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巷道围岩变温圈趋于稳定时的外缘半径处温度变化率趋于零,可近似理解为“变温圈趋于稳定时,半径为R0处围岩环形面单位面积导热量趋于0”;将此特点描述为变温圈内导热微分方程求解的第二类边界条件,避免了求解温度场分布时复杂的积分问题,降低了求解难度.通过分离变量法将巷道围岩内部导热微分方程转换成斯特姆—刘维尔解问题;引入特征函数与范数,利用傅里叶—贝塞尔级数展开式与贝塞尔函数积分性质,推导得出巷道围岩内部温度分布函数,求得围岩内部温度分布函数在壁面的温度梯度,得到巷道围岩不稳定传热系数的解析式.采用MATLAB软件的计算功能,对比分析了推导得出的巷道围岩不稳定传热系数解析式的可信度与计算精度,表明推导得出的围岩内部温度分布函数及不稳定传热系数解析式是正确的、可信的.
When the temperature of the surrounding rock turns to be stable, the rate of temperature change tends to be zero, which can be approximated as "When the temperature warmer tends to be stable, the thermal conductivity per unit area of the surrounding rock ring radius tends to 0 This feature is described as the second type of boundary conditions for solving the differential thermal equation in a variable temperature loop, which avoids the problem of complicated integration when solving temperature field distribution and reduces the difficulty of solving the problem. The differential thermal equation Converting into Sturm-Liuville solution to the problem; introducing the eigenfunction and norm, using the integral property of Fourier-Bessel series expansions and Bessel functions, deriving the temperature distribution function of surrounding rock in tunnel Get the temperature distribution function of the surrounding rock temperature gradient in the wall to get the analytical solution of the unstable heat transfer coefficient of the surrounding rock of the roadway.Using the calculation function of MATLAB software to analyze and contrast the unsteady heat transfer coefficient of the surrounding rock of the roadway The results show that the analytic formula of temperature distribution function and unstable heat transfer coefficient in the surrounding rock are correct and credible.