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Equations of Heat Conduction with Slow Combustion

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posted on 2021-11-07, 23:21 authored by Wake, Graeme C

A study is made of the equations of heat conduction with slow combustion. A mathematical model is established from an interpretation of the physical model, with a few simplifying assumptions. This gives rise to a coupled pair of partial differential equations which are the direct concern of this thesis, the dependent variables being the temperature and reactant concentration as functions of position and time. The model is shown to possess a unique solution for which some properties, such as Lipschitz conditions etc., are established. An investigation into the use of a comparison theorem is given, in which it is shown that no direct comparison theorem is possible for this and related systems. However, it is also shown that it is possible to obtain upper and lower estimates by appealing to the physical model. A discussion of the boundary layer is given and this is followed by a detailed discussion of stability. The latter has been one of the main concerns of earlier authors on this system. Their use of a space-averaging process to establish a criterion for stability is also discussed. Probably one of the most interesting features of this system is the subclass of problems for which the reactant is exhausted in a finite time. These hare been named the "cut-off" problems and they can be likened to the free boundary problems in fluid dynamics. A discussion of the cut-off problem is given with particular examples chosen to illustrate the main features. This thesis, contains no material which has been accepted for the award of any other degree or diploma in any University and to the best of my knowledge and belief, the thesis contains no material previously published or written by another person, except where due reference is made in the text of the thesis.

History

Copyright Date

1967-01-01

Date of Award

1967-01-01

Publisher

Te Herenga Waka—Victoria University of Wellington

Rights License

Author Retains Copyright

Degree Discipline

Mathematics

Degree Grantor

Te Herenga Waka—Victoria University of Wellington

Degree Level

Doctoral

Degree Name

Doctor of Philosophy

Victoria University of Wellington Item Type

Awarded Doctoral Thesis

Language

en_NZ

Victoria University of Wellington School

School of Mathematics, Statistics and Computer Science

Advisors

McNabb, A; Mackie, A G