Chapter 7, Problem 2DP

13.38 Consider the attic of a home located in a hot climate. The floor of the attic is characterized by a width of L₁ = 8 m while the roof makes an angle of 0 = 30° from the horizontal direction, as shown in the schematic. The homeowner wishes to reduce the heat load to the home by adhering bright aluminum foil (ε = 0.07) onto the surfaces of the attic space. Prior to installation of the foil, the surfaces are of emissivity & = 0.90. Attic A2, 82, T2 0 = 30° A1, E1, T₁ 土 L₁ = 8 m (a) Consider installation on the bottom of the attic roof only. Determine the ratio of the radiation heat transfer after to before the installation of the foil. (b) Determine the ratio of the radiation heat transfer after to before installation if the foil is installed only on the top of the attic floor. (c) Determine the ratio of the radiation heat transfer if the foil is installed on both the roof bottom and the floor top.

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13.1 Determine F2 and F2 for the following configura- tions using the reciprocity theorem and other basic shape factor relations. Do not use tables or charts. (a) Small sphere of area A, under a concentric hemi- sphere of area A₂ = 3A₁ A₂ A1 (a) (b) Long duct. Also, what is F₁₂? A₂ Αν (b) (c) Long inclined plates (point B is directly above the center of A₁) B 100 mm A₂ - 220 mm (c) (d) Long cylinder lying on infinite plane + A₁ Az (d) (e) Hemisphere-disk arrangement -A₂, hemisphere, diameter D A₂ A₁, disk, diameter D/2 (e) (f) Long, open channel 1 m AA₂ 2 m (f) (g) Long cylinders with A₁ = 4A₁. Also, what is F₁₂? -D₁ A1 -A₂ -D2 (e) (h) Long, square rod in a long cylinder. Also, what is F22? w=D/5 18 A₁ -A2 (h) -D