Question:
Is there an equation relating the thermal conductivity
and moisture
content of sandy soils(Sharp river sand). I am trying to find out
the thermal conductivity of sharp river sand with moisture content
of 18.84% in J/s/m/degree C.

I would also like to find out how to convert a thermal conductivity
value from W/m.K to J/s/m/ degree C.

Replies:
For this type of mixtures, one often conducts an experiment to empirically
arrive at a relationship for thermal conductivity as a function of moisture
content. Such data are most likely available in the literature; you can
search for them using one of the engineering data banks at your library.
You may also check text books on "heat transfer in porous (or multiphase)
media."

One can also drive equations from first principles but they have to be
validated experimentally. The problem you posed is somewhat complicated
because not only there is a mixture of two materials but also there is the
packing factor which is dependent on the size distribution of sand granular
in the mixture.

If you cannot find references, you can set up and conduct a simple
experiment. Take a plastic tube, about 20 mm in ID and about 200 mm in
length. Fill the tube with the mixture and block the two ends tight with
two thin (5-10 mm) cooper disks. Insert a few thermocouples at 20 mm
internals (from end to end) into the tube. Steadily heat one of the copper
disks at one end and cool the other copper piece at the other end. Moderate
heating is sufficient. Plot the measured temperature as a function of
distance along the tube length. The slope is q"/k where q" is the heat flux
(in Watts per unit area) applied at one end and k is the thermal
conductivity sought. You need to estimate q"; this is easy if you apply
heating with an electric heater (foil type). The other end of the tube can
be immersed in cold or ice water. Consult an introductory text book on
Heat Transfer for more information.

Regarding your unit conversion question, W (Watts) is a measure of power
which is energy (Jules, or J) per unit time (seconds , s). As such W and
J/s are identical; 1 W is one J/s.

AK

Ali Khounsary, Ph.D.
Advanced Photon Source
Argonne National Laboratory

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