Micropolar Effects and Energy Dissipation in a Three-Dimensional Flow of a Micropolar Fluid in a Cubic Cavity

K. V. Gubareva; E. Yu. Prosviryakov; A. V. Eremin

doi:10.17804/2410-9908.2026.3.049-063

K. V. Gubareva, E. Yu. Prosviryakov, A. V. Eremin

MICROPOLAR EFFECTS AND ENERGY DISSIPATION IN A THREE-DIMENSIONAL FLOW OF A MICROPOLAR FLUID IN A CUBIC CAVITY

DOI: 10.17804/2410-9908.2026.3.049-063

This paper presents a comprehensive study of energy dissipation mechanisms and micropolar effects in a three-dimensional flow of a micropolar fluid within a cubic cavity. Emphasis is laid on the analysis of different dissipation components, namely classical viscous dissipation, dissipation due to micro-rotation gradients, and dissipation arising from the interaction between macro-rotation and micro-rotation. Numerical modeling is used to obtain the spatial distributions of the micro-rotation vector and the energy dissipation field. The characteristics of macro-vortex and micro-vortex structures are compared. Quantitative estimates of the contribution of each dissipation mechanism to the overall flow energy balance are provided. The results elucidate the specific features of dissipative processes in micropolar media, and they can be used to optimize the processing of non-Newtonian fluids.

Keywords: micropolar fluid, energy dissipation, micro-rotation, micro-vortices, energy balance, numerical modeling, cubic cavity

References:

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К. В. Губарева, Е. Ю. Просвиряков, А. В. Еремин

МИКРОПОЛЯРНЫЕ ЭФФЕКТЫ И ДИССИПАЦИЯ ЭНЕРГИИ В ТРЕХМЕРНОМ ТЕЧЕНИИ МИКРОПОЛЯРНОЙ ЖИДКОСТИ В КУБИЧЕСКОЙ ПОЛОСТИ

В работе представлены результаты исследования механизмов диссипации энергии и особенностей микрополярных эффектов в трехмерном течении микрополярной жидкости в кубической полости. Основное внимание уделено анализу различных составляющих диссипации: классической вязкой диссипации, диссипации, связанной с градиентами микровращения, и диссипации от взаимодействия макро- и микровращений. На основе численного моделирования получены пространственные распределения вектора микровращения, поля диссипации энергии, проведено сравнение характеристик макро- и микровихревых структур. Приведены количественные оценки вклада каждого механизма диссипации в общий энергетический баланс течения. Полученные результаты раскрывают специфику диссипативных процессов в микрополярных средах и могут быть использованы для оптимизации процессов переработки неньютоновских жидкостей.

Ключевые слова: микрополярная жидкость, диссипация энергии, микровращение, микровихри, энергетический баланс, численное моделирование, кубическая полость

Библиография:

