煤自然发火期计算模型及其解析解

考虑对流、导热及源项作用，建立了均质、各向同性松散煤体最短自然发火期解算控制方程。采用泰勒级数、等价无穷小对源项进行处理，认为计算温度步长应小于2.4 K；以环交换理论为基础，通过行波约化将偏微分方程转化为常微分方程，并采用首次积分法给出了控制方程的一个解析解。在寻找控制方程解析解的过程中，建立了以划分温度区间、分别求解各温度区间的经历时间，进而通过累加获得煤自然发火期的计算方法。通过将多种已知煤样的计算结果与现有文献结果对比分析，验证了解析解计算结果的合理性。

An analytic solution of coal spontaneous combustion period calculation model

Considering convection，thermal conductivity and source term，a governing equation for calculating the shortest spontaneous combustion period of homogeneous and isotropic coal had been established.Taylor series and equivalent infinitesimal ware used to deal with the source term，and the temperature step should be less than 2.4 K.Based on the ring exchange theory，the nonlinear partial differential equation was transformed into an ordinary differential equation by using travelling wave reduced form method，and a reasonable solution of the equation was obtained by using the integral method.In the process of seeking analytical solution of the governing equation，a calculation cumulatively method of coal spontaneous combustion was obtained by dividing the temperature range and solving the time of temperature interval respectively.By comparing calculation results of several coal samples and literatures，the rationality of analytical solution was verified.