Analytical research on dynamic temperature field of overburden in goaf fire-area under piecewise-linear third boundary condition

Abstract

During the process of underground coal spontaneous combustion (UCSC) in mine goaf, the coal and country rocks (roof overburden) in the vicinity of coal fire are subjected to high temperature which may be in excess of 1000°C. Coal fires impose significant geomechanical changes to the overburden, which are called as combustion-metamorphic or burnt rocks. The highest temperature distribution in overburden decides the degree and range of burnt rocks. In order to study the temperature field evolution law and obtain the highest temperature distribution in overburden during the whole process of coal fire development (heating, continuous high-temperature and cooling stages) in mine goaf, we established a one-dimensional unsteady heat conduction mathematical model of convective heat transfer between overburden and boundary airflow whose temperature varies piecewise linearly, and the non-dimensional temperature analytical solution of one-tier super thick overburden is gained by using Laplace transform and inversion formula. The results show that: during heating and continuous high-temperature stages, temperature in overburden increases continually, and the maximum temperature have been located at the overburden boundary; during cooling stage, temperatures at each point increase first and then decrease, and the peak values of temperature curves decrease gradually and move to the interior of overburden; during the whole process of heat conduction, there is an envelope curve of temperature curve-cluster in overburden, and the highest temperature values at each point are determined by envelope curve. The envelope curve provides a basis for the range calculation under different threshold temperature, and by determining the judgement standards of burnt range and temperature influence range, their ranges are obtained by the envelope curve respectively. The influence of thermal conductivity coefficient k, specific heat capacity c, convective heat transfer coefficient h, Biot number Bi, and Fourier number Fo on envelope curves and heat-increment distribution were also analyzed.