large parallel plates, which are maintained at uniform temperatures $1=700$ K and $2=200$ K and have emissivities $1=0\mathrm{.}5$ and $2=0\mathrm{.}8,$ respectively $($See the figure$).$ Determine the net rates of radiation heat transfer $(12)$ between the two plates

a$)$ without shields per unit surface area

b$)$ with the shields per unit surface area

c$)$ the temperature $(34)$ of the radiation shields in steady operation.

a$)6010\mathrm{.}2$ W$/$m$2$ b$)535\mathrm{.}6$ W$/$m$2$

c$)607\mathrm{.}5$ K$,433\mathrm{.}9$ K