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On Certain Types of Solution of the Equation of Heat Conduction

Published online by Cambridge University Press:  18 May 2009

Stewart Paterson
Stewart Paterson
Affiliation:
Imfebial Chemical Industries Ltd Nobel Division Research Department Stevenston
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Let f(x, y, z, t) satisfy the equation

For certain purposes, particularly in connection with the propagation of a boundary of fusion etc., it is of interest to discover solutions of (1) which permit the equation:

to be solved explicitly in the form:

This suggests the examination of solutions of the type

where

and f, ϕ, ψ are functions to be determined. To save repetition, Roman capitals denote arbitrary constants throughout.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 1 , Issue 1 , January 1952 , pp. 48 - 52
Copyright
Copyright © Glasgow Mathematical Journal Trust 1952