An approximate equation is given for the solution of the rapidly heated or naturally cooled long highly-conducting cylinder in a conducting medium. The range of validity and accuracy of the approximation are indicated. The analogy with a loaded transmission line is shown, by which is illustrated the different types of solution according to the magnitude of the ratio of the effective specific heat of the cylinder to the specific heat of the medium. Some formulae for the rapid computation over certain ranges of the error integral with a complex argument are given.
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Samuel C. Whitehead (1944) studied this question.