Combustion pseudo-waves in a system with reactant consumption and heat loss. (English) Zbl 0887.35154
Summary: A model for the combustion of a reactant with heat loss in an infinite two-dimensional layer or an infinitely long circular cylinder is derived. Using center manifold techniques the model is shown to reduce to a one-dimensional model on an infinite region for both geometries. For an exothermic first-order reaction with Arrhenius temperature dependence, a numerical method is used to calculate solutions and comparisons are made with the no-reactant consumption case. Traveling pseudo-waves are shown to exist and their speeds determined. A first-order estimate of the reaction zone thickness, obtained by perturbation methods, is shown to be in excellent agreement with the full numerical solution.
MSC:
| 35Q80 | Applications of PDE in areas other than physics (MSC2000) |
| 80A25 | Combustion |
Keywords:
flame width; traveling pseudo-waves; model for the combustion of a reactant; center manifold techniques; numerical methodReferences:
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