Heat transfer rate between an underground concrete cistern and the soi
Heat transfer rate between an underground concrete cistern and the soi
(OP)
I am building an underground water heat transfer system. In order to calculate the heat capacity of the system, I need the heat exchange rate (BTU's per hour) between the red clay soil(typical of North Georgia), which is at 56 degree F and the water in the concrete cistern. Help, please! Typical equation would be nice.





RE: Heat transfer rate between an underground concrete cistern and the soi
We assuming no ground water movements in soil (no seepage) and that the cistern is an horizontal cylinder of diameter Do and leght L, buried ad a depth = X + Do/2.
The heat flow from the cistern is:
Q = ( tw - ta ) / Rt
Where:
tw = temperature of water (average along the predefined time)
ta = temperature of surface (average along the time as tw). In first approssimation, if the time = 1 year, ta = temperature of freatic layer.
Rt = Rc + Rs = total equivalent thermal resistance water-surface
Rc = 1 / (hw * Ai) + (Do - Di)/(2 * kc * Amc)
Rs = 1/(2 * ks * L * 3.14)* ln (4 * X / Do) = calculated by a conduction shape factor you'll find out on Rohsenow-Hartnett, Handbook of Heat transfer or on others reference textbooks on heat transfer.
hw = f(Reynolds, Pr) or f(Grashof) depending on the water movement (natural o forced)
Ai = inner surface of the cistern
Ao = outer surface of the cistern
Amc = (Ao - Ai) / ln (Ao/Ai) = mean surface of the cistern
kc = thermal conductivity of the concrete of the cistern
ks = thermal conductivity of the soil depends on % water
L = lenght of the cistern
X = distance centre of the cistern and surface
The evaluation of hw could be easy if you know the Nusselt correlations.
Otherwise take into account the following values hw = 500 W/m2K (natural) hw = 1200 W/m2K (forced).
For ks search on the Web with the key words: thermal conductivity soil.
I've found out several useful sources of data, for instance:
http://www.geo.umnw.ethz.ch/staff/homepages/fuhrer/dipl/node10.html
and http://newton.dep.anl.gov/askasci/env99/env140.htm from which I excerped this interesting text:
<< The thermal conductivity of soils is mostly controlled by water content, although, obviously, the type of soil is also important. For an average clay, the thermal conductivity in W/(m K) is 0.25 for no soil moisture,
about 1.0 for 10% soil moisture (% by volume), 1.25 at 14% (a bend in the thermal conductivity curve occurs here), 1.67 at 30%, and about 2.0 at 50%. That will give you a rough idea - David R. Cook - Atmospheric Section - Environmental Research Division - Argonne National Laboratory>>
Hoping this is useful to you for a ... good calculation
Gianfranco.
RE: Heat transfer rate between an underground concrete cistern and the soi
Thanks Jerre