Numerical estimation of thermal ignition conditions for reactive medium with Gaussian distribution of activation energy

The article investigates the solutions of the one-dimensional stationary integro-differential heat equation. The source of heat release is determined through the Gaussian distribution function of the activation energy. In such a statement, the critical conditions for the existence of a bounded solution depend on the distribution variance. With the help of numerical methods, such dependences are obtained; for their explanation, the analytical approximations of the thermal explosion theory are used.

Comments on the use of block methods for solving singular boundary value problems

Singular boundary-value problems appear frequently on the modellization of many physical phenomena as in catalytic diffusion reactions, chemical kinetics, thermal-explosion theory, or electro hydrodynamics, among others. The singular Lane-Endem equation is a typical kind of equation modelling some of those problems. Unfortunately, just in few occasions the exact solutions can be obtained. In this situation the block methods have been used largely for approximating different kind of differential problems. We propose its use for solving singular boundary value problems. The proposed strategy consist in a block method combined with an appropriate set of formulas which are developed at the first subinterval to circumvent the singularity at the left end of the integration interval. Some examples are presented to validate the efficiency of the proposed strategy.

The role of extinction on the re-ignition potential of wood-based embers in bushfires

The re-ignition potential of partially burnt wood-based embers was investigated theoretically by studying their extinction characteristics. An adaptation of Semenov’s thermal explosion theory was used in conjunction with a linear stability analysis to determine the critical particle size at which extinction occurs. Particles of various shapes were studied and the analysis was carried out for both thermally thin and thermally thick particles. The results of our analysis indicate that thermally thick embers are less susceptible to extinction than thermally thin ones and, as such, are more prone to re-ignition. The results also show that the extinction of wood embers is strongly affected by the particle temperature, particle shape, and reaction kinetics. The effects of ambient conditions were found to be less pronounced than particle properties.