Prediction of the steady flame spread rate by the principle of minimal entropy production

Abstract

The propagation of a two-dimensional diffusive flame over a combustible material is studied by solving steady-state conservation equations written in the coordinate system fixed on the flame front. The analysis of a two-dimensional problem featuring flame spread rate as an eigenvalue has shown that there is no unique solution relative to the flame spread rate unless some additional condition is involved. A novel approach to the prediction of flame spread rate is proposed using the principles of irreversible thermodynamics. The steady flame propagation is considered as a stationary non-equilibrium thermodynamic state, which can be characterized, according to the formulation of Prigogine, by minimal entropy production. A numerical algorithm for the prediction of flame spread rate has been developed and tested on the investigation of downward flame spread over thin sheets of paper. The adequate physical background of the proposed approach and satisfactory agreement with experimental data have been shown.