The article presents a mathematical model of coal self-heating in the stack in which the heat exchange and gas exchange processes are described by a system of two non-linear differential equations of the second order with respect to the temperature t of coal self-heating and the volume fraction C of oxygen in the voids of the stack with boundary and initial conditions. The differential equations took into account that self-heating of coal in the stack and appearance of spontaneous combustion are observed in a relatively small layer adjacent to the surface of its contact with the air and called the zone of oxygen influence. In the mathematical model, the influence on the process of coal self-heating of parameter F- specific heat release power was taken into account, which in addition characterises the stability of coal during storage. When compiling the differential equations, such physical parameters as thermal conductivity, diffusion coefficient, specific heat capacity of coal in the stack, bulk density, thermal effect of oxidation, stack voidness, temperature coefficient of exponential growth of heat release power were also used. For numerical implementation of the mathematical model, dimensionless variables and criteria were introduced, which allowed us to apply the net method. Analysis of the obtained results allowed to get: change in the stack temperature profiles with time; change in the stack oxygen concentration profiles with time; influence on the stack temperature profile of the specific heat release power; influence on the stack temperature profile of the parameter characterizing exponential growth of heat release intensity with temperature increase. It has been determined that the dynamics of coal self-heating in the stack is mostly influenced by the Lykov criterion, proportional to the diffusion coefficient, and the Nusselt criterion related to the effective thermal conductivity and to the effective thermal diffusivity of coal. The obtained results suggest that self-heating in the stack is due on the one hand to intensive penetration of air oxygen and on the other hand to a weakened heat transfer. Self-heating and the transition of self-heating into ignition are associated with the occurrence of turbulent diffusion in the stack, arising from increased thermal blowing, whose impact can be enhanced by directing it perpendicular to the surface of the stack.
Heat-release equation of state and thermal conductivity of warm dense carbon by proton differential heating
