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Note on the application of complex integration to the equation of Conduction of Heat, with special reference to Dr Peddie's problem

Published online by Cambridge University Press:  20 January 2009

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1. In Dr Peddie's problem of a sphere cooling in a well-stirred liquid, the conditions to be satisfied by the temperature v(r, t) are

(i) For every positive t, and every r from 0 to a, v is to be finite and one-valued, and is to possess finite derivatives , satisfying

(ii) For every positive t, and r = a,

where p = ⅓ (capacity of liquid)/(capacity of sphere).

(iii) = a given arbitrary function f(r), for every r less than a.

(iv) = initial temperature of liquid = 0 suppose.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1900