A house wall consists of 1/2 in. drywall, 3 5/8 in. glass fiber insulation, and

Question

A house wall consists of 1/2 in. drywall, 3 5/8 in. glass fiber insulation, and an outside brick wall 4 in. thick. Assume that there is perfect contact between each layer. The thermal conductivities of drywall, glass fiber, and brick are 0.17, 0.036, and 0.72W m^-1 K^-1, respectively. the inside temperature of the house is 70 degrees F; the outside air temperature is 0 degrees F.

A) Find the heat flux in Btu ft^-2 h^-1.

B) Find the temperature (K) at the junction between the drywall and the glass fiber insulation.

C) Find the location (in inches from the inside surface of the drywall) where moisture freezes.

Explanation / Answer

thermal resistance = 0.0127/.17 + 0.092/0.036 + 0.101/0.72 = 2.77 flux = temp diff/thermal resistance = (21.11 + 17.77)/2.77 = 14 W/m^2 = 4.44 Btu ft^-2 h^-1 thermal resistance = 0.0127/0.17 = 0.0747 14 = (T2-21.11)/0.0747 T2 = 22.1558 DEG C or 295.15 K This means temp is 0 deg C 14 = (21.11- 0)/ term reist term resist = 1.508 thermal resist by drywall = 0.0747 thermal resist by glass fiber = 2.55 this means the temp is in glass fiber at distance, 1.508 - 0.0747 = x/0.036 x = 0.0516 m so distance from inside surface is 0.0516+0.0127 = 64.3 mm = 2.53 in

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