Ignition thermal theory

The ignition criteria of the thermal theory of ignition are then represented by... 

Consideration of the history (to calculate quantities like ignition times) necessitates retention of time derivatives in the conservation equations. Just as in the previous section, to achieve the greatest simplicity we adopt a thermal theory, although in various applications that have been cited the full set of conservation equations has been considered. Let a reactive material occupy the region x > 0, and to avoid complications assume that the material remains at rest and has a constant density p, although coordinate transformations readily enable this assumption to be removed. Let the material, initially at temperature Tq, be exposed to a constant heat flux q — — A 5T/5x at X = 0 for all time t > 0, where A is the constant thermal conductivity of the material. The time-dependent equation for conservation of energy for the material, analogous to equation (9), is... 

Later, there were improvements in the thermal theories. Probably the most significant of these is the theory proposed by Zeldovich and Frank-Kamenetskii. Because their derivation was presented in detail by Semenov [4], it is commonly called the Semenov theory. These authors included the diffusion of molecules as well as heat, but did not include the diffusion of free radicals or atoms. As a result, their approach emphasized a thermal mechanism and was widely used in correlations of experimental flame velocities. As in the Mallard-Le Chatelier theory, Semenov assumed an ignition temperature, but by approximations eliminated... 

T. Boddington, P. Gray and D. I. Harvey, Thermal Theory of Spontaneous Ignition Criticality in Bodies of Arbitrary Shape, Phil. Trans. Roy. London, 270, 471 (1971). 

Thermal theories. Fire-retardant chemicals may increase the thermal conductivity of the wood to dissipate the heat from the surface faster than it is supplied by the igniting source, or they may affect chemical and physical changes so that heat is absorbed by the chemical, preventing the wood surface from igniting. 

The problems of simultaneously treating spatial distributions of both temperature and concentration are currently the concern of the chemical engineer in his treatment of catalyst particles, catalyst beds, and tubular reactors. These treatments are still concerned with systems that are kineticaliy simple. The need for a unified theory of ignition has been highlighted by contemporary studies of gas-phase oxidations, many features being revealed that neither thermal theory, nor branched-chain theory for that matter, can resolve alone. A successful theoretical basis for such reactions necessarily involves the treatment of both the enorgy balance and mass balance equations. Such equations are invariably coupled and cannot be solved independently of each other. However, much information is offered by the phase-plane analj s of the syst (e.g. stability of equilibrium solutions, existence of oscillations) without the need for a formal solution of the balance equations. 

Figure 4 Self-healing accompanying oxidation of hydrogen sulphide. Contour lines for temperature rises of 0, 10, 20, 30, and 40 K. The line L corresponds to the predicted ignition limit from purely thermal theory...

THERMAL THEORY OF SPONTANEOUS IGNITION IN CLOSED SYSTEMS... 

In the search for a better approach, investigators realized that the ignition of a combustible material requires the initiation of exothermic chemical reactions such that the rate of heat generation exceeds the rate of energy loss from the ignition reaction zone. Once this condition is achieved, the reaction rates will continue to accelerate because of the exponential dependence of reaction rate on temperature. The basic problem is then one of critical reaction rates which are determined by local reactant concentrations and local temperatures. This approach is essentially an outgrowth of the bulk thermal-explosion theory reported by Fra nk-Kamenetskii (F2). 

Although the thermal-ignition theory was developed for double-base propellants, several investigators have attempted to correlate the ignition characteristics of composite propellants using this approach. Baer and Ryan (Bl) have correlated ignition data for a polysulfide-ammonium perchlorate... 

Two observations on the correlations can be made. First, these results tend to invalidate one of the major objections to the application of the thermal-ignition theory to composite propellants, namely that heterogeneous interfacial reactions within the solid phase are not possible. Secondly, the effect of pressure on propellant ignitability can be qualitatively explained. 

Peaking and Non-isothermal Polymerizations. Biesenberger a (3) have studied the theory of "thermal ignition" applied to chain addition polymerization and worked out computational and experimental cases for batch styrene polymerization with various catalysts. They define thermal ignition as the condition where the reaction temperature increases rapidly with time and the rate of increase in temperature also increases with time (concave upward curve). Their theory, computations, and experiments were for well stirred batch reactors with constant heat transfer coefficients. Their work is of interest for understanding the boundaries of stability for abnormal situations like catalyst mischarge or control malfunctions. In practice, however, the criterion for stability in low conversion... 

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