139
shifts only by its intercept with the slope remaining constant.
Therefore, accurate placement of the temperature sensor is not critical
to obtaining an accurate measure of the thermal diffusivity.
Gaffney et al. (1980) discussed possible sources of error in the
determination of thermal diffusivity using this technique. A major
source of error was in the determination of the first eigenvalue (aj).
Since the eigenvalues are functions of the Biot number it is imperative
that the Biot number be determined accurately. Many times the Biot
number has been assumed to approach an infinite value. Gaffney et al.
(1980) stated that the Biot number should be at least 200 for the error
introduced by the assumption of an infinite Biot number to be
negligible. If the Biot number is less than 200, then a finite value
for the Biot number should be used to determine aj. The error
introduced was given as
(4-12)
1
Luikov (1968) presented an empirical relationship for determining the
first eigenvalue within 0.1 % for a finite Biot number.
(4-13)
The constants, I, s and (aj),,, are functions of geometry and are
presented in Table 4-2 for the cases of a sphere, an infinite cylinder
and an infinite slab.
Another factor to be considered in the measurement of the thermal