Thermal Explosion under Oscillations of the External Temperature

Abstract

†Classical thermal explosion theory implies that the external temperature T 0 is constant. Such an approach was pioneered by Semenov, Frank-Kamenetskii, Todes, and Merzhanov and colleagues. These works and formulas therein laid the foundations of the quantitation of conditions for the safe performance of many chemical engineering processes in which exothermal reactions take place. In addition, safe experimental methods of studying thermal explosion under laboratory conditions have been developed for small samples of individual substances and reactive mixtures (see [1] and references therein). Initiation of thermal explosion at a variable temperature T 0 has heretofore been considered only as applied to a linear increase in this temperature with time [2, 3]. Such processes directly refer to the theory and practice of differential thermal analysis. Considering the conditions of initiation of thermal explosion under oscillations of temperature T 0 is not only of theoretical interest but is also important for the quantitation of fire and explosion hazard parameters in particular systems. For example, in experiments for studying thermal explosion, a sample under consideration is placed in an appropriate thermostat (liquid or gas). It is evident that the temperature specified by an experimenter oscillates about some average value T ∗ with more or less constant amplitudes ∆ T and frequencies f = ( t 0 is the oscillation period). It is important to determine how strongly these parameters affect the parametric boundary (the so-called critical condition) that separates the area of thermal explosion from the area of the nonexplosive proceeding of a reaction. The solution of this problem is even more important for studying numerous processes of self-heating and selfignition of natural materials. As is known, self-heating that results in self-ignition of peat, straw, dry grass, etc., is a reason for numerous forest fires. It is worth noting that self-ignition processes under natural conditions † Deceased. 1 t0 evolve in the presence of relatively high-frequency (diurnal) and low-frequency (seasonal) oscillations of air temperature, their amplitude being rather large. The necessity of studying thermal explosion under oscillations of the external temperature was justified and the first calculations that characterize qualitative features of the process were performed in [4]. The present work is focused on an analysis of the effect of the frequency and amplitude of T 0 oscillations on the critical condition of thermal explosion.