Thermal conduction 17 explosion theory

Cook has propounded a rather different theory of the nature of the reaction zone. He emphasises that the demonstrable electrical conductivity of the detonation wave is evidence of a high thermal conductivity. Both these effects are ascribed to ionisation of the explosion products. In terms of the reaction zone, this implies a steady pressure with no peaks. 

A. Ma ek, ChemRevs 62, 44-47 (1962) (Thermal decomposition of explosives including a thermal explosion theory) 14) A.M. Grishin O.M. Todes, DoklAkadN 151(2), 366-68 (1963) CA 59, 12585(1963) (Thermal explosion with heat transfer by convection and conduction) 15) P.G. Ashmore T.A.B. Wesley, "A Test of Thermal-Ignition Theory in Autocatalytic Reactions , lOthSympCombstn (1965), pp 217-226... 

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,... 

The critical heat release rate following the Frank-Kamenetskii theory (see Section 13.4), which describes the passive behavior of the reactor without fluid circulation, when heat transfer occurs by thermal conduction only. The critical heat release rate is the highest power that does not lead to a thermal explosion and varies with the inverse of the squared radius ... 

Although direct measurement of reactant temperatures have enabled more quantitative assessment of such reactions, precise tests of thermal explosion theory require a reaction for which the mechanism and Arrhenius parameters are sufficiently well established to give accurate estimates of rates under explosive conditions. Typically the reaction rates involved will be around ten times those determined by static kinetic methods. In addition the thermal conductivity of each gas mixture used and the stoicheiometry and heat of reaction must be known. Pritchard and Tyler suggest the thermal isomerization of methyl isocyanide as a suitable candidate. They report temperature-time records for diluted mixtures in which temperature excesses of 70—80 K occur without explosion. However, the roll-call of missing data—improved heats of formation, isothermal kinetic data at higher temperatures, thermal conductivity measurements up to 670 K, and the recognition and elucidation of side reactions (if any) indicate the extent of further investigations necessary if their proposal is to be fully realized. 

A geometrical interpretation of the theory of thermal explosion in a conductive region is given. 

The accurate theory of thermal explosion (Frank-Kamenetskii) permits to estimate whether the explosion is a chain (chemical) or a thermal reaction. In particular, this theory yields a definite dependence of the explosion temperature on the reactor diameter which can be checked experimentally. This was conducted [145] for the third ignition limit of the detonating gas assumed to be of a thermal nature. 

Gray and Lee give an elegant review of the theory of thermal explosions. The first numerical solution of the nonlinear heat conduction equation with zero-order Arrhenius kinetics was obtained by Zinn and Mader. They did not use a finite difference scheme, and their results have been used as a standard for comparison with the faster and more general treatments like those in the TEPLO or SIN codes. 

J.W. Enig,. D. Shanks and R.W. Southworth, "The Numerical Solution of the Heat Conduction Equation Occurring in the Theory of Thermal Explosions," NAVORD Rept. 4377,... 

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