Date: May 2004
My students are creating blue prints for fruit cellars
and want to know what the temperatures will be in a cellar 6 foot
deep? Temperatures in a cold climate i.e. Iowa and what would be the
temperature in a tropical climate in South America?
I regret that my scope of my engineering and science expertise does not
include knowing the temperature of the ground. To get that temperature you
would need to find out information from earth sciences people. If the
cellar is completely underground you could the ground temperature. Deep
underground the temperature is constant. Closer to the surface, the ground
temperature swings up and down according to the seasons.
I think the temperature of near-surface ground is about the same as the temperature of the air above,
or same as the surface of the earth facing the air,
except it's low-pass filtered for progressively slower response, the deeper you go.
By several feet down, response is slowed to the point that the cellar holds a nearly constant temperature all year round,
equal to the annual average air temperature of that locale.
The cellar could be made arbitrarily warmer by concentrations of geothermal heat, but most places won't have that.
I think the global average geothermal heat flow upwards from the hot center of the earth is negligible for shallow depths.
The cellar should be some degrees cooler because of evaporation of ground-moisture,
if the wall-sealing and ventilation and roof-insulation are optimized.
How much cooler, depends on temperature and air humidity and other things. Around 10 degrees F?
On hot day in the dry Mojave desert, our evaporative cooler was about 20 degrees F cooler. That's about the max.
So look up the annual average temperature of Iowa and your spot in South America, and also the average humidity.
I think an Excel spreadsheet or a Basic program could, with simple linear approximations,
figure the daily or annual average cooling accomplished by evaporation, in the face of cycles of temperature and humidity.
A separate spreadsheet could calculate the temperature of 10 or 100 layers of earth, during annual temperature cycles.
That way you could figure for yourself how deep the cellar needs to be,
just by guessing thermal conductivity and specific heat of dirt and rock.
The most optimistic guess would be same as water: 0.01W/cm.degC and 1 calorie/cm3.degC, very slow, and
I think least optimistic would be about 0.2W/cm.degC and 0.5 cal/cm3.degC for rock, 40 times faster for a given depth.
Probably one should explicitly omit considerations of extra thermal conductivity
from water evaporating, percolating thru porous earth, and condensing.
Perhaps you want to consider the case of active control of ventilation, so that air enters when cool/dry and stops when hot/wet.
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Update: June 2012