A double-glazed window consists of two sheets of glass separated by an \(L=0.2-\mathrm{mm}\)-thick gap. The gap is evacuated, eliminating conduction and convection across the gap. Small cylindrical pillars, each \(L=0.2 \mathrm{~mm}\) long and \(D=0.20 \mathrm{~mm}\) in diameter, are inserted between the glass sheets to ensure that the glass does not break due to stresses imposed by the pressure difference across each glass sheet. A contact resistance of \(R_{t, c}^{\prime \prime}=2.0 \times 10^{-6} \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}\) exists between the pillar and the sheet. For nominal glass temperatures of \(T_{1}=20^{\circ} \mathrm{C}\) and \(T_{2}=-10^{\circ} \mathrm{C}\), determine the conduction heat transfer rate through an individual AISI 302 stainless steel pillar.