Effect of Momentum and Heat Losses on the Hydrodynamic Instability of a Premixed Equidiffusive Flame in a Hele–Shaw Cell

The linear stage of hydrodynamic instability of a laminar premixed flame propagating in a Hele–Shaw cell is investigated. Our theoretical model takes into account momentum and heat losses, temperature-dependent transport coefficients, and the continuous internal structure of the flame front. The dispersion relation is obtained numerically as a solution to an eigenvalue problem for the linearized governing equations. The obtained results are in good qualitative and quantitative agreement with previous studies. It is shown that the wall heat losses tend to weaken the hydrodynamic flame instability. On the contrary, momentum losses enhance the flame instability. It is demonstrated that for the adiabatic walls, an increase in the Hele–Shaw cell width results in a reduction of the instability growth rate. For the non-adiabatic walls, there is a competition between momentum and heat losses in narrow channels that may result in a non-monotonic dependence of the instability growth rate on the Hele–Shaw cell width. It is shown that the effects of the Prandtl number and the thermal expansion vary with the wall heat loss coefficient. A possibility of non-monotonic dependence of the maximum instability growth rate on the thermal expansion has been demonstrated.