TY - JOUR

T1 - Multiplicity and stability of travelling wave solutions in a free boundary combustion-radiation problem

AU - Baconneau, O.

AU - van den Berg, G.J.B.

AU - Brauner, C.-M.

AU - Hulshof, J.

N1 - MR2056330

PY - 2004

Y1 - 2004

N2 - We study travelling wave solutions of a one-dimensional two-phase Free Boundary Problem, which models premixed flames propagating in a gaseous mixture with dust. The model combines diffusion of mass and temperature with reaction at the flame front, the reaction rate being temperature dependent. The radiative effects due to the presence of dust account for the divergence of the radiative flux entering the equation for temperature. This flux is modelled by the Eddington equation. In an appropriate limit the divergence of the flux takes the form of a nonlinear heat loss term. The resulting reduced model is able to capture a hysteresis effect that appears if the amount of fuel in front of the flame, or equivalently, the adiabatic temperature is taken as a control parameter.

AB - We study travelling wave solutions of a one-dimensional two-phase Free Boundary Problem, which models premixed flames propagating in a gaseous mixture with dust. The model combines diffusion of mass and temperature with reaction at the flame front, the reaction rate being temperature dependent. The radiative effects due to the presence of dust account for the divergence of the radiative flux entering the equation for temperature. This flux is modelled by the Eddington equation. In an appropriate limit the divergence of the flux takes the form of a nonlinear heat loss term. The resulting reduced model is able to capture a hysteresis effect that appears if the amount of fuel in front of the flame, or equivalently, the adiabatic temperature is taken as a control parameter.

U2 - 10.1017/S0956792503005333

DO - 10.1017/S0956792503005333

M3 - Article

SN - 0956-7925

VL - 15

SP - 79

EP - 102

JO - European Journal of Applied Mathematics

JF - European Journal of Applied Mathematics

IS - 1

ER -