Systematic non-dimensional parametric investigation for the thermo-fluid dynamics of two-layered fluid systems

Fluid dynamics and heat transfer of immiscible two-layered fluid systems have been of great importance in a variety of industrial as well as extraterrestrial exploration applications. Control and optimization of such a liquid–liquid arrangement need complete understanding of complex synergistic phenomena, especially those induced by surface tension at the fluid interface. Previously-reported investigations for the natural and Marangoni convection of two-layered immiscible systems have been incoherent, having no systematic presentation based on the key dimensionless parameters that govern the flow. The paper here presents a rigorous scheme and the results of a non-dimensional analysis, which allows a systematic and coherent interpretation of the system flow. The approach leads to ten non-dimensional parameters to completely characterize the thermo-fluid dynamics under the hypothesis of flat non-deformable interface. The system for a set of dimensionless parameters can have five degrees of freedom in physical variables, with fifteen dimensional physical variables appearing in the governing equations. The effect and importance of each non-dimensional parameter have also been numerically analyzed in search of a further reduction of the parameters describing the phenomena.