Heat release, finite rate

Composition of explosion prbducts changes during the course of their expansion. The chemical equilibrium hypothesis allows closure of the gasdy-namic conservation equations and calculations of the product composition without invoking the chemical kinetics equations. The rate of the change in concentrations of the reaction products depends on instantaneous values of the thermodynamic parameters of a flowing gas, its finiteness implies a certain deviation of the product composition and, consequently, of the heat released in the gas from their equilibrium counterparts. The chemical equilibrium model may be applied only in the case when this deviation is small. This defines the suflS.cient condition for model applicability to explosion products. 

The influence of the Raman process at To = 0.1 K can be well observed if we take into account a finite cooling rate. In comparison with the results using the one-phonon process only and for > 20 K, Q is smaller and shows a slightly different time dependence. Note that the results for Ti > 20 K resemble those obtained taking into account the one-phonon process only but with a smaller charging temperature T. We note also that at T) < 20 K the heat release still shows a rf-dependence but reaches its saturation at a smaller T) in comparison with the results with the one-phonon process only (Fig. 4.4). 

There are different attempts to link the high-temperature T> 10 K) with the low-temperature properties of disordered solids [13, 14]. In particular, it has been proposed that the maximum in the attenuation of phonons observed in amorphous materials at T > 10 K can be interpreted assuming a thermally activated relaxation of the two-level systems. In this Section we discuss the influence of thermally activated relaxation rate on the heat release for a finite cooling rate. 

Figure 4.5 Heat release at t = 1.5 x 10 s as a function of charging temperature Tj calculated with and without thermally activated processes and a finite cooling rate.

From the theoretical results, discussed above, and for a finite cooling rate, thermally activated relaxation (Eq. 16) should influence the absolute value of the heat release, but only slightly its time dependence in our time and temperature ranges. In Figure 4.16 we show the results of the numerical calculations with and without thermally activated processes for a charging temperature Ti = 80 K and using the parameters obtained from the acoustical data (Wmin 10 °). We note that the experimental data lie between the two computed curves (2)... 

Figure 4.16 Heat release as a function of time. ( ) PMMA at measuring temperature To = 0.090 K and cooling from Ti = 80 K ( ) Polystyrene (sample PSl) with Tq = 0.090 K and T = 80 K, (O) (sample PSl) with To = 0.300 K and Tj = 80 K. Bar PS the curves (1), (3), and (4) are calculated according to the tunneling model with finite cooling rate using the parameters from the fits to the acoustic data. R)r PMMA the curves (2) and (5) are calculated. In curves (1) and (2) no thermally activated processes are taken into account but for (3), (4) and (5). The parameter = 10 with exception of curve (4) where n,in = 6 x 10 has been chosen.

This section will examine the modeling of heat transfer, resin decomposition and both solid and gas phase eombustion using finite difference programming, as it has evolved from the physical Henderson model to more eomplex models which can discriminate the point of ignition and accurately prediet mass loss, temperature profiles, and the flux rates of volatile and heat release. 

The illusttation shows the conformity of the actual rate of heat release to the estimated one. The estimated line appears with a time lag of approximately 3 min due to the chosen finite estimation time of the Kalman-Bucy filter. 

Radiative heat transfer or thermal radiation is a distinctly separate mechanisms from conduction and convection for the transport of heat. Thermal radiation is associated with the rate at which energy is emitted by the material as a result of its finite temperature. The mechanism of emission is related to energy released as a result of oscillations or transitions of the many electrons that constitute the material. These oscillations are, in turn, supported by the internal energy for this reason the temperature drops. The emission of thermal radiation is thus associated with thermally excited conditions within the matter. 

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