TM-5-855-4
CHAPTER 3
UNDERGROUND HEAT TRANSFER
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Underground heat conduction fundamentals.
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a. The essential difference between aboveground and underground spaces is the nature of the
environment. Aboveground, the main consideration is the exposure to ambient air with little or no
references to conduction through the ground. No credit is taken for summer cooling by the ground. For
winter heat losses from walls and floors in contact with the ground but less than 3 feet below grade, ground
temperatures are ignored and losses computed as proportional to ambient air to air temperature
differentials and perimeter factors dependent on construction materials.
b. For heated basement walls and floors more than 3 feet below grade, the steady state heat loss is
calculated along concentric circular paths centered on the intersection of the ground and the wall and
continued under the floor by similar arcs centered on the intersection of the wall and the floor. This heat
loss is proportional to the ground conductivity, the design temperature difference between the inside air
and the ground at a depth of 4 inches, and the reciprocal of the path length.
and ground design temperature from local meteorological records. Many designers prefer the older and
simpler rule of thumb, which assumes a heat flux of 0.2 Btuh/ft2 for each "F temperature difference
between basement and ground water temperature. Ground thermal properties are discussed in paragraph
3-6.
d. Underground the situation is reversed with the heat exchange to or from the environment
normally controlled by conduction through the materials surrounding the space, in the absence of
significant water percolation.
(1) This constructive heat transfer is complicated by the complexity of this environment, which
may include known or unknown discontinuities, such as stratification, faults, inclusions, and fissures.
However, it will be assumed that a single homogeneous isotropic solid may be substituted to the concrete,
rock, clay, sand, or other materials actually involved.
(2) The properties of this ideal solid, referenced herein as "rock," will be based on available data
and engineering judgment, more weight being given to actual material properties close to the cavity walls
than farther away.
e. Another characteristic of the underground environment is the variable or transient nature of the
heat transfer. The air temperature in an occupied underground space is usually maintained above the
initial temperature of the surrounding rock.
(1) During the initial warm-up period, the heat will diffuse in the rock faster than it can be
transferred at the boundary, and the rock surface temperature slowly builds up under constant and
maximum flux conditions.
(2) When the walls have reached the desired temperature, the warm-up or conversions period is
completed and a thermostatted or holding period begins where the heat flux through the rock gradually
decreases at constant wall temperature.
(3) This thermostatted heating period ends and a cooling period begins if and when the internal
heat load exceeds the heat absorption capacity of the rock. At that point, the space temperature will rise
again unless the excess heat is removed by other means of cooling, such as ventilation or air
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conditioning.
f. Finally, and depending on the burial depth, interaction with aboveground ambient conditions may
have to be included. The steady state solutions to this problem are well known and covered in most
textbooks for cavities of different shapes. The designer will still have to judge how much to retain of the
transient deep burial solution to obtain a realistic representation.
g. Solutions to the fundamental problem of transient heat conduction from a single geometrically
simple cavity in a uniform, isotropic, and infinite solid are available but involve infinite series or
harmonic functions, such as the Bessel function. These functions are still beyond the reach of ordinary
electronic calculators and would require tedious and nontrivial table look-ups to numerically evaluate
each case.
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