Thermal explosion coefficient

Let us compare this result with Semenov s [2] interpretation of thermal explosion (Fig. 2), which operates with quantities averaged over the volume. When the coefficient of heat transfer per unit volume is decreased (which may be accomplished by increasing the dimensions of the vessel) we obtain consecutively two steady solutions At and A2, the explosion limit B, and absence of steady solutions for still smaller heat transfer (line C). 

The model presented for a thermal explosion predicts that for a reaction mixture of fixed composition and fixed initial temperature, there will be a critical pressure above which explosion will occur and below which a normal stationary reaction will take place. The relation between the critical pressure and temperature is given by a modified Arrhenius equation with a negative temperature coefficient [Eq. (XIV.3.8)] which is... 

CVD also has a number of disadvantages. One of the primary disadvantages lies in the properties of the precursors. Ideally, the precursors need to be volatile at near-room temperatures. This is non-trivial for a number of elements in the periodic table, although the use of metal-organic precursors has eased this situation. CVD precursors can also be highly toxic (Ni(CO) ), explosive (B Hg), or corrosive (SiCl ). The byproducts of CVD reactions can also be hazardous (CO, H, or HP). Some of these precursors, especially the metal-organic precursors, can also be quite costly. The other major disadvantage is the fact that the films are usually deposited at elevated temperatures. This puts some restrictions on the kind of substrates that can be coated. More importantly, it leads to stresses in films deposited on materials with different thermal expansion coefficients, which can cause mechanical instabilities in the deposited films. 

From the literature analyses we see that organic fillers have thermal expansion coefficients (TEC) values close to those of thermoplasts [7], they have low abrasiveness, their density is similar to that of thermoplasts [6, 8] but as a rule, their grindig is difficult [9], they are combustible and explosive, not thermostable and not always cheap [9]. Mineral fillers are comparatively easy to grind, their cost is low, they are thermostable and non-combustible, but their TEC s are an order lower than those of thermoplasts. As a rule, their density 2-3 times higher than the thermoplasts [6]. Their abrasiveness is too high. 

The initial conditions are (p = 1 and 6 = 6q (Tq — T )E/(R Ti) at t = 0. The simplest approximation to the function /(cp) is / — cp. Here a is the ratio of a transfer coefficient for fuel to that for heat, 6 is a ratio of the thermal energy at wall temperature to the activation energy (see Section B.3), y is a ratio of the thermal energy at wall temperature to the total energy released by the reaction, and eyS is the ratio of the cooling time to the characteristic time of chemical reaction at the wall temperature. Frank-Kamenetskii [28] has emphasized that in combustion, the parameters e and y are small. He also introduced the parameter 3, defined in equation (55), as occupying a role of central importance in thermal explosions. 

The theory on light induced thermal explosions is limited. Some theoretical analysis can be found in [27-30]. The photothermal initiation mechanism is complicated because of phase changes, melting, sublimation and vaporation processes, which are not usually taken into account. The same holds for the change of the absorption and reflection coefficient by these processes. 

Such reactions have been used to explain the three limits found in some oxidation reactions, such as those of hydrogen or of carbon monoxide with oxygen, with an "explosion peninsula between the lower and the second limit. However, the phenomenon of the explosion limit itself is not a criterion for a choice between the critical reaction rate of the thermal theory and the critical chain-branching coefficient of the isothermal-chain-reaction theory (See Ref). For exothermic reactions, the temperature rise of the reacting system due to the heat evolved accelerates the reaction rate. In view of the subsequent modification of the Arrhenius factor during the development of the reaction, the evolution of the system is quite similar to that of the branched-chain reactions, even if the system obeys a simple kinetic law. It is necessary in each individual case to determine the reaction mechanism from the whole... 

This is of the same form as Equation 30, but involves the mixed diffusion coefficient, Jci9, instead of the thermal conductivity of the mixture. However, as seen from the kinetic theory of gases, the thermal conductivity is proportional to the diffusion coefficient. Therefore agreement of experimental results with either Equation 30 or 53a is not an adequate criterion for distinguishing between first explosion limits in branching chain reactions and purely thermal limits. It has been reported (52), that, empirically,... 

Coefficient of Thermal Conductivity or Specif, ic Heat Conductivity ( is the quantity of heat transmitted per second thru a plate of material 1cm thick and 1cm2 in area, when the temp difference between the two sides of the plate is one degree centigrare. Some values are given in Ref and under individual compds described in this Encyclopedia Ref Clift Fedoroff, Vol 2(1943), Table of Physical Constants of Compounds Used in Explosives Industry and Definition of Terms Used in Table of Physical Constants [See also S. Nagayama Y.Mizushima KKK 21, 8-11 (I960) CA 55, 9877 (1961) Explosivst 1964, 2l]... 

Explosives and Binders Coefficients of Thermal Expansion CTE, Glass Transition Temperatures Tgr and Pressed Densities... 

Once the values of the two coefficients, a and b, of Eq. (59) holding for the induction period of the quasi-autocatalytic reaction of 2 cm of a powdery chemical of the quasi-AC type confined in the closed cell and subjected to the isothermal storage test are fixed, it becomes possible to calculate, for the chemical, in the same manner as performed for a high explosive of the true AC type, an arbitrary value of T as well as the SADT, corresponding to an arbitrary value of At, i.e., an arbitrary exposure time, such as 1 h, 1 d or 30 d. Such a value of temperature may be useful as the upper limit temperature in temperature control to prevent the chemical from exploding thermally after the corresponding exposure time. 

---