by A thesis submitted to the University of Plymouth in ... - PEARL home

Hutchings (1938) as having developed the approximate solution for this
particular problem. Whitehead (1944) was chiefly concerned with heat
conduction effects to and from underground pipes and cables.
Carslaw and Jaeger (1948 pp. 280-286) noted that their solution for radial heat
transport in a composite cylinder, e. g. a thermal probe within a cylindrical or
infinite sample, "corresponds roughly to the transient heating of a buried cable
carrying electric current" although "a still closer approximation" would include
contact resistance between the cable and the surrounding medium. This contact
resistance was also described as outer or exterior conductivity, termed H, with
units WM-2 K-1 (Carslaw and Jaeger, 1948 pp. 13-14). H was considered a
constant, with the heat flux between two touching faces of material given as
H(T, -T2), showing that its effect was dependent on the temperature difference
between the two faces. No calculations were given to allow the determination of
H theoretically, although some example values were given. These showed that,
at similar temperatures
and pressures, H could vary greatly between one
material, e. g. a thermal probe, and various other materials, such as water and
air
It was maintained that, where a heat flux existed across two materials,
temperature at their touching surfaces could only be assumed equal where
there was intimate contact, such as in a soldered joint. A contact resistance
would still exist even where two optically flat surfaces were pressed together
(Carslaw and Jaeger, 1948 pp. 17-18).
This was carried forward to a description of thermal resistivity in a composite
wall where the total thermal resistance was described as being made up of the
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