A SEMENOV APPROACH TO THE MODELING OF THERMAL RUNAWAY OF DAMP COMBUSTIBLE MATERIAL

Semenov theory for the self-heating of a reactive slab is extended to take account of the presence of water vapour. In this paper, mass chan ges due to evaporation/condensation are neglected but heat exchange is retained in the energy equation. By doing this, a simple easily solva ble set of equations can be set up to represent the thermal behaviour of the slab. No account is taken of possible wet exothermic reactions in this paper. The aim is simply to understand the effects of evaporat ion/condensation on the overall thermal history. Using a simple model which treats the mass changes within the material as negligible, the c ompetitive effects of condensation and evaporation are shown to produc e a two-time situation which depends crucially on the surface mass tra nsfer/heat transfer ratio h(m). Either self-heating occurs at a lower rate than that due to dry oxidation, or else a maximum temperature is reached before a lower equilibrium steady-state temperature is achieve d. Thus, compared to the dry case, in general terms, evaporation certa inly encourages stability. However, the final strictly subcritical ste ady state will not always be achieved due to the competitive process b etween recondensation and evaporation loss at the surface at medium ti me-scales. A set of quasi-steady states is identified which yield plot s of a more restrictive critical value of temperature against the Fran k-Kamenetskii parameter (proportional to the thickness of the slab and its reactivity). If the value of h(m) is such that the maximum temper ature reaches this critical value, then thermal runaway can still take place even though the starting value of temperature was strictly belo w the true (damp) final steady-state critical value.