This is the first of two papers concerning an improved transient‐flow method for determining the thermal conductivity and diffusivity of insulating materials in bulk. The work was first suggested by the geophysical problem of determining the thermal constants of natural rock in situ. A cylindrical ``thermal probe,'' containing heat‐source and thermometer, is inserted in the medium and constants deduced from a record of probe temperature versus elapsed time; this method has been used before but the work described here is an attempt to eliminate, or evaluate the effect of, physical idealizations inherent in previous applications. The first paper is concerned with development of a new approximate mathematical treatment, using methods of the operational calculus first suggested by S. Goldstein, in 1932. A subsequent paper will deal with the experimental results obtained with the new theory.

Topics
Thermal conductivity, Thermal instruments, Operator theory, Flow simulations
1.
E. M. F.
van der Held
 and
F. G.
van Drunen
,
Physica
15
,
865
–
881
(
1949
);
Crossref
Search ADS
 
F. C.
Hooper
 and
F. R.
Lepper
,
J. Am. Soc. Heating Ventilating Engrs.
22
,
129
(
1950
).
2.
J. H.
Blackwell
 and
A. D.
Misener
,
Proc. Phys. Soc. (London)
A64
,
1132
(
1951
).
3.
S.
Goldstein
,
Proc. London Math. Soc.
34
,
51
(
1932
).
4.
H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Oxford University Press, London, 1947), p. 18.
5.
Reference 4, page 16.
6.
H. S. Carslaw and J. C. Jaeger, Operational Methods in Applied Mathematics (Oxford University Press, London, 1947), second edition, p. 76.
7.
Reference 6, p. 92.
8.
N. W. McLachlan, Complex Variable and Operational Calculus (Cambridge University Press, Cambridge, 1946), p. 100.
9.
Reference 4, p. 283.
10.
Reference 6, p. 278.
11.
For Case (i) see
J. H.
Blackwell
,
Can. J. Phys.
31
,
472
–
479
(
1953
).
Crossref
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12.
Ingersoll, Zobell, and Ingersoll, Heat Conduction (McGraw‐Hill, Book Company, Inc., New York, 1948), p. 255.
13.
Reference 4, p. 248.
14.
Reference 4, p. 284.
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© 1954 American Institute of Physics.
1954
American Institute of Physics
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