The composite insulation shown, which was described in Chapter 1 (Problem 1.72e), is being considered as a ceiling material. It is proposed that the outer and inner slabs be made from low-density particle board of thicknesses L, = L₃ = 12.5 mm and that the honeycomb core be constructed from a high-density particle board. The square cells of the core are to have length L₂ = 50 mm, width W = 10 mm, and wall thickness t = 2 mm. The emissivity of both particle boards is approximately 0.85, and the honeycomb cells are filled with air at 1-atm pressure. To assess the effectiveness of the insulation, its total thermal resistance must be evaluated under representative operating conditions for which the bottom (inner) surface temperature is T_{s, i} = 25?C and the top (outer) surface temperature is T_{s, o} = - 10? C. To assess the effect of free convection in the air space, assume a cell temperature difference of 20? C and evaluate air properties at 7.5? C. To assess the effect of radiation across the air space, assume inner surface temperatures of the outer and inner slabs to be -5 and 15?C, respectively.

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T>T Surface slabs Cellular air spaces