Cylindrical pillars similar to those of Problem 4.22 are positioned between the glass sheets with a pillar to- pillar spacing of W. The inside surface of one glass sheet is treated with a low-emissivity coating characterized by ε₁ = 0.05. The second inner surface has an emissivity of ε₂ = 0.95. Determine the ratio of conduction to radiation heat transfer through a square unit area of dimension W X W for W = 10, 20, and 30 mm. The stainless steel pillar is located at the center of the unit area and has a length of L = 0.4 mm and diameter of D  = 0.15 mm. The contact resistances and glass temperatures are the same as in Problem 4.22.

Data From Problem 4.22

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 mm long and D = 0.15 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  = 1.5 X 10^-6 m² · K/W exists between the pillar and the sheet. For nominal glass temperatures of T₁ = 20 C and T₂ =–10 C, determine the conduction heat transfer through an individual stainless steel pillar.