Download or read book Lectures on Mathematical Combustion written by John D. Buckmaster and published by SIAM. This book was released on 1983-12-01 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lectures on Mathematical Combustion Lecture 2 Governing Equations Asymptotics and Deflagrations written by J. D. Buckmaster and published by . This book was released on 1983 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Lectures on Mathematical Combustion Lecture 1 Pre Asymptotic Combustion Revisited written by and published by . This book was released on 1983 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lectures on Mathematical Combustion written by J. D. Buckmaster and published by Society for Industrial and Applied Mathematics. This book was released on 1983-12-01 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Problems from Combustion Theory written by Jerrold Bebernes and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph evolved over the past five years. It had its origin as a set of lecture notes prepared for the Ninth Summer School of Mathematical Physics held at Ravello, Italy, in 1984 and was further refined in seminars and lectures given primarily at the University of Colorado. The material presented is the product of a single mathematical question raised by Dave Kassoy over ten years ago. This question and its partial resolution led to a successful, exciting, almost unique interdisciplinary col laborative scientific effort. The mathematical models described are often times deceptively simple in appearance. But they exhibit a mathematical richness and beauty that belies that simplicity and affirms their physical significance. The mathe matical tools required to resolve the various problems raised are diverse, and no systematic attempt is made to give the necessary mathematical background. The unifying theme of the monograph is the set of models themselves. This monograph would never have come to fruition without the enthu siasm and drive of Dave Eberly-a former student, now collaborator and coauthor-and without several significant breakthroughs in our understand ing of the phenomena of blowup or thermal runaway which certain models discussed possess. A collaborator and former student who has made significant contribu tions throughout is Alberto Bressan. There are many other collaborators William Troy, Watson Fulks, Andrew Lacey, Klaus Schmitt-and former students-Paul Talaga and Richard Ely-who must be acknowledged and thanked.
Download or read book Lectures on Combustion Theory written by Samuel Z. Burstein and published by . This book was released on 1978 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Mathematical Combustion Lecture 7 Pulsating Flames written by J. D. Buckmaster and published by . This book was released on 1983 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: In section 5. it was found that plane NEFs to sufficiently large Lewis number are unstable. Since Im(a) 0 on the stability boundary, the instability is likely to result in either a pulsating flame or a flame that supports traveling waves. Such flames are the subject of this lecture.
Download or read book Lectures on Mathematical Combustion Lecture 10 Free Boundary Problems written by J. D. Buckmaster and published by . This book was released on 1983 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: Throughout these lectures we have ensured that the reaction terms vanish everywhere except in a thin (flame) sheet, whose location has to be found as part of the solution. So far this free boundary has been either a plane, a circular cylinder, a sphere, or a perturbation of one of these; we now consider problems with more complicated free boundaries. (Author).
Download or read book Lectures on Combustion Theory written by S. Z. Burstein and published by . This book was released on 1978 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Mathematical Combustion Lecture 3 General Deflagrations written by J. D. Buckmaster and published by . This book was released on 1983 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Lectures on Mathematical Combustion Lecture 6 Cellular Flames written by J. D. Buckmaster and published by . This book was released on 1983 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: We shall now examine the left stability boundary that was uncovered in lecture 5 in our discussion of NEFs (figure 5.3). The boundary is associated with instabilities leading to cellular flames, i.e. flames whose surfaces are broken up into distinct luminous regions (cells) separated by dark lines. Each line is a ridge of high curvature, convex towards the burnt gas. For a nominally flat flame these cells are very unsteady, growing and subdividing in a chaotic fashion; but curvature, for example, can make stationary.
Download or read book Lectures on Mathematical Combustion Lecture 8 Counterflow Diffusion Flames written by J. D. Buckmaster and published by . This book was released on 1983 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental characteristic of diffusion flames is that the two reactants, fuel and oxidizer, are supplied in different parts of the combustion field, so that they must come together and mix by diffusion before reaction can take place. Counterflowing streams provide one method of bringing them together; the resulting diffusion flames, whose main properties were established by Linan, is the subject of this lecture.
Download or read book Lectures on Mathematical Combustion Lecture 4 SVFs and NEFs written by J. D. Buckmaster and published by . This book was released on 1983 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: For want of a complete analysis of multidimensional flows in preasymptotic days, it was natural to try to identify special characteristics that play particularly important roles in the understanding of flame behavior. Flame speed and temperature are examples of such characteristics that have already been identified; a more subtle characteristic, introduced by Karlovitz, is flame stretch. The authors start by discussing this concept, so as to have it available when we come to discussing general slowly varying and near-equidiffusional flames. (Author).
Download or read book The Mathematics of Combustion written by John D. Buckmaster and published by SIAM. This book was released on 1985-01-01 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book delves into the rapidly changing area of combustion, in which asymptotic methods and bifurcation theory have made a significant impact as have the constant-density, small-heat-release models and other important contributions.
Download or read book Lectures on Mathematical Combustion Lecture 9 Spherical Diffusion Flames written by J. D. Buckmaster and published by . This book was released on 1983 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: Law has shown that the analysis of spherical diffusion flames is quite similar to that of counterflow diffusion flames, so that some explanation is needed for devoting a separate lecture to them. There are two good reasons. First, the constant-density approximation has been used throughout these lectures in discussing all but plane flames, so there is room for a problem which does not neglect variations in density. (Plane diffusion flames have to be chambered, i.e. the reactants must be supplied at finite locations, which leads to distracting complications). Secondly, the spherical diffusion flame can lead to quite different (and unusual) responses. These arise in the technologically important application to the quasi-steady phase of fuel-drop burning, when a more realistic boundary condition than the conventional one is used. (Author).
Download or read book Reacting Flows written by G. S. S. Ludford and published by American Mathematical Soc.. This book was released on 1986-12-31 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: These two volumes represent the culmination of the Special Year `84-'85 in Reacting Flows held at Cornell University. As the proceedings of the 1985 AMS/SIAM Summer Seminar in Applied Mathematics, the volumes focus on both mathematical and computational questions in combustion and chemical reactors. They are addressed to researchers and graduate students in the theory of reacting flows. Together they provide a sound basis and many incentives for future research, especially in computational aspects of reacting flows. Although the theory of reacting flows has developed rapidly, researchers in the two subareas of combustion and chemical reactors have not communicated. The main goal of this seminar was to synthesize the mathematical theory and bring it to the interface with large-scale computing. All of the papers have high research value, but the first five introductory lectures should be especially noted.
Download or read book Lecture Notes on Fundamentals of Combustion written by and published by Joseph Michael Powers. This book was released on with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt:
