Heat and mass transport in developing chars

摘要

The physics of heat and mass transport in chars is explored in the context of a developing char layer. The most important features of the problem are discussed and a section of the relevant literature is briefly reviewed. A mathematical model is then developed and analysed in order to illustrate some of the important phenomena. The model relates to the simplified case of a polymer which degrades to produce char and volatile gases in a single step at a critical temperature. Transport of gas through the char is modelled by Darcy's law and for simplicity it is assumed that there is no overall volume change as char is formed. Conservation of mass, Darcy's law and the perfect gas law are combined to give a non-linear diffusion equation describing the evolution of pressure in the developing char. This equation, together with equations expressing conservation of energy in the char and the virgin polymer and appropriate boundary/initial conditions complete the description. Exact solutions are derived for isothermal conditions in the char and these are used to frame the numerical results for the full model. A key parameter in the model is a dimensionless number λ akin to the Lewis number, namely the ratio of pressure diffusivity to thermal diffusivity. Generally, for realistic parameter values, λ is very large and the results show that under such conditions the developing char offers no resistance to the flow of gases. In other words, one may effectively assume that the mass flux of volatile gases through the char is uniform. Numerical solutions of the full model are presented and discussed and the question of integrity of the char is briefly explored.