Results 1 
3 of
3
High Lewis number combustion wavefronts: a perturbative Melnikov analysis
 SIAM J. Appl. Math
"... Abstract. The wavefronts associated with a onedimensional combustion model with Arrhenius kinetics and no heat loss are analyzed within the high Lewis number perturbative limit. This situation, in which fuel diffusivity is small in comparison to that of heat, is appropriate for highly dense fluids. ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
(Show Context)
Abstract. The wavefronts associated with a onedimensional combustion model with Arrhenius kinetics and no heat loss are analyzed within the high Lewis number perturbative limit. This situation, in which fuel diffusivity is small in comparison to that of heat, is appropriate for highly dense fluids. A formula for the wavespeed is established by a nonstandard application of Melnikov’s method and slow manifold theory from dynamical systems, and compared to numerical results. A simple characterization of the wavespeed correction is obtained: it is proportional to the ratio between the exothermicity parameter and the Lewis number. The perturbation method developed herein is also applicable to more general coupled reactiondiffusion equations with strongly differing diffusivities. The stability of the wavefronts is also tested using a numerical Evans function method. Key words. Combustion waves, high Lewis number, Melnikov’s method, slow manifold reduction, Evans function AMS subject classifications. 80A25, 35K57, 35B35, 34E10, 34C37
Virtual Commons Citation
"... Golovaty, Dmitry; Gross, Laura K.; and Joyner, James T. (2010). Frontal reaction in a layered polymerizing medium. In Mathematics ..."
Abstract
 Add to MetaCart
(Show Context)
Golovaty, Dmitry; Gross, Laura K.; and Joyner, James T. (2010). Frontal reaction in a layered polymerizing medium. In Mathematics
A Mathematical Study of Onestep Models of Polymerization
"... ABSTRACT A mathematical model for the free radical polymerization in the presence of the material diffusion is presented. We assume both the temperature of the mixture and the initial monomer concentration depends on the space variable. By actual solutions, we prove the existence and uniqueness of ..."
Abstract
 Add to MetaCart
ABSTRACT A mathematical model for the free radical polymerization in the presence of the material diffusion is presented. We assume both the temperature of the mixture and the initial monomer concentration depends on the space variable. By actual solutions, we prove the existence and uniqueness of solution of the model. We show that temperature is nondecreasing function of time. We use the parameterexpanding method and seek direct eigenfunctions expansion to obtain analytical solution of the model. The results are presented graphically and discussed. It is discovered that the mixture temperature and monomer concentration are significantly influenced by the FrankKamenetskii number, material diffusion coefficient and thermal diffusivity of the mixture.