Mathematical Modeling and Numerical Analysis of Heat Transfer in Solids of Complex

Yu. SKOB; M. KALINICHENKO; I. MAMONTOV; R. MAIBORODA; N. RASHKEVICH; Yu. OTROSH

doi:10.15407/scine21.05.097

Authors

Yu. SKOB National Aerospace University https://orcid.org/0000-0003-3224-1709
M. KALINICHENKO National Aerospace University https://orcid.org/0000-0002-8685-065X
I. MAMONTOV Kyiv National University of Civil Engineering and Architecture https://orcid.org/0000-0002-7040-6247
R. MAIBORODA National University of Civil Defence of Ukraine https://orcid.org/0000-0002-3461-2959
N. RASHKEVICH National University of Civil Defence of Ukraine https://orcid.org/0000-0001-5124-6068
Yu. OTROSH National University of Civil Defence of Ukraine https://orcid.org/0000-0003-0698-2888

DOI:

https://doi.org/10.15407/scine21.05.097

Keywords:

numerical modelling, heat transfer, thermal conductivity, solid body of complex shape, isotherms, temperature field

Abstract

Introduction. Emergency situations may lead to explosions accompanied by the release of heat and pressure waves that destroy structures in their path and cause fires.
Problem Statement. Modeling heat transfer in solids of complex geometry remains a critical task, as predicting the distribution of temperature fields is essential in the design of protective structures. Therefore, the development of a new mathematical model that adequately describes transient thermal processes in solids, as well as the
creation of an efficient numerical method and its implementation as a modern information system for engineering analysis and prediction, is highly relevant.
Purpose. To perform mathematical modeling of unsteady temperature fields in solids within regions of significant temperature gradients arising from accidental explosions of gas mixtures.
Materials and Methods. Numerical modeling of transient heat transfer processes in multiply connected solids of complex geometry, surrounded by a thermally conductive gaseous medium, has been carried out using a unified
finite-diff erence algorithm.

Results. A coupled direct problem involving the flow of a continuous gaseous medium, heat transfer between the gas and solid, and heat conduction within the solid has been considered. The mathematical model accounts for the spatial transfer of mass, momentum, and energy, as well as the complex geometry of streamlined solids. The model has been verified through comparison with analytical solutions to benchmark problems involving an infi nite steel plate. Three-dimensional temperature fields in spatially complex solids have been obtained for individual geometric primitives and their combinations. Heat transfer simulations
have been performed for a turbine blade with a continuous cross-section and internal cooling channels.
Conclusions. The newly developed mathematical model has demonstrated suitability for engineering applications in thermal analysis and predictive modeling. The resulting three-dimensional temperature fields can be used to assess the thermal stress state and strength characteristics of structural elements located within the impact zone of high excess pressure caused by accidental explosions of gas mixtures at industrial sites.

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References

Skob, Y., Ugryumov, M., G ranovskiy, E. (2023). Numerical Evaluation of Wind Speed Influence on Accident Toxic Spill Consequences Scales. Environ.Clim. Technol., 27(1), 450—463. https://doi.org/10.2478/rtuect-2023-0033

Kovalov, A., Otrosh, Y . , Vedula, S., Danilin, О., Kovalevska, T. (2019). Parameters of fire-retardant coatings of steel constructions under the influence of climatic factors. Scientific Bulletin of National Mining University, 3, 46—53. https://doi.org/10.29202/nvngu/20193/9

Skob, Y., Ugryumov, M., Granovskiy, E. (2019). Numerical Evaluation of Probability of Harmful Impact Caused by Toxic Spill Emergencies. J. Environ. Clim. Technol., 23, 1—1. https://doi.org/10.2478/rtuect-2019-0075

Skob, Y., Ugryumov, M., G ranovskiy, E. (2021). Numerical assessment of hydrogen explosion consequences in a mine tunnel. Int. J. Hydrog. Energy., 46, 12361—12371. https://doi.org/10.1016/j.ĳhydene.2020.09.067

Skob, Y., Ugryumov, M., Dreval, Y. (2020). Numerical Modelling of Gas Explosion Overpressure Mitigation Effects. Materials Science Forum, 1006, 117—122. https://doi.org/10.4028/www.scientific.net/MSF.1006.117

Кorytchehko, K., Ozerov , A., Vinnikov, D., Skob, Y., Dubinin, D., Meleshchenko, R. (2018). Numerical simulation of influence of the non-equilibrium excitation of molecules on direct detonation initiation by spark discharge. Probl. At. Sci. Technol., 116, 194—199. URL: http://dspace.nbuv.gov.ua/handle/123456789/147358 (Last accessed: 20.05.2025).

