The dynamics of thermal explosion in a fuel droplets/hot air mixture is investigated using the geometrical version of the method of integral manifolds. The results are applied to the modelling of the ignition process in diesel engines. Effects of the thermal radiation, semi-transparency of droplets and oxidizer are taken into account. In contrast to the previous studies, the difference between gas temperature (responsible for convective heating of droplets) and external temperature (responsible for radiative heating of droplets) is taken into account. The dynamics of the explosion is presented in terms of the dynamics of a multi-scale, singularly perturbed system. The relevant parametric regions of this system are analyzed. Explicit analytical formulae for the ignition delay in the presence of thermal radiation are derived. It is shown that the effect of thermal radiation can lead to considerable reduction (up to about 30%) of the total ignition delay time.

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We introduce and study certain distributions generalizing the operation of curvilinear integration for the case where the path of integration is not rectifiable. Then we apply that distributions for solving of boundary value problems of Riemann-Hilbert type in domains with non-rectifiable boundaries.

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We consider interactions of smooth and discontinuous germs as generalized integrations over non‐rectifiable paths with applications in theory of boundary value problems of complex analysis. Copyright © 2017 John Wiley & Sons, Ltd.