ASHRAE Journal - April 2020 - 16

TECHNICAL FEATURE

been left open at the bottom to avoid winter condensation and summer mold growth problems. In these houses
the stack pressure doubles with the envelope equivalent
or effective leakage areas (ELA) limited by the tightness
of the top edge seal. In fact, it is practically impossible to
depressurize most standard basement walls envelopes.
From Figure 2, this suggests typically insulated basement
envelope ELAs of much greater than 50 in.2 (0.03 m2) and
likely more than 500 in.2 (0.3226 m2). These homes may
have had baseboard heating or forced air heating and
cooling systems in the 1,000 cfm to 1,500 cfm (472 L/s to
708 L/s) range. This suggests winter basement insulation
air barrier leakage rates approaching 50% or more of the
house conditioned air circulation rate.
This circulation can cause cold surface condensation turning into ice buildup, especially in humidified
homes, behind the insulation on the aboveground
portion of the foundation. When spring comes, this
condensation will melt and drain to the bottom of the
wall where it creates mold growth. In the summer, stack
pressure flow decreases. The moisture wicking via foundation walls will dampen floor-level cellulose materials with an associated microbial growth particularly in
corners where temperatures behind the insulation are
lowest and humidity highest.

Heat Loss
Estimating Foundation Temperatures
A transient conduction model was made using heating
degree days (HDD) weather data for Seattle with the following conditions:
Density of soil = 120 lb/ft3
Thermal conductivity of soil = 0.8 Btu·ft/h·ft2·°F
Specific heat of soil = 0.345 Btu/lb°F
Density of concrete = 65.5 lb/ft3
Concrete thickness = 8 in.
Thermal conductivity of concrete = 0.439 Btu·ft/h·ft2·°F
Fiberglass insulation = 3.5 in. k (thermal
conductivity/in.) = 0.27 Btu·in./h·ft2·°F
0.5 in. plywood = C (conductance) = 2.12 Btu/h·ft2
Inside air film = h (heat transfer coefficient) =
1.5 Btu/h·ft2·°F
f = 1/(1/1.5 + 3/0.27 + 1/2.12) = 0.0816 Btu/h·ft2·°F to
inside of concrete
Outside effective heat transfer coefficient =
6.0 Btu/h/ft2·°F based on forced convection (15 mph
wind max) and sky radiation
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ASHRAE JOURNAL

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APRI L 2020

Far field (groundwater) temperature = 52°F
Daily temperature time = θ = (nday /365)(2π)-0.75π
(Jan. 1 is nday = 1) radians
Daily temperature variation = Tmean = 52 + 12.45sin(θ)
Hourly variation = Toutside = Tmean +
12(time of day/24)-2π
Solution time step = 0.01 hours

Effect of Daily Variation in Temperature
The first simulation was run to determine the shortterm temperature variation on cold days (20°F [-6.7°C]
mean temperature). The inner concrete wall temperatures seemed to reach a (slowly ramping down) equilibrium after 72 hours. The sinusoidal variation in concrete
temperature with time reduces with depth. At about
0.5 ft (152 mm) depth (line B in Figure 3), the sinusoidal
variation is nearly gone, and the long-term seasonal
variation is more significant. This thermal behavior justifies the use of overall daily averages in the calculation
of energy loss.
An equation was fit to the average temperature from
the heating degree days (HDD) for the Seattle area and is
compared in Table 1.
The second simulation was run for 13 months, starting
January 1, to have correct initial conditions for the following January. The seasonal mean temperature for Seattle
was applied as the air temperature boundary condition.
The warmest month was August, with an average
upper soil surface temperature near 64°F (18°C), while
the coldest month had an average upper soil temperature near 40°F (4.4°C) (Figure 4).
The average inner surface temperature contours for
the insulated wall show that the upper sections are
warmer than the lower sections during summer and
the reverse during winter (Figure 5). This raises the possibility for internal condensation on cooler wet surfaces
due to evaporation from warmer wet surfaces within the
envelope during any time of year, especially when the
envelope is tightly sealed.
When these surface temperatures are converted to
heating degree days, a clear distinction exists between
the heating requirements of the house compared to the
basement (Figure 6).
To estimate the energy penalty of leakage through
the envelope, some simple assumptions are made:
that the stack pressure drives the flow, the stack pressure is derived from the averaged wall temperatures,
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ASHRAE Journal - April 2020

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