Consider a flat ceiling that is built around 38-mm × 90-mm wood studs with a center-to-center distance of 400 mm. The lower part of the ceiling is finished with 13-mm gypsum wallboard, while the upper part consists of a wood subfloor (R = 0.166 m²·°C/W), a 13-mm plywood, a layer of felt (R = 0.011 m²·°C/W), and linoleum (R = 0.009 m²·°C/W). Both sides of the ceiling are exposed to still air. The air space constitutes 82 percent of the heat transmission area, while the studs and headers constitute 18 percent. Determine the winter R-value and the U-factor of the ceiling assuming the 90-mm-wide air space between the studs

(a) Does not have any reflective surface,

(b) Has a reflective surface with ε = 0.05 on one side,

(c) Has reflective surfaces with ε = 0.05 on both sides. Assume a mean temperature of 10°C and a temperature difference of 5.6°C for the air space.

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