Q$2.($b$)$ Two co$-$axial parallel circular disks of equal diameter of $0\mathrm{.}5$ m are separated by $0\mathrm{.}25$ m apart. The top disk is maintained at $800$ K and has an emissivity of $0\mathrm{.}92$ while the bottom disk is maintained at $400$ K and has an emissivity of $0\mathrm{.}6.$ The disks are exposed through the opening between them into a very large room area which is maintained at $300$ K and has an emissivity of $0\mathrm{.}95.$

$($i$)$ Sketch the corresponding radiation network $($i$.$e$.,$ electrical analogy$)$ with appropriate physical parameters $($i$.$e$.,Q_1^{},E_{b1},R_1,J_1,R_{12},..Q_2^{}$dots etc.$)$; and

$(3$ marks$)$

$($ii$)$ Determine the net rate of radiation heat transfer between the two disks, and the net rate of radiation heat transfer from the two disks to the room during the steady operation.

$(12$ marks$)$