Mathematical Model of Heat and Mass Transfer of Coal in a Stack

Abstract

A mathematical model of coal’s self-heating in the stack is presented, where the heat exchange and gas exchange processes are described by a system of two non-linear differential equations of the second order concerning temperature t of coal’s self-heating and volume fraction C of oxygen in the cavities of the stack with boundary and initial conditions. The differential equations took into account that self-heating of coal in the stack and initiation of self-ignition are observed in a relatively small layer adjacent to the surface of the stack and called the zone of oxygen influence. In this mathematical model authors have taken into account the influence on the process of coal’s self-heating of parameter Ф – specific heat release power, which in addition characterises the preservation of coal during storage. There were also used such physical parameters as thermal conductivity, diffusion coefficient, specific heat capacity of coal in the stack, bulk density, thermal effect of oxidation, stack cavity, temperature coefficient of exponential growth of heat release power when compiling the differential equations. For numerical implementation of this mathematical model, there were introduced dimensionless variables and criteria, which allowed to apply the grid method. Analysis of the final results allowed to obtain: changes in stack temperature profiles in time; changes in stack oxygen concentration profiles in time; influence on stack temperature profile of specific heat release power; influence on stack temperature profile of the parameter characterising exponential growth of heat release intensity with increasing temperature. It has been found that the greatest influence on the dynamics of self-heating of coal in the stack has the Lykov criterion, proportional to the diffusion coefficient, and the Nusselt criterion related to the effective thermal conductivity and the effective thermal diffusivity of coal. The results obtained 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 impaired heat dissipation. Self-heating and the transition of self-heating into ignition is associated with the occurrence of turbulent diffusion in the stack, arising from increased heat blowing, the effect of which can be enhanced when directed perpendicular to the surface of the stack.