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re: solar/earth cooling
22 dec 1999
toby wrote:
>hi nick,
hi toby,
>we were debating what the thermal capacitance of dirt is. you contended
>30, i said 60 btu/f/cuft.
i suppose you saw my posting with results from a 1949 study that measured
the heat capacity of 9 kinds of soil. the average was 30.8 btu/f-ft^3.
if you still think soil stores as much heat as water by volume, why don't
you get that study by interlibrary loan and read it? (m. s. kersten,
"thermal properties of soils," bull. univ. of minnesota inst. of tech.
eng. exp. stat. bull., vol. 28, 1949.)
while you are at it, why not buy a copy of the 1998 schaum's outline on
heat transfer ($14.95) or jan krieder's $100 1994 "heating and cooling
of buildings" book, which cited that soil study?
> ok, i did the test again...
>=================== test#2 results ===============
>time taylor oven
>probe probe
>0 74 72 room temperature
>0 62 60 initial dirt temperature [who cares?]
>0 66 64 initial water temperature, tw
>0 spread dirt in pan, 3/4" thick, and
> placed in oven for 20 minutes
what temperature was the oven? why not simply leave the dirt in the oven
until all the water evaporates and it becomes about the same temp as the
oven, as measured, vs all this mixing and cooling crap?
>20 took dirt out of oven, and let cool
> for 5 minutes, stirring…
>25 111 108 dirt temperature, td, after it was heated
>30 83 81 temperature of mixed and stirred water
> and dirt, tm
>40 81 79 tm
>50 80 78 tm
>60 80 78 tm...
>now, what is r?
>thomas bligh... took measurements which show that the sun's heat
>penetrates 26 feet deep into the earth in 6 months.
the earth is not a constant temperature laboratory!
>so, in a volume of dirt 1 sqft by 26ft
>
>rc = 6 months = r hr-sqft-f/btu/ft * 26 ft * 40 btu/f/cuft
when you get your schaum's outline, check out chapter 4 on time-varying
conduction. for starters, look at the "biot modulus," which is a number
(the ratio of "resistance to internal heat flow" to "resistance to external
heatflow," eg a convection heatflow) that helps you decide whether you can
do this kind of "lumped analysis" (if bi < 0.1) or not. in this case,
you can't, even if the earth were a constant temperature lab, with no
seasons or plants or rain or snow or evaporation or groundwater movement
or molten core or volcanoes or clouds or sun or thermal nitwits.
then please look at section 4.5 of the book ("one dimensional systems:
convective boundary conditions"), and notice that this kind of heatflow
is described by more complicated equations involving the "error function"
related to a gaussian distribution. maybe somebody knows some simpler way
to correlate real-world ground warming and cooling with soil properties,
but i'm reasonably sure your way makes no sense. like someone who says
"the heat capacity of soil is 60, because the price of cheese on the
moon was $4.53 last week."
nick
94n16 earth coupled heat storage and loss. d93d01 94n15
copyright norman b. saunders, p. e. 15 ellis road, m3, weston ma 02193
may be freely quoted if in context with appropriate credit.
a crawl space is thermally coupled to the earth. water moving laterally
through earth within ten feet around or below the foundation washes the heat
away. see 94n15 ground coupling for tempering houses. heat from non-flowing
water warmer than the space above moves up by vapor rising through the
intersticies of the soil. while heat or lack of it is carried downward
by rain or surface water percolating down.
consider however dry sand with conductivity of 0.355 w/mk and heat storage
of 355 wh/m^3k which thereby has a time delay of 1,000 hr/m^2...
[ie 355wh/m^3k/(0.355w/mk) = 1000 h/m^2...]
or basalt with 2, 2,000 and 1,000. most rock has similar time delay with
conductivity and storage falling between. thus in a half year a temperature
change has propagated down about two meters.
[ie 4000h x 1m^2/1000h = 4m^2 or (2m)^2...]
the sand under a 1,076 ft^2 floor (100 m^2) for a 10 kelvin change has
stored perhaps 300 kwh, possibly a day's worth of heat. basalt then would
have stored nearly a week's worth. if the crawl space were filled with
400 barrels of water with space for moving air to circulate, heat storage
is increased by some 500 kwh...
about a meter a year of rain falls. since very little flows westerly
through adjacent streams, this gives a mean ground water flow of about
a liter a minute per meter north-south of earth cross section. since
the house extends 15m, about 10kw continuous could be pulled out of
only that part of the sheet of water flowing under the house. such
capability is not unusual in the northern united states...
first the heat flow in the ground around the house. the seasonal
temperature change at the surface diffuses downward, being delayed so
that at a 2m or so depth it is 6 months behind, and the temperature
change is also attenuated so that below 3m it is negligible.
all soil contains some moisture. when heat is moving downward, the
conductivity of the water speeds the temperature change slightly, even
as water's thermal capacitance slows it. a warm wet strata below is
another matter. vapor is always forming, and because of its low density,
it rises through the inevitable pores until the lower temperature causes
it to condense, releasing the considerable heat from change of state.
see penrod, "measurement of the thermal diffusivity of a soil by the
use of a heat pump," j. app. phys. 21 may 1950.
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