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An estimate of the thermal conductivity was needed to determine the
Biot number. This was obtained by calculating the volumetric heat
capacitance of the soil based upon the mass average of the various
constituents of the soil as described by DeVries (1975). The thermal
conductivity was determined by rearranging equation (4-2) and
substitution of the values of thermal diffusivity and volumetric heat
capacitance. The Biot number for the sample could then be calculated
and used to determine aj. The error (e) in the thermal diffusivity
associated with calculation of the eigenvalues was calculated using
equation (4-12). If the absolute value of the error was greater than
107 then the thermal diffusivity was calculated using the new
eigenvalue. This iterative procedure was repeated until the error
calculated by substitution of the previous value of aj for (aj)*, was
less than 107.
The values of thermal diffusivity for each of the nine tests for
each water content and density treatment were averaged to determine the
mean value of the thermal diffusivity (Figure 4-3). The error bars
shown in Figure 4-3 indicated the 95 % confidence limits associated
with the experimental measurement and were approximately 5 percent of
the mean for each. Thermal diffusivity was found to increase with
increasing density (Figure 4-3). However, the relative change in
diffusivity from a density of 1300 to 1500 kg/m3 was larger than the
change from 1500 to 1600 kg/m3. The thermal diffusivity increased with
water content to a maximum then decreased as water content continued to
increase. Initially the soil pore spaces were filled predominantly
with air. Air has a relatively low thermal conductivity and volumetric
heat capacitance. Contact area between soil particles was also limited