Homework 4: Please complete one of the following problems. Follow all instructions. 9.10 Time T₁ 1 2 دیا A roof element is constructed as shown below. The steel members have an

R-value of 0.12 m²- C/W and occupy 3% of the cross-sectional area and the airspace has an R-value of 0.18 m²- C/W. The remaining volume is filled with air. 10 mm built-up roofing Outdoors at 32 C 4 5 6 7 8 25.6 The hourly values of the temperature and solar radiation for summer conditions are given in the Table 2. The material properties, thermal resistance, UA value, and capacitance are provided for each layer in Table 2. Table 1: Hourly temperature and solar radiation for summer conditions Gt Time T₂ Gt Time T₂ W/m² W/m² 24.4 23.9 23.9 concrete 23.9 24.4 25.6 26.7 0 0 0 0 0 153 373 576 I sonne 9 10 11 12 13 14 15 16 F Room at 24 C 27.8 29.4 31.1 32.2 33.3 34.4 35.0 35.0 752 4 cm roofing insulation (fiberboard) 10 cm Steel Joists 891 984 1026 20 mm plaster ceiling 17 18 19 20 1014 21 949 22 835 23 679 24 35.0 34.4 33.3 32.2 31.1 29.4 27.8 26.7 Gt W/m² 490 279 59 0 0 0 0 0