On July 15 at 2 p.m. solar time, the direct beam and diffuse solar radiation intensities at a location, with a northern latitude of 40°, are 580 Wmí2 and 165 Wmí2 respectively. The ambient temperature...

On July 15 at 2 p.m. solar time, the direct beam and diffuse solar radiation intensities at a location, with a northern latitude of 40°, are 580 Wmí2 and 165 Wmí2 respectively. The ambient temperature is 31°C. The thickness and thermal conductivity of a flat roof at the location are 55 mm and 0.12 Wmí1 Kí1 respectively. The emissivity of the roof surface is 0.8. The inside air temperature is 24°C. The overall heat transfer coefficients for the outside and inside air films are respectively 28 Wmí2 Kí1 and 8.5 Wmí2 Kí1 . Calculate (i) the sol-air temperature, (ii) the surface temperature of the roof, and (iii) the heat flow rate into the building. Assume that the heat capacity of the roof is negligible.