Theoretical research of heat exchange between air flow and shaft lining subject to convective heat transfer

Authors: Semin M A, Levin L Y

The heat and mass transfer in a mine shaft under construction is researched theoretically under temperature conditions in the shaft lining lower than the temperature of air flow fed in the shaft via a ventilation duct. The research was aimed to ensure stable airing of mine shafts in the period of construction before cutting a shaft-to-shaft connection with artificial freezing of surrounding rock mass. The multi-parametric numerical modeling of nonstationary aeroand thermo-dynamic parameters in a mine shafts was performed using 3D convective heat transfer model in ANSYS. It is found that convective heat can exert considerable influence on the heat and mass exchange in the air space of the shaft when the shaft lining temperature is lower than the temperature of air flow from the ventilation duct at the shaft bottom. Inside the shaft, the back convective flows appear and air circulates in convective cells, which increases air flow rate in the shaft. As a consequence, the heat transfer factor at the shaft lining–air interface is much higher than the calculated factor without regard to the convective heat. The influence of the temperature difference at the air and shaft lining interface and the shaft lining roughness on the average values of the heat transfer factor and heat flow at the shaft lining and air interface is investigated. The empirical formulas are proposed for calculating the heat transfer factor and specific heat flow at the shaft lining and air interface depending on the temperature difference, shaft diameter and roughness of walls of underground openings.

Keywords: mine shaft, mine ventilation, air flow, artificial rock freezing, mixed convection, convective heat transfer, heat loss, convective stratification.
For citation:

Semin M.A., Levin L. Yu. Theoretical research of heat exchange between air flow and shaft lining subject to convective heat transfer. MIAB. Mining Inf. Anal. Bull. 2020;(6):151167. [In Russ]. DOI: 10.25018/0236-1493-2020-6-0-151-167.

Issue number: 6
Year: 2020
Page number: 151-167
ISBN: 0236-1493
UDK: 622.45, 622.253.3
DOI: 10.25018/0236-1493-2020-6-0-151-167
Article receipt date: 14.01.2020
Date of review receipt: 20.02.2020
Date of the editorial board′s decision on the article′s publishing: 20.05.2020
About authors:

M.A. Semin1, Cand. Sci. (Eng.), Researcher, e-mail:, Scopus ID: 56462570900, ORCID:,
L.Yu. Levin1, Dr. Sci. (Eng.), Deputy Director for Research, Scopus ID: 56358515000, ORCID:,
1 Mining Institute of Ural Branch, Russian Academy of Sciences, 614007, Perm, Russia.

For contacts:

M.A. Semin, e-mail:


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].

Our partners

Подписка на рассылку

Раз в месяц Вы будете получать информацию о новом номере журнала, новых книгах издательства, а также о конференциях, форумах и других профессиональных мероприятиях.