Chapter 4, Problem 4.22P

A double-glazed window consists of two sheets of glass separated by an $L=0.2$ -mm-thick gap. The gap is evacuated, eliminating conduction and convection across the gap. Small cylindrical pillars, each $L=0.2\text{mm}$ long and $D=0.15\text{mm}$ 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 $R_{t,c}^n=1.5\times {10}^{-6}{\text{m}}^{\text{2}}\cdot \text{K/W}$ exists between the pillar and the sheet. For nominal glass temperatures of $T_1=20°\text{C}$ and $T_2=-10°\text{C,}$ determine the conduction heat transfer through an individual stainless steel pillar.