Reaction Behavior of Porous TiAl3 Intermetallics Fabricated by Thermal Explosion with Different Particle Sizes

Porous TiAl3 intermetallics were prepared by the thermal explosion (TE) and space holder method with different particle sizes of Ti and Al powders, and their reaction behaviors were investigated. The results showed that with the increase in the particle size of the Ti and Al powders, the interfacial contact between the particles decreased, resulting in low interfacial energy and reaction activity, making the process difficult to initiate. Meanwhile, the heat flow rose from 358.37 J/g to 730.17 J/g and 566.74 J/g due to the extension of the solid–liquid diffusion time. The TiAl3 structures obviously expanded, and the formation of connected pore channels promoted the porosity. Only when the Ti and Al particle sizes were both small did the solid–solid diffusion significantly appear. At the same time, the TE reaction weakened, so the product particles had no time to fully grow. This indicates that the particle size of the raw materials controlled the TE reaction process by changing the solid–liquid diffusion reaction time and the degree of solid-phase diffusion.

Thermal explosion characteristics of a combustible gas containing fuel droplets

This paper investigated the critical ignition conditions of combustible gas containing liquid fuel droplets. The analysis is done based on the criteria of the thermal explosion theory. It includes analytical and numerical solutions of modeling equations of fuel droplets heating and evaporation by convection and radiation from the surrounding reactive hot gas. The exothermic reaction is usually modeled as a single-step reaction obeying an Arrhenius temperature dependence. The thermal conductivity of the fuel droplet is dependent on temperature. The analytical solution produced relations between the main critical characteristic parameters in all planes of the solution. The results obtained from investigating the effect of the characteristic parameters on the explosion behavior of gas and fuel droplets and the thermal radiation proved that both of them are significant. The study proved that the criticality definitions of the thermal explosion of a single-phase system can be used effectively and efficiently to determine the critical conditions of a multi-phase system. Finally, the application of the numerical solutions of the modeling equations was used to analyze the explosion characteristics of a diesel fuel spray system.

Positive Solutions for a Singular Elliptic Equation Arising in a Theory of Thermal Explosion

In this paper, the thermal explosion model described by a nonlinear boundary value problem is studied. Firstly, we prove the comparison principle under nonlinear boundary conditions. Secondly, using the sub-super solution theorem, we prove the existence of a positive solution for the case K(x)>0, as well as the monotonicity of the maximal solution on parameter λ. Thirdly, the uniqueness of the solution for K(x)<0 is proved, as well as the monotonicity of the solutions on parameter λ. Finally, we obtain some new results for the existence of solutions, and the dependence on the λ for the case K(x) is sign-changing.