Mathematical modelling of a slow flameless combustion of a two-dimensional paper

We present a mathematical model for the slow combustion (smoldering) of a two-dimensional sheet of paper. We describe the evolution of the char region, and we investigate the effects of an orthogonal air flow on the shape of the combustion front. The mathematical formulation consists in a set of two nonlinear PDEs for the temperature and the oxygen concentrations coupled with one ODE for the cellulose concentration. The (dimensionless) problem is solved numerically by means of a spectral collocation scheme based on Chebyshev polynomials. Our results show that the Péclet and the Lewis number strongly influence the shape of the ignition front and that the advancement of the combustion front does not occur if advection and diffusion are neglected (zero Péclet and Lewis numbers). In particular we observe that the burning region and the ignition front are strongly influenced by the velocity of the airflow and by the mass and heat transport phenomena due to diffusion and advection. We shall see that the increasing of the ratio between the convective and diffusive characteristic times (Péclet number) and the decreasing of the ratio between the mass and heat diffusive characteristic times (Lewis number) have a “flattening effect” on the combustion front.