## Abstract

In the conductive theory of thermal explosion, an exothermic system is considered to be an ignition hazard only if the numerical value of the dimensionless group δ = Qσa_{0} ^{2}A exp (- E/RT_{a} κ(RT_{a} ^{2}/E) exceeds a critical value. [Here Q is the exothermicity, σ the density, a_{0} the half-width, A exp(- E RT_{a}) the rate constant at ambient temperature, and κ the thermal conductivity.] This classical approach implicitly assumes that the material is initially assembled at or near to ambient temperature. Such initial conditions represent only a subclass of the whole problem. In some situations of technical importance the reactant may be initially considerably above T_{a}. The present paper considers the temperature evolution in bodies subject to Frank-Kamenetskii boundary conditions but which are assembled with a positive, uniform temperature-excess. It is shown that in the usual exponential approximation, any system with δ ≤ δ_{cr} has a critical initial temperature, above which thermal runaway occurs. Exact numerical results for the critical conditions are presented for the three class A geometries (infinite slab, infinite cylinder, and sphere). Very accurate analytical approximations are also provided. For an Arrhenius rate-law, ignition cannot occur in this way for very low δ < δ_{ex}, where δ_{ex} ∼ O[exp(-ε{lunate}^{- 1 2})] and ε{lunate} = RT_{a} E. A comparison is made between the predictions of this model and the critical conditions observed in an actual, practical example; the spontaneous ignition of piles of bagasse (extracted sugar cane) for which δ ≈ 0.02 ≪ δ_{cr}.

Original language | English |
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Pages (from-to) | 227-236 |

Number of pages | 10 |

Journal | Combustion and Flame |

Volume | 61 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 1985 |