A Semenov approach to the modelling of thermal runaway of damp combustible material

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Abstract
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 changes due to evaporation/condensation are neglected but heat exchange is retained in the energy equation. By doing this, a simple easily solvable 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 evaporation/condensation on the overall thermal history. Using a simple model which treats the mass changes within the material as negligible, the competitive effects of condensation and evaporation are shown to produce a two-time situation which depends crucially on the surface mass transfer/heat transfer ratio hm . 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 achieved. Thus, compared to the dry case, in general terms, evaporation certainly encourages stability. However, the final strictly subcritical steady state will not always be achieved due to the competitive process between recondensation and evaporation loss at the surface at medium timescales. A set of quasi-steady states is identified which yield plots of a more restrictive critical value of temperature against the Frank-Kamenetskii parameter (proportional to the thickness of the slab and its reactivity). If the value of hm is such that the maximum temperature reaches this critical value, then thermal runaway can still take place even though the starting value of temperature was strictly below the true (damp) final steady-state critical value.

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