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Old Mar 1st 2017, 03:00 PM   #1
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Heat flux: porous media/air interaction

Dear community,
I have a question concerning the thermodynamic behaviour of a theoretical column experiment:

Assume I have a "1D"-column of 50 m sand. At the top the surface air temperature is -25C.
At the beginning of the experiment the sediment column is almost completely filled with tap water, resulting in a saturated sediment of 49 m. Tap water is kept constantly at a temperature of 10 C.

During the experiment I decrease step wise the water level in the column by 5 m; let's say 5 times. At the same time I am measuring the resulting equilibrium temperature at the top of the air-column-interface (temperature at column surface). At the end of the experiment the resulting saturated sediment column is 24 m and the isolating sediment layer is 26 m.

Now my questions concerning that experiment are:
1. Is during the experiment the resulting equilibrium surface temperature dropping linearly or exponentially or otherwise? Why?
2. Does the thickness of the increasing isolating sediment layer play a role in the time equilibrium temperatures are achieved at the column surface? How long will it take approx. until equilibrium conditions are reached?
3. Is the expected behaviour the same if the air temperature is for example 25C?

I would be very grateful to receive an answer on this one.
Surely it shouldn't be a problem for experts.
Kind regards
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Old Mar 1st 2017, 07:04 PM   #2
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If I understand correctly, you have water at 10C under a column of insulating sand, with the top exposed to air at -25C, correct? You ask what the equilibrium temp at the surface is - well, it would be at, or just slightly above, -25C. Think of the sand as an insulator, with a hot reservoir at one end (i.e. the water) and a cool reservoir at the other (air). The temp gradient across the width of the sand will be linear (assuming no heat transfer through the sides of the column) between the hot to the cold ends. There is a bit of complication as this assumes that there is efficient heat transfer at the surface from sand to air - that is, that we don't have to worry about how convection plays into it.
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