TM-5-855-4
3-3. Underground conduction shortcut calculation method.
a. This method is empirical and based on the lumped heat capacity of the rock around the space
effectively involved in the heat transfer. The volume V of this rock shell is determined by the
configuration of the isothermal surfaces around the underground cavity. Figure 3-6 shows the location of
typical isotherms around a rectangular space.
(1) The outer isotherms tend to the cylindrical shape with hemispherical caps. In particular, heat
does not penetrate the corners to the same depth as at the sides. As a result, the rock volume enclosed by
these isotherms is approximately prismatic with beveled edges and pyramidal at the corners, as shown in
figure 3-7.
(2) For a penetration depth D at the sides, the prismatic shell volume is the sum of three terms
corresponding to the 6 faces, the 12 edges, and the 8 corners of the rectangular space, or
v
(3) The actual greenstone rock tested in the NBS experiment (report 2942) had a diffusivity of .0388
2
ft /h, and the temperature profiles corresponding to different warm-up duration to are shown in figure 3-8.
b. For any reasonable warm-up time in excess of 100 hours, the effective depth of penetration is about
10 feet which is the recommended value of D to consider in the calculation of the volume by equation 3-17.
(1) By integrating the temperature profiles for warmup time to over the penetration depth D, the
average temperature increase N of the whole shell volume is expressed as a fraction of that at the face
(figure 3-9) or
With correction for rock diffusivity different from that of greenstone, the total warm-up heat transfer is
then
By integration over time the total holding heat transfer is
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