Abstract
Here we briefly summarize the derivation that follows from this correction. We are interested in determining the heat loss from a tube of water as it flows through permafrost (which is in a cyclic steady state) as shown schematically in Figure 1. Referring to Figure 1, we equate the heat lost from the water, _ mc[Tw(1) Tw(2)], to the heat flowing out through the sides of the pill box, f 2prD z, where Tw(1) is the temperature of the water at point 1, Tw(2) is the temperature of the water at point 2, z is the height of the pill box, r is the radius of the pill box, and f is the radial heat flow through the sides of the pill box and is approximated (cylindrical symmetry is approximately valid) by
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