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of the copper were known, the convective heat transfer coefficient
could be calculated from the slope of the logarithmic plot of the
temperature ratio and the Fourier number.
Results and Discussion
The determination of the thermal diffusivity of each sample
required that the slope of the logarithm of the dimensionless
temperature ratio as a function of time be determined. The bath
temperature used in calculation of the temperature ratio was the time
averaged bath temperature over the length of the test. The logarithm
of the temperature ratio was then plotted against time (Figure 4-1) for
the sample. The slope of the line was obtained by linear regression
for the data excluding the initial and final transients. The R2 values
for the regressions were 0.995 or greater This procedure was
conducted for each of the samples and the corresponding data for the
copper cylinder (Figure 4-2).
Using the solution of the transient heat conduction equation
(equation 4-4) and the transcendental equation for an infinite cylinder
(equation 4-6) the convective heat transfer coefficient was calculated
from the slope of the copper cylinder temperature response curve.
Values of the convective heat transfer coefficient ranged from 4400 to
5900 W/m2 oK. Next, it was assumed that the Biot number for the soil
sample was infinite. Using the value of (al), the radius of the
cylinder and the slope of the temperature response, an initial estimate
of the thermal diffusivity was determined from the following
Dt = R2 (4-14)
a2
1