Lectures on Mathematical Combustion. Lecture 2. Governing Equations, Asymptotics, and Deflagrations
Lectures on Mathematical Combustion. Lecture 2. Governing Equations, Asymptotics, and Deflagrations

Author: J. D. Buckmaster

Publisher:

Published: 1983

Total Pages: 24

ISBN-13:

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The problem of formulating the governing equations of combusion consists, as its simplest, in characterizing the flow of a viscous, heat-conducting mixture of diffusing, reacting gases. This is a formidable task that could fill a week of lectures by itself, most of which would not be of great interest to a mathematical audience. Mindful of this, we shall limit ourselves to a description, rather than a derivation, of the simplest equations that can be brought to bear on combustion problems. Only the most important assumptions normally used to justify the equations will be discussed; for a more extensive treatment the reader is referred to Buckmaster & Ludford (1982).

Lectures on Mathematical Combustion
Lectures on Mathematical Combustion

Author: John D. Buckmaster

Publisher: SIAM

Published: 1983-12-01

Total Pages: 127

ISBN-13: 089871186X

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An introduction to far-reaching developments in theoretical combustion, with special emphasis on flame stability, a topic that has, to date, benefited most from the application of modern asymptotic methods. The authors provide a modern view of flame theory, and a complete description of the longstanding ignition and explosion problems, including the solutions that were made available independently by Kapila and Kassoy through activation-energy asymptotics, the main theme of this monograph.

Energy Research Abstracts
Energy Research Abstracts

Author:

Publisher:

Published: 1983

Total Pages: 756

ISBN-13:

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Includes all works deriving from DOE, other related government-sponsored information and foreign nonnuclear information.

Lectures on Mathematical Combustion. Lecture 1. Pre-Asymptotic Combustion Revisited
Lectures on Mathematical Combustion. Lecture 1. Pre-Asymptotic Combustion Revisited

Author:

Publisher:

Published: 1983

Total Pages: 26

ISBN-13:

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The description of reacting systems can be simplified when the so- called activation energy is large; the notion is an old one, but its full power is only released by modern singular perturbation theory. More than forty years ago, Frank-Kamenetskii introduced approximations based on large activation energy to construct a thermal theory of spontaneous combustion, and we shall start there. His problem, which neglects the fluid-mechanical effects of main concern to us, focuses attention on the reaction and thereby acts as a precursor for the lectures that follow. The problem and its generalizations have been the happy hunting grounds of mathematical analysts for many years, but it was not until quite recently that a complete description of the ignition and explosion processes was made available of Kapila and Kassoy (working separately) through activation-energy asymptotics, the main theme of these lectures.

Lectures on Mathematical Combustion. Lecture 3. General Deflagrations
Lectures on Mathematical Combustion. Lecture 3. General Deflagrations

Author: J. D. Buckmaster

Publisher:

Published: 1983

Total Pages: 22

ISBN-13:

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In the last lecture we examined the plane, steady, adiabatic, premixed flame and deduced an explicit formula for its speed. By using judicious choice of parameters this formula can be made to agree roughly with experiment; precision is not a reasonal goal, given the crude nature of our model. Noteworthy is the extreme sensitivity of the speed to variations in the flame temperature: an 0(1) change generates an exponentially large change in flame speed. Such variations in speed (caused, for example, by changes in mixture strength) are not excessive numerically (at least for fuels burnt in air), because activation energies and fractional changes in temperature are modest; but in an asymptotic analysis they present a potential obstacle to discussion of multidimensional and/or unsteady flames. Then signigicant variations, spatial and/or temporal, in the flame temperature can be expected and, if the sensitivity mentioned above is any guide, there will be correspondingly large spatial and/or temporal variations in the flame speed. A mathematical framework in which to accommodate these is not obvious. (The first lecture dealt with special circumstances for which such variations were manageable).

The Mathematics of Combustion
The Mathematics of Combustion

Author: John D. Buckmaster

Publisher: SIAM

Published: 1985-09-04

Total Pages: 258

ISBN-13: 0898710537

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Explores the rapidly changing area of combustion, in which asymptotic methods and bifurcation theory have made a significant impact.