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The Quarterly Journal of Mechanics and Applied Mathematics 1966 19(2):167-181; doi:10.1093/qjmam/19.2.167
© 1966 by Oxford University Press
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APPROXIMATE METHODS FOR TWO-DIMENSIONAL PROBLEMS IN HEAT FLOW

J. CRANK and I. B. PARKER

( Brunel College )

Approximate methods are developed for the solution of two-dimensional problems in which the flow of heat is predominantly in one direction. Two advantages of the methods are that they are less laborious for numerical evaluation than the classical solution in the form of a double infinite series and extensions can be made to cover some non-linear situations. New light is thrown on what are commonly regarded as ‘thin-sheet’ solutions in which a constant profile of temperature is assumed to be a good approximation. Consideration of the rate of heat loss from the surfaces as well as of thickness is seen to be necessary.


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