Calculation method of unsteady heat-transfer dimensionless number for surrounding rock and airflow in roadway

QIN Yueping; WANG Peng; TANG Fei; GUO Mingyan; WANG Shibin

doi:10.13225/j.cnki.jccs.2024.1143

Abstract：Heat release from surrounding rock is the dominant heat source in deep high-temperature mines,and its key parameter-the unsteady heat-transfer dimensionless number Kuτ-directly determines the accuracy of air-temperature prediction.Existing methods for obtaining Kuτ(analytical series,charts,tables,piecewise regressions,or case-by-case nu-merical simulations)are either computationally cumbersome,suffer from large interpolation errors,or cannot be imple-mented in batches,thus failing to meet engineering demands for rapid,accurate and unified calculations.To address the above issues,a study on the calculation method of the unsteady heat-transfer dimensionless number between roadway sur-rounding rock and airflow has been carried out.Taking a circular roadway as the research object,a dimensionless transi-ent heat-conduction equation in polar coordinates is established and expresses Kuτ as a function of the Biot number Bi and the Fourier number Fo.The finite-volume method is employed for discretisation;the nodal radii and time steps are ar-ranged in geometric progressions to guarantee accuracy during the violent unsteady stage while maintaining computation-al efficiency at later times.An in-house solver developed in Visual Studio is used to obtain high-precision discrete solu-tions over the ranges of different Bi and 0.01≤Fo ≤ 1 000.Through a variable transformation,a highly linear relation-ship between(Bi-Kuτ)-1 and Fo-0.5 is discovered,on the basis of which a unified quadratic-polynomial regression formula is constructed.The numerical results agree well with classical analytical solutions,validating the model and the code.The regression formula is concise and free of piecewise definitions;its average relative error is 1.8％and its maximum relative error is 4.2％,outperforming existing piecewise regressions.A case study shows that the unsteady heat-transfer dimension-less number drops to 29.0％,7.7％and 5.0％of its initial value after 5 days,1 year and 10 years of ventilation,respect-ively,consistent with field observations.A unified explicit expression of Kuτ valid over the entire continuous ranges of Bi and Fo is presented,eliminating the limitations of piece-wise fitting.Owing to its compact form,the formula can be dir-ectly embedded in mine air-temperature prediction software to achieve second-level accurate calculation of heat dissipa-tion from surrounding rock for hundreds of roadways,offering a reliable and efficient tool for rapid thermal-hazard assess-ment and cooling design in deep mines.The method is readily extendable to non-circular cross-sections and heterogen-eous rock,and future work will couple air temperature-humidity processes to enable dynamic prediction of the thermal en-vironment of entire mines.