### Abstract

A qualitative model for studying shock-wave chemistry interactions in combustion theory is introduced. The model studied bears the analogous relationship to reacting gas flow as Burgers' equation does to ordinary compressible fluid flow. When the corresponding physical assumptions of the Chapman-Jouget and von Heumann-Zeldovich-Doring theories are introduced in this model, explicit and completely analogous phenomena occur. Without any approximations, combustion profiles with finite reaction rate and finite diffusion are examined in detail. In the context of this model, the validity of the approximate theories mentioned above depends on the relative size of two critical parameters - the energy liberated by chemical reaction and a parameter which measures the ratio of the width of the shock layer to the reaction zone.

Original language | English (US) |
---|---|

Pages (from-to) | 70-93 |

Number of pages | 24 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 41 |

Issue number | 1 |

State | Published - Aug 1981 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*41*(1), 70-93.

**QUALITATIVE MODEL FOR DYNAMIC COMBUSTION.** / Majda, Andrew.

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 41, no. 1, pp. 70-93.

}

TY - JOUR

T1 - QUALITATIVE MODEL FOR DYNAMIC COMBUSTION.

AU - Majda, Andrew

PY - 1981/8

Y1 - 1981/8

N2 - A qualitative model for studying shock-wave chemistry interactions in combustion theory is introduced. The model studied bears the analogous relationship to reacting gas flow as Burgers' equation does to ordinary compressible fluid flow. When the corresponding physical assumptions of the Chapman-Jouget and von Heumann-Zeldovich-Doring theories are introduced in this model, explicit and completely analogous phenomena occur. Without any approximations, combustion profiles with finite reaction rate and finite diffusion are examined in detail. In the context of this model, the validity of the approximate theories mentioned above depends on the relative size of two critical parameters - the energy liberated by chemical reaction and a parameter which measures the ratio of the width of the shock layer to the reaction zone.

AB - A qualitative model for studying shock-wave chemistry interactions in combustion theory is introduced. The model studied bears the analogous relationship to reacting gas flow as Burgers' equation does to ordinary compressible fluid flow. When the corresponding physical assumptions of the Chapman-Jouget and von Heumann-Zeldovich-Doring theories are introduced in this model, explicit and completely analogous phenomena occur. Without any approximations, combustion profiles with finite reaction rate and finite diffusion are examined in detail. In the context of this model, the validity of the approximate theories mentioned above depends on the relative size of two critical parameters - the energy liberated by chemical reaction and a parameter which measures the ratio of the width of the shock layer to the reaction zone.

UR - http://www.scopus.com/inward/record.url?scp=0019599446&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0019599446&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0019599446

VL - 41

SP - 70

EP - 93

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 1

ER -