TM-5-855-4
c. Size. The effect of the size of the chamber is reflected in the equivalent radius rl defined in
equation 3-4 as a function of the three dimensions L, W, and H. of the space. The radius rl appears only
in the first term of the denominator of the warm-up flux. This resistance term increases with r 1 but less
than linearly due to the smaller argument of the logarithm. As a result, the warm-up flux decreases as the
radius increases, a trend clearly shown in the figures.
d. Rock conductivity k and diffusivity a.
(1) The warm-up flux will increase with k in the numerator but less than linearly because of the
simultaneous but slower increase of the thermal resistance shown in the denominator. The second term
in the denominator is proportional to k, but the first increases only through the argument of the logarithm.
This argument increases with the diffusivity, which in turn varies as the conductivity when the heat
capacity, which is the product of the density and the specific heat, is constant.
(2) What is true of the conductivity is then also applicable to the diffusivity; an increase in the
diffusivity of the rock will increase the amount of heat necessary to warm up a given space in a given
time. This fact is clearly reflected in the higher fluxes of figure 3-17, which is based on the higher
conductivity and diffusivity when compared to the corresponding points of figure 3-18.
e. Heat transfer coefficient U.
(1) This parameter is a measure of the surface conductance and is inversely proportional to the
thermal resistance or insulation of the boundary. The 1.2 U value is that of bare rock while the 0.4 U value
represents a certain amount of extra insulation between the rock and the space, such as would be provided
by an internal structure.
(2) The warm-up flux decreases as the U value with the addition of insulation. However, the
internal resistance of the rock represented by the first term in the denominator increases with the warm-
up time, and for long warm-up periods the flux reduction is much less pronounced than for shorter ones.
As a result, both sets of curves converge with time as shown on figures 3-16 and 3-18.
period. They are based on substituting f(F1, B) from equation 3-15 and Y1 from equation 3-5 into equation
3-14 to compute the thermostatted flux q as a function of time. The trend of the different parameters is
qualitatively the same as those discussed above for the warm-up conditions.
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