Modelling forest fires. Part I: a complete set of equations derived by extended irreversible thermodynamics

In this study we derive a three-dimensional forest fire combustion model. The forest is modelled as a diphasic medium composed of a gaseous and a porous vegetal pyrolysis phase. A formal averaging method and a thermodynamic closure by use of extended irreversible thermodynamics are used to give a complete set of coupled non-linear equations for this diphasic medium. This set of equations deals with the processes of drying, the pyrolysis of the vegetal phase, and the combustion of the pyrolysis gases in this gaseous phase. A three-dimensional reaction diffusion equation for the forest fire propagation with a non-local radiation term is then derived under some simplified hypotheses.