TM-5-855-4
(1) To overcome this problem, two approximate methods of calculation have been evolved. These
methods are based on analytical numerical solutions evaluated by means of the digital computer
facilities of the National Bureau of Standards (NBS).
(2) The first method is a graphical solution which, in this manual, was curve fitted to allow
analytic representation with elementary functions covering the whole design range.
(3) The other method is a shortcut method based on the results of a series of tests also conducted by
the NBS. Though less specific than the first method, this alternate is useful for preliminary calculations.
3-2. Underground conduction standard calculation method.
a. The standard calculation method is the recommended method for estimating heat transfer to rock.
It is based on relating the radial heat transfer characteristics of a cylindrical or spherical cavity of the
same sidewall area to the more complicated three-dimensional conduction around the rectangular space
actually utilized.
(1) The term "rectangular space" is used in this chapter to describe the rectangular parallelepipeds
of length L, width W, and height H commonly used for manmade underground rooms. For practical
reasons, it will be assumed that H and W are respectively limited to 20 feet and 50 feet, and satisfy
equation 3-1.
(eq 3-1)
(2) If the ceiling is arched, or if other major irregularities in shape exist, or if there are doors or
partitions of significant size, the corresponding adjustments are obvious and will not be discussed.
Projected areas can be used because irregularities left in walls, ceilings, or floors after blasting or
excavation may safely be ignored.
b. The total exposed area of the rectangular space is
A
(eq 3-2)
When compared to a cylinder of length L and lateral area A, or to a sphere of total area A, the the heat
transfer from this rectangular space always exceeds the radial heat transfer from either of the other two
shapes. The shape that best approximated the rectangular space is the one with the highest wall flux ratio
Y. For elongated spaces,
(eq 3-3)
the cylinder is the better fit with a radius rl
(eq 3-4)
(eq 3-5)
For shorter spaces, the sphere is preferred with radius r2
(eq 3-6)
and wall flux ration Y2 (figure 3-1) or
3-2
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