Bibliography: 1. Federal'nye normy i pravila v oblasti promyshlennoy bezopasnosti «Pravila bezopasnosti pri vedenii gornykh rabot i pererabotke tverdykh poleznykh iskopaemykh» [Federal Code of Industrial Safety: Safety regulations in solid mineral mining and processing], 2013, 186 p.
2. Pravila bezopasnosti pri stroitel'stve podzemnykh sooruzheniy PB 03-428-02 [Safety regulations in underground construction PB 03-428-02], 2009, 407 p.
3. Bolotskikh N. S., Bondarenko N.A., Gal'chenko P. P. Stroitel'stvo stvolov shakht i rudnikov: spravochnik. Pod red. O. S. Dokukina, N. S. Bolotskikh [Construction of shafts and mines: handbook. Dokukin O. S., Bolotskikh N. S. (Eds.)], Moscow, Nedra, 1991, 344 p.
4. Trupak N. G. Zamorazhivanie gruntov pri stroitel'stve podzemnykh sooruzheniy [Ground freezing in underground construction], Moscow, Nedra, 1979, 344 p.
5. Yao Z., Cai H., Xue W., Wang X., Wang Z. Numerical simulation and measurement analysis of the temperature field of artificial freezing shaft sinking in Cretaceous strata. AIP Advances. 2019. Vol. 9, no 2. Art. no 025209. DOI: 10.1063/1.5085806.
6. Zhelnin M., Kostina A., Plekhov O., Panteleev I., Levin L. Numerical analysis of application limits of Vyalov’s formula for an ice-soil wall thickness. Frattura ed Integrita Strutturale. 2019. Vol. 13, no 49. Pp. 156—166. DOI: 10.3221/IGF-ESIS.49.17.
7. Kazakov B. P., Shalimov A. V., Semin M.A. Stability of natural ventilation mode after main fan stoppage. International Journal of Heat and Mass Transfer. 2015. Vol. 86. Pp. 288—293. DOI: 10.1016/j.ijheatmasstransfer.2015.03.004.
8. Nikolaev A. V., Alymenko N. I., Kamenskikh A.A., Alymenko D. N., Nikolaev V.A., Petrov A. I. Factors defining value and direction of thermal pressure between the mine shafts and impact of the general mine natural draught on ventilation process of underground mining companies. IOP Conference Series: Earth and Environmental Science. 2017. Vol. 87, no 5. Art. no 052020. DOI: 10.1088/1755-1315/87/5/052020.
9. Nie B. S., Peng B., Guo J. H., Liu X. F., Liu X. T., Shen J. S. Research on Characteristics of Air Flow Disorder in Inlet Shafts. Journal of Mining Science. 2018. Vol. 54, no 3. Pp. 444—457. DOI: 10.1134/S1062739118033846.
10. Taler D., Taler J. Simple heat transfer correlations for turbulent tube flow. E3S Web of Conferences. 2017 Vol. 13. Art. no 02008. DOI:10.1051/e3sconf/20171302008.
11. Colburn A. P. A method of correlating forced convection heat transfer data and a comparison with fluid friction. Transactions of American Institute of Chemical Engineers. 1933. Vol. 29. Pp. 174—210.
12. Taler D. A new heat transfer correlation for transition and turbulent fluid flow in tubes. International Journal of Thermal Sciences. 2016. Vol. 108. Pp. 108—122.
13. Levin L.Yu., Semin M.A., Klyukin Yu.A., Nakaryakov E. V. Analysis of aeroand thermo-dynamic processes at the early stage of through ventilation in mines. Vestnik Permskogo natsional'nogo issledovatel'skogo politekhnicheskogo universiteta. Geologiya. Neftegazovoe i gornoe delo. 2016. Vol. 15, no 21, pp. 367—377. [In Russ]. DOI: 10.15593/2224-9923/2016.21.9.
14. Gershuni G. Z., ZHukhovitskiy E. M., HepomnyashchiyA.A. Ustoychivost' konvektivnykh techeniy [Stability of convective flows], Moscow, Nauka, 1989, 320 p.
15. Jha B. K., Oni M. O. Theory of fully developed mixed convection including flow reversal. A nonlinear Boussinesq approximation approach. Heat Transfer — Asian Research. 2019. Vol. 48, no 8. Pp. 3477—3488. DOI: 10.1002/htj.21550.
16. SHalimov A. V., Kormshchikov D. S., Gazizullin R. R., Semin M.A. Modeling of thermal depression dynamics and its effect on ventilation of underground openings. Vestnik Permskogo natsional'nogo issledovatel'skogo politekhnicheskogo universiteta. Geologiya. Neftegazovoe i gornoe delo. 2014. Vol. 13, no 12, pp. 41—47. [In Russ].
17. Tannehill J. Computational fluid mechanics and heat transfer. Washington, DC: Taylor & Francis. 1997. 792 p.
18. Wilcox D. C. Formulation of the k— turbulence model revisited. AIAA Journal. 2008. Vol. 46. Pp. 2823—2838. DOI: 10.2514/1.36541.
19. Sanjay S., Sundararaj S., Thiagarajan K. B. Numerical simulation of flat plate boundary layer transition using OpenFOAM®. AIP Conference Proceedings. AIP Publishing. 2019. Vol. 2112, no 1. Art no 020134.
20. Puchkov L.A., Kaledina N. O., Kobylkin S. S. Methodology of system design of mine ventilation. Gornyy informatsionno-analiticheskiy byulleten’. 2014, no S1. [In Russ].
21. Mohammed H.A., Salman Y. K. Heat transfer by natural convection from a uniformly heated vertical circular pipe with different entry restriction configurations. Energy Conversion and Management. 2007. Vol. 48, no 7. Pp. 2244—2253. DOI:10.1016/j.enconman.2006.12.005.
22. Yan W. M., Lin T. F. Theoretical and experimental study of natural convection pipe flows at high rayleigh number. International Journal of Heat and Mass Transfer. 1991. Vol. 34, no 1. Pp. 291—303. DOI: 10.1016/0017-9310(91)90195-k
23. Karwa R. Empirical relations for natural or free convection. Heat and mass transfer. 2016. Pp. 623—664. DOI: 10.1007/978-981-10-1557-1-9.
24. Valueva E. P. Laminar mixed convection in vertical flat channel with constant density heat flow on wall. Teplofizika vysokikh temperatur. 2019. Vol. 57, no 3, pp. 408—415. [In Russ].
25. Kazakov B. P., Shalimov A. V., Semin M.A., Klyukin Yu.A. Mathematical modeling of thermodynamic processes in air conditioning systems in potash mines. Gornyi Zhurnal. 2019, no 8, pp. 81—84. DOI: 10.17580/gzh.2019.08.16. [In Russ].