Просвиряков Е. Ю., Горулева Л. С., Альес М. Ю. Класс точных решений уравнений Обербека–Буссинеска с учетом диссипативной функции Рэлея // Химическая физика и мезоскопия. – 2024. – Т. 26 (2). – С. 164–178. – DOI: 10.62669/17270227.2024.2.15.
Baranovskii E. S. The stationary Navier–Stokes–Boussinesq system with a regularized dissipation function // Mathematical Notes. – 2024. – Vol. 115. – P. 670–682. – DOI: 10.1134/S0001434624050031.
Goruleva L. S., Obabkov I. I., Prosviryakov E. Yu. Exact solutions to thermal diffusion equations for Stokes slow flows // Diagnostics, Resource and Mechanics of materials and structures. – 2024. – Iss. 6. – P. 241–267. – DOI: 10.17804/2410-9908.2024.6.241-267. – URL: http://dream-journal.org/issues/2024-6/2024-6_481.html
Shelukhin V. V., Neverov V. V. Rotational sedimentation in neutrally buoyant particle suspensions // Journal of Applied Mechanics and Technical Physics. – 2024. – Vol. 65. – P. 985–993. – DOI: 10.1134/S0021894424050195.
Effects of thermo physical aspects of radiant-heating on an unsteady magnetohydrodynamic hybrid nanofluid flow / K. Viswanath, A. P. Lingaswamy, K. Raghavendra, R. Kodi, R. R. Vaddemani // Theoretical and Mathematical Physics. – 2025. – Vol. 223. – P. 1087–1102. – DOI: 10.1134/S0040577925060182.
Siddiqui A., Turkyilmazoglu M. Film flow of nano-micropolar fluid with dissipation effect // Computer Modeling in Engineering & Sciences. – 2024. – Vol. 140 (3). – P. 2487–2512. – DOI: 10.32604/cmes.2024.050525.
Saraswathy M., Prakash D., Durgaprasad P. MHD micropolar fluid in a porous channel provoked by viscous dissipation and non-linear thermal radiation: an analytical approach // Mathematics. – 2023. – Vol. 11 (1). – P. 183. – DOI: 10.3390/math11010183.
Numerical modelling of the viscoelastic polymer melt flow in material extrusion additive manufacturing / X. Xu, W. Qiu, D. Wan, J. Wu, F. Zhao, Y. Xiong // Virtual and Physical Prototyping. – 2024. – Vol. 19 (1). – P. e2300666. – DOI: 10.1080/17452759.2023.2300666.
Thermal dissipation of two-step combustible tangent hyperbolic fluid with quadratic Boussinesq approximation and convective cooling / A. D. Ohaegbue, S. O. Salawu, R. A. Oderinu, E. O. Fatunmbi, A. O. Akindele // Results in Materials. – 2024. – Vol. 22. – P. 100565. – DOI: 10.1016/j.rinma.2024.100565.
Tassaddiq A. Impact of Cattaneo–Christov heat flux model on MHD hybrid nano-micropolar fluid flow and heat transfer with viscous and joule dissipation effects // Scientific Reports. – 2021. – Vol. 11. – Art. No 67. – DOI: 10.1038/s41598-020-77419-x.
Burmasheva N. V., Prosviryakov E. Yu. Exact solutions to the Navier–Stokes equations for unidirectional flows of micropolar fluids in a mass force field // Diagnostics, Resource and Mechanics of materials and structures. – 2024. – Iss. 3. – P. 41–63. – DOI: 10.17804/2410-9908.2024.3.041-063. – URL: http://dream-journal.org/issues/2024-3/2024-3_438.html
Baranovskii E. S. Exact solutions for the non-isothermal Poiseuille flow of a FENE-P fluid // Polymers. – 2025. – Vol. 17 (17). – P. 2343. – DOI: 10.3390/polym17172343.
Baranovskii E. S., Prosviryakov E. Y., Ershkov S. V. Mathematical analysis of steady non-isothermal flows of a micropolar fluid // Nonlinear Analysis: Real World Applications. – 2025. – Vol. 84. – P. 104294. – DOI: 10.1016/j.nonrwa.2024.104294.
Micropolar effects on the effective shear viscosity of nanofluids / R. Bondarenko, Yu. Bukichev, A. Dzhaga, G. Dzhardimalieva, Yu. Solyaev // Physics of Fluids. – 2024. – Vol. 36. – 062004. –DOI: 10.1063/5.0208850.
Exact solutions to the Oberbeck–Boussinesq equations for describing t hree-dimensional flows of micropolar liquids / E. S. Baranovskii, S. V. Ershkov, E. Yu. Prosviryakov, A. V. Yudin // Symmetry. – 2024. – Vol. 16 (12). – P. 1669. – DOI: 10.3390/sym16121669.
Three-dimensional analysis of precursors to non-viscous dissipation in an experimental turbulent flow / P. Debue, V. Valori, C. Cuvier, F. Daviaud, J.-M. Foucaut, J.-P. Laval, C. Wiertel, V. Padilla, B. Dubrulle // Journal of Fluid Mechanics. – 2021. – Vol. 914. – P. A9. – DOI: 10.1017/jfm.2020.574.
Exploring convective conditions in three-dimensional rotating ternary hybrid nanofluid flow over an extending sheet: a numerical analysis / S. A. Lone, Z. Raizah, H. Alrabaiah, S. Shahab, A. Saeed, A. Khan // Journal of Thermal Analysis and Calorimetry. – 2025. – Vol. 150. – P. 2651–2666. – DOI: 10.1007/s10973-024-13070-2.
Детерминистские и случайные аттракторы волновых уравнений со знакопеременной диссипацией / Ч. Чанг, Д. Ли, Ч. Сун, С. В. Зелик // Известия Российской академии наук. Серия математическая. – 2023. – Т. 87 (1). – C. 161–210. – DOI: 10.4213/im9250.
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A numerical study of viscous dissipation with first order chemical reaction and ohmic effects on MHD nanofluid flow through an exponential stretching sheet / D. Gopal, S. Jagadha, P. Sreehari, N. Kishan, D. Mahendar // Materials Today: Proceedings. – 2022. – Vol. 59. – P. 1028–1033. – DOI: 10.1016/j.matpr.2022.02.368.

Библиографическая ссылка на статью

Gubareva K. V., Prosviryakov E. Yu., Eremin A. V. Micropolar Effects and Energy Dissipation in a Three-Dimensional Flow of a Micropolar Fluid in a Cubic Cavity // Diagnostics, Resource and Mechanics of materials and structures. - 2026. - Iss. 3. - P. 49-63. -
DOI: 10.17804/2410-9908.2026.3.049-063. -
URL: http://dream-journal.org/issues/2026-3/2026-3_540.html
(accessed: 26.09.2026).