巷道变温圈内温度分布及不稳定传热系数求解方法

发布时间：2018-04-28 18:24

本文选题：巷道围岩 + 传热　；参考：《湖南科技大学学报(自然科学版)》2015年04期

【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.
[Abstract]:When the surrounding rock temperature circle of roadway tends to be stable, the rate of temperature change at the radius of the outer edge tends to be zero, which can be roughly understood as "when the variable temperature circle tends to be stable," The heat conductivity per unit area of surrounding rock annular plane at radius R0 tends to be 0 ", which is described as the second kind of boundary condition for solving heat conduction differential equation in variable temperature circle, which avoids the complex integral problem and reduces the difficulty in solving the temperature field distribution. The differential equation of heat conduction in surrounding rock of roadway is transformed into Stem-Liuville solution by the method of separating variables, the characteristic function and norm are introduced, and the Fourier Bessel series expansion and the integral property of Bessel function are used. The temperature distribution function of surrounding rock of roadway is derived, the temperature gradient of temperature distribution function of surrounding rock is obtained, and the analytical formula of unstable heat transfer coefficient of surrounding rock of roadway is obtained. By using the calculation function of MATLAB software, the reliability and calculation accuracy of the analytical formula of unsteady heat transfer coefficient of surrounding rock of roadway are analyzed and compared. It is shown that the analytical expressions of temperature distribution function and unstable heat transfer coefficient of surrounding rock are correct and reliable.
【作者单位】：湖南科技大学能源与安全工程学院;煤矿安全开采技术湖南省重点实验室;
【基金】：湖南省科技计划资助项目(2012FJ2001) 国家自然科学基金资助项目(51074072,51134005)
【分类号】：TD727.2

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