| 摘要: |
| 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. |
| 关键词: 巷道围岩 传热 温度分布 不稳定传热系数 分离变量法 |
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| A calculation method of temperature distribution and unsteady heat transfer coefficient in control-heat circle of roadway |
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| Abstract: |
| The outer edge radius temperature tends to zero when control-heat circle of roadway surrounding rock to be stable,can be interpreted as:“when the control-heat circle tends to be stable,at radius R0,the circle surface of the surrounding rock, the conduction of per unit area heat tends to zero”,and this characteristic was described as the second boundary-condition for the solutions of heat conduction differential equation in the control-heat circle,in this way,avoided the complicated integral problems of temperature distribution and reduced the difficulty;by the method of variables separation,the heat conduction differential equation in rocks converted to Sturm-Liouville problems;through introducing the eigenfunction and norm,and using the Fourier-Bessel series expansion and the integral properties of Bessel function,the wall surface temperature gradient and the unsteady heat transfer coefficient formula in roadway surrounding rock was obtained.By using the computing functions of MATLAB software,the reliability and accuracy of the unsteady heat transfer coefficient formula were compared and analyzed in roadway surrounding rock,the results showed that the temperature distribution function in rocks and the unsteady heat transfer coefficient formula are correct and believable. |
| Key words: roadway surrounding rock heat transfer temperature distribution unsteady heat transfer coefficient separation of variables |
