The exterior wall of a building has 10 mm thick gypsum (k = 0.16 Wmí1 Kí1 ) board on the inside. Next to it is a vapor retarder, of negligible thermal resistance, that bears on a wood frame (k = 0.15...

The exterior wall of a building has 10 mm thick gypsum (k = 0.16 Wmí1 Kí1 ) board on the inside. Next to it is a vapor retarder, of negligible thermal resistance, that bears on a wood frame (k = 0.15 Wmí1 Kí1 ), made of 38 mm × 140 mm studs. The space between the studs is filled with fiberglass insulation (k = 0.042 Wmí1 Kí1 ). This is followed by a 20 mm thick layer of sheathing (k = 0.055 Wmí1 Kí1 ), 40 mm thick layer of expanded polystyrene (k = 0.035 Wmí1 Kí1 ) and 100 mm thick layer of brick (k = 0.85 Wmí1 Kí1 ). The area of the framing is 20% of the area of the wall. The inside air temperature and relative humidity are respectively 20°C, 30%. The outside air at í15°C is saturated. The inside and outside heat transfer coefficients are 8 Wmí2 Kí1 and 24 Wmí2 Kí1 respectively. (a) Calculate the average heat transfer coefficient using: (i) the parallel path method and (ii) the isothermal plane method. (b) Considering the heat flow path through the insulation, calculate the minimum vapor diffusion resistance of the vapor retarder, needed to avoid condensation of water vapor in the wall.