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The influence of the flow of the reacting gas on the conditions for a Thermal Explosion

G. I. Barenblatt·A. J. Chorin·A. Kast
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Abstract

The classical problem of thermal explosion is modified so that the chemically active gas is not at rest but is flowing in a long cylindrical pipe. Up to a certain section the heat-conducting walls of the pipe are held at low temperature so that the reaction rate is small and there is no heat release; at that section the ambient temperature is increased and an exothermic reaction begins. The question is whether a slow reaction regime will be established or a thermal explosion will occur. The mathematical formulation of the problem is presented. It is shown that when the pipe radius is larger than a critical value, the solution of the new problem exists only up to a certain distance along the axis. The critical radius is determined by conditions in a problem with a uniform axial temperature. The loss of existence is interpreted as a thermal explosion; the critical distance is the safe reactor's length. Both laminar and developed turbulent flow regimes are considered. In a computational experiment the loss of the existence appears as a divergence of a numerical procedure; numerical calculations reveal asymptotic scaling laws with simple powers for the critical distance.

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G. I. Barenblatt, A. J. Chorin, A. Kast. 1999-09-17. The influence of the flow of the reacting gas on the conditions for a Thermal Explosion. https://arxiv.org/abs/math/9909105

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