A flat concrete roof of a house may be treated as a single slab of thickness d and area 30m2. During a summer afternoon the air outside is at 42∘C while the ceiling of the room just beneath the roof stays at 27∘C. The thermal conductivity of concrete may be taken as 1.5W m−1K−1. The house-owner wants to limit the heat entering the room through the roof to no more than 3.24×106J in one hour.
(a) Determine the minimum thickness d of the concrete roof that will satisfy the owner’s requirement.
(b) If the actual roof constructed is only half of the thickness obtained in part (i), calculate the additional heat energy that will enter the room through the roof in an 8h day-time period under the same temperature conditions.