Thermal diffusivity of the condensed phase

Similar to the expression for the condensed phase, the thermal diffusivity in the gas phase is given by g = Xg/pgCg and is assumed to be independent of temperature. The thermal wave thickness in the gas phase 6g is defined according to 6g = Og/Mg. Then, Eq. (3.46a) can be written as ... 

In the case of combustion of a condensed substance, conservation of enthalpy and similarity occur only in the gas phase and only in part of the space. In the c-phase the diffusion coefficient is much smaller than the thermal diffusivity, and we have heating of the c-phase by heat conduction without dilution by diffusion. The enthalpy of the c-phase at the boundary, for x — 0 (from the side x < 0), is larger than the enthalpy of the c-phase far from the reaction zone and larger than the enthalpy of the combustion products. The advantage of the derivation given here is that the constancy of the enthalpy in the gas phase and its equality to H0 (H0 is the enthalpy of the c-phase far from the combustion zone, at x — —oo) are obtained without regard to the state of the intermediate layers of the c-phase. We should particularly emphasize that the constancy of the enthalpy in the combustion zone occurs only for a steady process. The presence of layers of the c-phase with increased enthalpy opens the possibility in a non-steady process of a temporary change in the enthalpy of the gas and the combustion temperature (on this see 5). 

The course of this process can be subdivided into several steps, in which a series of resistances have to be overcome. The fraction of these individual resistances in the total resistance can be very different. First, as a result of flow (convective transport) and molecular motion (diffusion transport), the vapour reaches the phase interface. In the next step the vapour condenses at the phase interface, and finally the enthalpy of condensation released at the interface is transported to the cooled wall by conduction and convection. Accordingly, three resistances in series have to be overcome the thermal resistance in the vapour phase, the thermal resistance during the conversion of the vapour into the liquid phase, and finally the resistance to heat transport in the liquid phase. 

The condensed phase density p, specific heat C, thermal conductivity A c, and radiation absorption coefficient Ka are assumed to be constant. The species-A equation includes only advective transport and depletion of species-A (generation of species-B) by chemical reaction. The species-B balance equation is redundant in this binary system since the total mass equation, m = constant, has been included the mass fraction of B is 1-T. The energy equation includes advective transport, thermal diffusion, chemical reaction, and in-depth absorption of radiation. Species diffusion d Y/cbfl term) and mass/energy transport by turbulence or multi-phase advection (bubbling) which might potentially be important in a sufficiently thick liquid layer are neglected. The radiant flux term qr... 

Intumescent additives functioning in the condensed phase form a thermal barrier that protects the substrate and limits diffusion of combustible gases out of the substrate and oxygen into the substrate. Significant effort in developing these systems is underway, as they are characterized by relatively low heat release. 

Detailed investigations of the reaction of Csl with boric acid in the condensed phase over the temperature range 400-1000 C under Ar, Ar-H2, and Ar—Ha-steam atmospheres were performed by Bowsher and Nichols (1985). The results showed that Csl decomposition in these reactions starts at temperatures above 400 °C and increases considerably beyond 700 °C, with the HI produced being partly converted to I2 (and/or iodine atoms) by thermal dissociation. Under such conditions, HI as well as I2 may react with the iron and nickel content of stainless steels under formation of the corresponding iodides (see below). Up to 960 °C, Csl and molten boric acid or boron oxide react in a diffusion-controlled reaction the rate of which is determined by the diffusion of the partners to the reaction zone. The reaction data measured in these experiments were consistent with Arrhenius law, showing an activation energy of 190 30kJ/mol. 

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