Condensation and Freezing of Moisture in Walls The condensation and even freezing of moisture in walls without effective vapor retarders is a real concern in cold climates, and it undermines the effectiveness of insulations. Consider a wood frame wall that is built around 38 mm × 90 mm (2×4 nominal)

Question

Condensation and Freezing of Moisture in Walls

The condensation and even freezing of moisture in walls without effective vapor retarders is a real concern in cold climates, and it undermines the effectiveness of insulations. Consider a wood frame wall that is built around [latex] 38 mm imes 90 mm [/latex] ([latex] 2 imes 4 [/latex] nominal) wood studs. The 90-mm-wide cavity between the studs is filled with glass fiber insulation. The inside is finished with 13-mm gypsum wallboard and the outside with 13-mm wood fiberboard and [latex] 13-mm imes 200-mm [/latex] wood bevel lapped siding. Using manufacturer’s data, the thermal and vapor resistances of various components for a unit wall area are determined to be as:

Construction	R-Value, [latex]m^{2} \cdot ^{\circ}C/W [/latex]	[latex] R_{ u }-Value, s \cdot m^{2} \cdot Pa/ng [/latex]
1. Outside surface, 24 km/h wind	0.030	—
2. Painted wood bevel lapped siding	0.14	0.019
3. Wood fiberboard sheeting, 13 mm	0.23	0.0138
4. Glass fiber insulation, 90 mm	2.45	0.0004
5. Painted gypsum wallboard, 13 mm	0.079	0.012
6. Inside surface, still air	0.12	—
TOTAL	3.05	0.0452

The indoor conditions are [latex] 20^{\circ}C [/latex] and 60 percent relative humidity while the outside conditions are [latex] - 16^{\circ}C [/latex] and 70 percent relative humidity. Determine if condensation or freezing of moisture will occur in the insulation.

Accepted Answer

SOLUTION The thermal and vapor resistances of different layers of a wall are given. The possibility of condensation or freezing of moisture in the wall is to be investigated.

Assumptions 1 Steady operating conditions exist. 2 Heat transfer through the wall is one-dimensional. 3 Thermal and vapor resistances of different layers of the wall and the heat transfer coefficients are constant.

Properties The thermal and vapor resistances are as given in the problem statement. The saturation pressures of water at [latex] 20^{\circ}C [/latex] and [latex] - 16^{\circ}C [/latex] are 2339 Pa and 151 Pa, respectively (Table 14–9).

Analysis The schematic of the wall as well as the different elements used in its construction are shown in Figure 14–25. Condensation is most likely to occur at the coldest part of insulation, which is the part adjacent to the exterior sheathing. Noting that the total thermal resistance of the wall is [latex] 3.05 m^{2} \cdot ^{\circ}C/W [/latex], the rate of heat transfer through a unit area [latex] A = 1 m^{2} [/latex] of the wall is

[latex] \dot{Q}_{wall} = A \frac{T_{i} - T_{o}}{R_{total}}[/latex]

[latex] = \left ( 1 m^{2} ight ) \frac{\left [ 20 - \left ( - 16 ight )^{\circ}C ight ]}{3.05 m^{2} \cdot ^{\circ}C/W} = 11.8 W [/latex]

The thermal resistance of the exterior part of the wall beyond the insulation is [latex]0.03 + 0.14 + 0.23 = 0.40 m^{2} \cdot ^{\circ}C/W [/latex]. Then the temperature of the insulation– outer sheathing interface is

[latex] T_{I} = T_{o} + \dot{Q}_{wall} R_{ext} [/latex]

[latex] = - 16^{\circ}C + \left ( 11.8 W ight )\left ( 0.40^{\circ}C/W ight ) = - 11.3^{\circ}C [/latex]

The saturation pressure of water at - 11.3°C is 234 Pa, as shown in Table 14–9, and if there is condensation or freezing, the vapor pressure at the insulation– outer sheathing interface will have to be this value. The vapor pressure at the indoors and the outdoors is

[latex] P_{ u, 1} = \Phi _{1} P_{sat, 1} = 0.60 imes \left ( 2340 Pa ight ) = 1404 Pa [/latex]

[latex] P_{ u, 2} = \Phi _{2} P_{sat, 2} = 0.70 imes \left (151 Pa ight ) = 106 Pa [/latex]

Then the rate of moisture flow through the interior and exterior parts of the wall becomes

[latex] \dot{m}_{ u , interior} = A \left ( \frac{\Delta P}{R_{ u }} ight )_{interior} = A \frac{P_{ u , 1} - P_{ u , 1}}{R_{ u , interior}} [/latex]

[latex] = \left ( 1 m^{2} ight ) \frac{\left ( 1404 - 234 ight ) Pa}{\left ( 0.012 + 0.0004 ight ) Pa \cdot m^{2} \cdot s/ng} = 94,355 ng/s = 94.4 \mu g/s [/latex]

[latex] \dot{m}_{ u , exterior} = A \left ( \frac{\Delta P}{R_{ u }} ight )_{exterior} = A \frac{P_{ u , 1} - P_{ u , 1}}{R_{ u , exterior}} [/latex]

[latex] = \left ( 1 m^{2} ight ) \frac{\left ( 234 - 106 ight ) Pa}{\left ( 0.019 + 0.0138 ight ) Pa \cdot m^{2} \cdot s/ng} = 3902 ng/s = 3.9 \mu g/s [/latex]

That is, moisture is flowing toward the interface at a rate of [latex] 94.4 \mu g/s [/latex] but flowing from the interface to the outdoors at a rate of only [latex] 3.9 \mu g/s [/latex]. Noting that the interface pressure cannot exceed 234 Pa, these results indicate that moisture is freezing in the insulation at a rate of

[latex] \dot{m}_{ u , freezing} = \dot{m}_{ u , interior} - \dot{m}_{ u , exterior} = 94.4 - 3.9 = 90.5 \ mu g/s [/latex]

This corresponds to 7.82 g during a 24-h period, which can be absorbed by the insulation or sheathing, and then flows out when the conditions improve. However, excessive condensation (or frosting at temperatures below 0°C) of moisture in the walls during long cold spells can cause serious problems. This problem can be avoided or minimized by installing vapor barriers on the interior side of the wall, which will limit the moisture flow rate to [latex] 3.9 \mu g/s [/latex]. Note that if there were no condensation or freezing, the flow rate of moisture through a [latex] 1 m^{2} [/latex] section of the wall would be [latex] 28.7 \mu g/s [/latex] (can you verify this?).

TABLE 14–9

Saturation pressure of water at
various temperatures

Temperature, °C	Saturation Pressure, Pa
-40	13
-36	20
-32	31
-28	47
-24	70
-20	104
-16	151
-12	218
-8	310
-4	438
0	611
5	872
10	1,228
15	1,705
20	2,339
25	3,169
30	4,246
35	5,628
40	7,384
50	12,349
100	101,330
200	[latex] 1.55 imes 10^{6} [/latex]
300	[latex] 8.58 imes 10^{6} [/latex]

Question : Condensation and Freezing of Moisture in Walls The condensat...

This Question has been Answered.

Already have an account?

Login