Combustion fronts in a porous medium with two layers

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dc.creatorMota, Jesus Carlos da
dc.creatorSchecter, Stephen
dc.date.accessioned2017-09-12T18:41:25Z
dc.date.available2017-09-12T18:41:25Z
dc.date.issued2006
dc.description.resumoWe study a model for the lateral propagation of a combustion front through a porous medium with two parallel layers having different properties. The reaction involves oxygen and a solid fuel. In each layer, the model consists of a nonlinear reaction–diffusion–convection system, derived from balance equations and Darcy’s law. Under an incompressibility assumption, we obtain a simple model whose variables are temperature and unburned fuel concentration in each layer. The model includes heat transfer between the layers. We find a family of traveling wave solutions, depending on the heat transfer coefficient and other system parameters, that connect a burned state behind the combustion front to an unburned state ahead of it. These traveling waves are strong: they correspond to connecting orbits of a system of five ordinary differential equations that lie in the unstable manifold of a hyperbolic saddle and the stable manifold of a nonhyperbolic equilibrium. We argue that for physically relevant initial conditions, traveling waves that correspond to connecting orbits that approach the nonhyperbolic equilibrium along its center direction do not occur. When the heat transfer coefficient is small, we prove that strong traveling waves exist for a small range of system parameters, near parameter values where the two layers individually admit strong traveling waves with the same speed. When the heat transfer coefficient is large, we prove that strong traveling waves exist for a very large range of parameters. For small heat transfer, combustion typically does not occur simultaneously in the two layers; for large heat transfer, it does. The proofs use geometric singular perturbation theory. We give a numerical method to solve the nonlinear problem, and we present numerical simulations that indicate that the traveling waves we have found are in fact the dominant feature of solutions.pt_BR
dc.identifier.citationMOTA, J. C. da; SCHECTER, S. Combustion fronts in a porous medium with two layers. Journal of Dynamics and Differential Equations, Nova York, v. 18, n. 3, 2006.pt_BR
dc.identifier.doi10.1007/s10884-006-9019-0
dc.identifier.urihttp://repositorio.bc.ufg.br/handle/ri/12426
dc.language.isoengpt_BR
dc.publisher.countryBrasilpt_BR
dc.publisher.departmentInstituto de Matemática e Estatística - IME (RG)pt_BR
dc.rightsAcesso Abertopt_BR
dc.subjectReaction–diffusion–convection systempt_BR
dc.subjectTraveling wavept_BR
dc.subjectNonhyperbolic equilibriumpt_BR
dc.subjectGeometric singular perturbation theorypt_BR
dc.subjectMelnikov integralpt_BR
dc.titleCombustion fronts in a porous medium with two layerspt_BR
dc.typeArtigopt_BR

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