Skob, Y., Yakovlev, S., Korobchynskyi, K., Kalinichenko, M. (2023). Numerical Assessment of Terrain Relief Influence on Consequences for Humans Exposed to Gas Explosion Overpressure. Computation, 11(2), 19. https://doi.org/10.3390/computation11020019

Skob, Y., Ugryumov, M. , Dreval, Y., Artemiev, S. (2021). Numerical Evaluation of Safety Wall Bending Strength during Hydrogen Explosion. Materials Science Forum, 1038, 430—436. https://doi.org/10.4028/www.scientific.net/MSF.1038.430

Dveirin, O. Z., Andree v, O. V., Kondrat’ev, A. V., Haidachuk, V. Ye. (2021). Stressed State in the Vicinity of a Hole in Mechanical joint of Composite Parts. International Applied Mechanics, 57, 234—247. https://doi.org/10.1007/s10778- 021-01076-4

Surianinov, M., Andron o v, V., Otrosh, Y., Makovkina, T., Vasiukov, S. (2020). Concrete and Fiber Concrete Impact Strength. Materials Science Forum, 1006, 101—106. https://doi.org/10.4028/www.scientific.net/MSF.1006.101

Kovalov, A., Otrosh, Y., Surianinov, M., Kovalevska, T. (2019). Experimental and Computer Researches of Ferroconcrete Floor Slabs at High-Temperature Influences. Materials Science Forum, 968, 361—367. https://doi.org/10.4028/www. scientific.net/MSF.968.361

Kondratiev, A., Píštěk , V., Smovziuk, L., Shevtsova, M., Fomina, A., Kučera, P. (2021). Stress-Strain Behaviour of Reparab le Composite Panel with Step-Variable Thickness. Polymers, 13(21), 3830. https://doi.org/10.3390/polym13213830

Kovalov, A., Otrosh, Yu., Kovalevska, T., Safronov, S. (2019). Methodology for assessment of the fire-resistant quality of reinforced-concrete floors protected by fire-retardant coatings. IOP Conference Series: Materials Science and Engineering (20—22 November 2019, Kharkiv, Ukraine), 708(1), 012058. https://doi.org/10.1088/1757-899X/708/1/012058

Kondratiev, A., Gaidac huk, V. (2019). Weight-Based Optimization of Sandwich Shelled Composite Structures with a Honeycomb Filler. East.-Eur. J. Enterp. Technol., 1(1), 24—33. https://doi.org/10.15587/1729-4061.2019.154928

Bashynska, O., Otrosh, Y., Holodnov, O., Tomashevskyi, A., Venzhego, G. (2020). Methodology for calculating the technical state of a reinforced-concrete fragment in a building influenced by high temperature. Materials Science Forum, 1006, 166—172. https://doi.org/10.4028/www.scientific.net/MSF.1006.166

Krutii, Y., Kovrov, A., Otrosh, Y., Surianinov, M. (2020). Analysis of Forced Longitudinal Vibrations of Columns Taking into Account Internal Resistance in Resonance Zones. Materials Science Forum, 1006, 79—86. https://doi.org/10.4028/www.scientific.net/MSF.1006.79

Kovalov, A., Purdenko, R., Otrosh, Y., Tоmеnkо V., Rashkevich, N., Shcholokov, E., Pidhornyy, M., Zolotova, N., Suprun, O. (2022). Assessment of fire resistance of fireproof reinforced concrete structures. Eastern-European Journal of Enterprise Technologies, 5(1(119)), 53—61. https://doi.org/10.15587/1729-4061.2022.266219

Chen, W. (2023). Hydro dynamic heat transfer in solids. Int. J. Heat Mass Transf., 215, 124455. https://doi.org/10.1016/ j.ĳheatmasstransfer.2023.124455

Wyczółkowski, R. (2021 ) . Experimental Investigations of Effective Thermal Conductivity of the Selected Examples of Steel Porous Charge. Solids, 2(4), 420—436. https://doi.org/10.3390/solids2040027

Kozhukhar, A., Bilous, P . (2015). Practical methods of calculating the autoclaves thermal stresses at building industry. Odes’kyi Politechnichnyi Universytet. Pratsi, 2(46), 46—50. https://doi.org/10.15276/opu.2.46.2015.09

Brunetkin, А. (2014). In tegrated approach to solving the fluid dynamics and heat transfer problems. Odes’kyi Politechnichnyi Universytet. Pratsi, 2(44), 108—115. https://doi.org/10.15276/opu.2.44.2014.21

Pandey, R. (2017). App r oximate Solution of One-dimensional Heat Conduction Problem. Int. j Res. Appl. Eng. Sci. Tech., 5(X), 178—183. https://doi.org/10.22214/ijraset.2017.10029

Brovka, G., Sychevskii , V. (1999). Calculation of temperature fields and thermal conductivity in structurized systems. J. Eng. Phys. Thermophys, 72, 579—585.

Men’shikov, V., Skob, Y., Ugryumov, M. (1991). Solution of the three-dimensional turbomachinery blade row flow field problem with allowance for viscosity effects. Fluid Dynamics, 26(6), 889—896.

Toro, E. (2001). Godun o v Methods. Theory and Applications. Springer, New York.