Energy Stability Analysis of Rayleigh-Bénard-Marangoni Convection in Homogeneous and Heterogeneous Nanoliquids

This study delves into the examination of stability characteristics in both linear and non-linear systems, comparing terrestrial and microgravity environments. The primary focus is on the dynamic behavior exhibited by a range of binary nanoliquids, encompassing homogeneous and heterogeneous compositions such as Water-Copper, Water-Alumina, Ethylene glycol-Copper, Ethylene glycol-Alumina, Water-Copper-Alumina, Ethylene glycol-Copper-Alumina, Water-Ethylene glycol-Copper, and Water-Ethylene glycol-Alumina. The Khanafer-Vafai-Lightstone single-phase model is employed for this investigation. Thermophysical properties are determined through the application of established laws of phenomenology and mixture theory, as discussed in existing literature. Stability analysis, particularly non-linear, is performed using the energy method, with a comparative assessment between linear and non-linear stability analyses. The shooting method is employed to compute the eigenvalues of the boundary value problem in both linear and energy stability analyses. The results reveals the presence of subcritical instability. The study explores the influence of key parameters such as Rayleigh number and Marangoni number, presenting comprehensive findings in tabular form. Among all the combinations considered in the paper, it is observed that Ethylene glycol serves as the best base liquid, while Copper emerges as the most effective nanoparticle for advancing the onset of Marangoni convection. Alumina serves the purpose of stabilizing the nanoliquid. Ultimately, the implications of the results are discussed and contrasted with prior research, considering the findings as a limiting case.