Comparison of heat flows in underground openings of plane and spherical symmetry

Heat flow in different-purpose underground openings is analyzed in modeling them as plane and spherical symmetry objects, with introduction of notion of an equivalent radius. The aim of the study is to determine a possible transition zone between spherical and plane symmetry in heat problem solution. The simple analytic dependences are obtained for determining heat flow at the boundary of different symmetry openings as a function of the Fourier criterion. The quantitative changes in heat flow in different symmetry openings at the first order boundary condition are compared. The rational zone is determined for possible transition from the spherical to plane symmetry at the quantitative error of heat flow prediction not higher than the permissible value in the engineering practice. The limit cross-sections of underground openings and the heat flow durations such that the spherical-to-plane symmetry transition is possible for analytical solution of heat problems are found. In particular, it is shown that at short durations of heat processes, for instance, fire in an underground structure, it is entirely admissible to use plane symmetry to predict temperature condition in rock mass for underground openings of small cross-section (less than 10 m2).

Keywords: underground structure, underground opening, modeling, spherical symmetry, heat flow, equivalent radius, optimized cross-section, calculation error.
For citation:

Galkin A. F., Kurta I. V., Pankov V. Yu. Comparison of heat flows in underground openings of plane and spherical symmetry. MIAB. Mining Inf. Anal. Bull. 2020;(10):133-141. [In Russ]. DOI: 10.25018/0236-1493-2020-10-0-133-141.

Issue number: 10
Year: 2020
Page number: 133-141
ISBN: 0236-1493
UDK: 536:24:622.413
DOI: 10.25018/0236-1493-2020-10-0-133-141
Article receipt date: 14.05.2020
Date of review receipt: 15.06.2020
Date of the editorial board′s decision on the article′s publishing: 20.09.2020
About authors:

A.F. Galkin1, Dr. Sci. (Eng.), Professor, Senior Researcher, e-mail:,
I.V. Kurta1, Cand. Sci. (Eng.), Assistant Professor, Vice-Rector for Research,
V.Yu. Pankov, Cand. Sci. (Geol. Mineral.), Assistant Professor,
M.K. Ammosov North-Eastern Federal University, 677000, Yakutsk, Republic of Sakha, Russia,
1 Ukhta State Technical University, 169300, Ukhta, Republic of Komi, Russia.


For contacts:

A.F. Galkin, e-mail:


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