Two thick walls are separated by a vacuum gap of thickness \(L\). A cylinder of diameter \(D\) runs between the walls. All surfaces are highly polished (their emissivity is small). The walls are at temperatures \(T_{b, 1}\) and \(T_{b, 2}\) at locations far from the cylinder.

(a) Draw the thermal resistance network.

(b) Derive an expression for the shape factor, \(S\), associated with conduction between \(T_{b, 1}\) and \(T_{b, 2}\).

(c) Determine the value of the shape factor for \(D=0.01 \mathrm{~m}, L=0.5 \mathrm{~m}\), and \(k=23 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\).