ANALYSING RAYLEIGH - BENARD - MARANGONI CONVECTION: 2D AND 3D FLUID SURFACES THROUGH MATHEMATICAL MODELLING
DOI:
https://doi.org/10.55766/sujst10426Keywords:
Buoyancy-driven, Surface tension-induced, Density gradient, Rayleigh number, Marangoni number, Rayleigh-Bénard-Marangoni convectionAbstract
Rayleigh-Bénard-Marangoni convection represents a complex interplay of buoyancy-driven, surface tension-induced, and density gradient effects in fluid systems. This review study uses mathematical modelling techniques to give an in-depth description of the Rayleigh-Bénard-Marangoni convection process, distinguishing between 2D and 3D fluid surfaces. The investigation delves into the distinctive characteristics of convection patterns and flow behaviours in these two-dimensional and three-dimensional domains. Through a comprehensive literature survey, this paper examines the fundamental mechanisms of each convection type and their interactions, elucidating the underlying physics and mathematical formalisms. The review highlights key mathematical models employed to simulate Rayleigh-Bénard-Marangoni convection, discussing their strengths and limitations in capturing the intricacies of each dimensionality. This work also addresses how several parameters, like the Rayleigh number, Marangoni number, and others, affect the observed convection processes. The findings offer valuable insights into the nuanced behaviour of convection processes on 2D and 3D fluid surfaces, providing a foundation for future research and engineering applications involving heat transfer, fluid dynamics, and materials processing.
References
Bombe, D., Kumar, R., Nandi, S. K., & Agrawal, A. (2024). Semi-analytical formulation for single-track laser powder-bed fusion process to estimate melt-pool characteristics considering fluid-flow and Marangoni effect. International Journal on Interactive Design and Manufacturing (IJIDeM), 18(7), 5121-5137. https://doi.org/10.1007/s12008-023-01593-1
Botarelli, T., Fanfani, M., Nesi, P., & Pinelli, L. (2025). Using physics-informed neural networks for solving Navier-Stokes equations in fluid dynamic complex scenarios. Engineering Applications of Artificial Intelligence, 148, Article 110347. https://doi.org/10.1016/j.engappai.2025.110347
Costa, S., Capela, P., Hassui, A., Ribeiro, J., Pereira, M., & Soares, D. (2025). CFD analysis of multi-layer cooling channels in three-dimensionally structured grinding wheels. Applied Thermal Engineering, 279, Article 127633. https://doi.org/10.1016/j.applthermaleng.2025.127633
Dubey, A., Mishra, S., Diwakar, S. V., & Amiroudine, S. (2025). Rayleigh - Bénard - Marangoni convection in binary fluids - Effect of miscibility on oscillatory mode [Preprint]. arXiv. https://doi.org/10.48550/arXiv.2504.10324
Elbousefi, B., Schupbach, W., & Premnath, K. N. (2025). Marangoni convection of self-rewetting fluid layers with a deformable interface in a square enclosure and driven by imposed nonuniform heat energy fluxes. Energies, 18(13), 3563. https://doi.org/10.3390/en18133563
Huang, Y. F., Zhuo, R. L., Yang, J. C., & Ni, M. J. (2024). Interface coupling effect and multi-mode Faraday instabilities in a three-layer fluid system. Journal of Fluid Mechanics, 982, A8. https://doi.org/10.1017/jfm.2024.43
Jiang, H., Liao, W., & Chen, E. (2024). Bénard-Marangoni convection in an open cavity with liquids at low Prandtl numbers. Symmetry, 16(7), Article 844. https://doi.org/10.3390/sym16070844
Liapidevskii, V. Y. (2024). Two-layer equilibrium model of miscible inhomogeneous fluid flow. Fluid Dynamics, 59(4), 709-722. https://doi.org/10.1134/S0015462824603395
Maharani, N. S., Karim, S., Liliawati, W., & Sandion, A. (2024). Development of website media based on Google Sites to improve students’ conceptual understanding on dynamic fluid materials. Mimbar Pendidikan, 9(2), 72-86. https://doi.org/10.17509/mimbardik.v9i2.75165
Rahman, M. S. (2024). Computational fluid dynamics for predicting and controlling fluid flow in industrial equipment. European Journal of Advances in Engineering and Technology, 11(9), 1-9.
Saini, M., Sanjay, V., Saade, Y., Lohse, D., & Popinet, S. (2025). Implementation of integral surface tension formulations in a volume of fluid framework and their applications to Marangoni flows [Preprint]. arXiv. https://doi.org/10.48550/arXiv.2502.02712
Sari, I., Wu, M., Ludwig, A., & Kharicha, A. (2024). Effect of Marangoni flow during the solidification of a Fe-0.82wt.%C steel alloy. Journal of Physics: Conference Series, 2766(1), Article 012198. https://doi.org/10.1088/1742-6596/2766/1/012198
Schindler, F., Kim, N., Vogt, T., & Eckert, S. (2025). Impact of fluid flow on the thermal boundary layer dynamics in turbulent liquid metal Rayleigh-Bénard convection. International Journal of Heat and Mass Transfer, 247, Article 127129. https://doi.org/10.1016/j.ijheatmasstransfer.2025.127129
Song, J., Shishkina, O., & Zhu, X. (2024). Direct numerical simulations of rapidly rotating Rayleigh-Bénard convection with Rayleigh number up to 5 × 1013. Journal of Fluid Mechanics, 989, A3.
Umavathi, J. C., Buonomo, B., Manca, O., & Sheremet, M. A. (2025). MHD couple stress boundary-layer flow with heat and mass transfer under thermal radiation and Marangoni effect: A numerical study. Case Studies in Thermal Engineering, 71, Article 106159. https://doi.org/10.1016/j.csite.2025.106159
Veena, B. N., & Siddheshwar, P. G. (2024). Energy stability analysis of Rayleigh-Bénard-Marangoni convection in homogeneous and heterogeneous nanoliquids. Journal of Nanofluids, 13(6), 1177-1191. https://doi.org/10.1166/jon.2024.2203
Verma, G., Kumar, A., Soni, S., Yadav, K., & Li, W. (2024). Probing interplay of light momentum and fluid mechanics in two-layer liquids. Physical Review Fluids, 9(3), Article 034801. https://doi.org/10.1103/PhysRevFluids.9.034801
Wang, M., Chen, X. Y., Wang, W., & Wei, P. (2023). Heat transport and flow structure in thermal convection with two liquid layers. Journal of Fluid Mechanics, 978
Waris, W., & Lappa, M. (2024). Thermographic analysis of topographically controlled Marangoni-Rayleigh-Bénard convection in a fluid with temperature-dependent properties. International Journal of Thermal Sciences, 196, Article 108718. https://doi.org/10.1016/j.ijthermalsci.2023.108718
Yan, H., Wang, L., Huang, J., & Yu, Y. (2025). Thermocapillary migration of a self-rewetting droplet on an inclined surface: A phase-field simulation. Applied Thermal Engineering, 263, Article 125345. https://doi.org/10.1016/j.applthermaleng.2024.125345
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