Analysing Rayleigh - Benard - Marangoni Convection: 2d and 3d Fluid Surfaces Through Mathematical Modelling

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.