Chapter 13, Problem 13.110P

The composite insulation shown, which was described in Chapter 1 (Problem 1.86e), 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 $L_1=L_3=12.5\text{mm}$ and that the honeycomb core be constructed from a high-density particle board. The square cells of the core are to have length $L_2=50\text{mm}$ , width $W=10\text{mm}$ , and wall thickness $t=2\text{mm}$ . The emissivity of both particle boards is approximately 0.85, and the honeycomb cells are tilled 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 $T_{s,i}=25°\text{C}$ and the top (outer) surface temperature is $T_{s,i}=-10°\text{C}$ . 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.