本文選題：巷道圍巖 + 傳熱　； 參考：《湖南科技大學(xué)學(xué)報(bào)(自然科學(xué)版)》2015年04期

【摘要】：巷道圍巖變溫圈趨于穩(wěn)定時(shí)的外緣半徑處溫度變化率趨于零,可近似理解為"變溫圈趨于穩(wěn)定時(shí),半徑為R0處圍巖環(huán)形面單位面積導(dǎo)熱量趨于0";將此特點(diǎn)描述為變溫圈內(nèi)導(dǎo)熱微分方程求解的第二類邊界條件,避免了求解溫度場(chǎng)分布時(shí)復(fù)雜的積分問(wèn)題,降低了求解難度.通過(guò)分離變量法將巷道圍巖內(nèi)部導(dǎo)熱微分方程轉(zhuǎn)換成斯特姆—?jiǎng)⒕S爾解問(wèn)題;引入特征函數(shù)與范數(shù),利用傅里葉—貝塞爾級(jí)數(shù)展開(kāi)式與貝塞爾函數(shù)積分性質(zhì),推導(dǎo)得出巷道圍巖內(nèi)部溫度分布函數(shù),求得圍巖內(nèi)部溫度分布函數(shù)在壁面的溫度梯度,得到巷道圍巖不穩(wěn)定傳熱系數(shù)的解析式.采用MATLAB軟件的計(jì)算功能,對(duì)比分析了推導(dǎo)得出的巷道圍巖不穩(wěn)定傳熱系數(shù)解析式的可信度與計(jì)算精度,表明推導(dǎo)得出的圍巖內(nèi)部溫度分布函數(shù)及不穩(wěn)定傳熱系數(shù)解析式是正確的、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.
【作者單位】： 湖南科技大學(xué)能源與安全工程學(xué)院;煤礦安全開(kāi)采技術(shù)湖南省重點(diǎn)實(shí)驗(yàn)室;
【基金】：湖南省科技計(jì)劃資助項(xiàng)目(2012FJ2001) 國(guó)家自然科學(xué)基金資助項(xiàng)目(51074072,51134005)
【分類號(hào)】：TD727.2

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本文編號(hào)：1816372