The previously developed approach to modelling of critical phenomena, based on the geometrical theory of singular perturbations and asymptotic expansions by Mishchenko-Rozov, is generalised to the case of non-adiabatic combustion with limited supply of oxygen and non-integer chemical reaction rates. The results of the asymptotic analysis of these phenomena are presented and discussed. The combustion process is described in terms of the system of three ordinary differential equations for ambient gas temperature and fuel and oxygen vapour mass fractions, using the Arrhenius form of the chemical term. It is pointed out that depending on the values of the input parameters the solution to this system describes either slow combustion or explosion. The transition between these solutions is described in terms of the critical phenomenon. The mathematical results are applied to the analysis of the final stage of the combustion process in Diesel engines (when all fuel droplets have evaporated). It is pointed out that in relatively large engines the explosion is most likely to be expected, while there is a possibility for the development of the slow combustion in small engines. (c) 2022 The Author(s). Published by Elsevier Inc. on behalf of The Combustion Institute. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )
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