Numerical Modeling of the Ignition Characteristics of a Cylindrical Heat-Generating Sample in a Medium with Stochastic Temperature Variations

Abstract

The problem of thermal stability of a cylindrical sample with nonlinear heat generation placed in a medium with the ambient temperature random walk was studied. The behavior of this system was examined depending on the parameters of the problem (heat generation intensity, random walk variance). A numerical algorithm based on averaging multiple random trajectories of the ambient temperature was proposed. A numerical method was developed for solving the heat transfer problem with the heat source and stochastic boundary which combines both explicit and implicit schemes for linearized transfer equations and the Euler–Maruyama method. The distributions of ignition characteristics and their moments were obtained. Their dependencies on the parameters of the problem were investigated.

Keywords

• thermal explosion
• stochastic differential equation
• mathematical modeling
• monte carlo method