Rotational impact on Rayleigh–Bénard convection in layered nanofluids: An analytical and numerical study

Thermal instability in a two-layer nanofluid system—comprising a non-porous nanofluid layer overlying a porous nanofluid layer under the influence of the Coriolis force—is investigated in this study. The model integrates the enhanced thermal conductivity of nanofluids with rotational effects, improving heat transfer efficiency and fluid stability, making it relevant for applications in solar energy, rotating machinery, and thermal management systems. A linear stability analysis (LSA) is performed on the dimensionless momentum, energy, and nanoparticle conservation equations. The normal mode technique is applied to the perturbed equations, and the resulting eigenvalue problem is solved using the Chebyshev–Tau numerical method, implemented in MATLAB to obtain graphical results. Two configurations are examined: one with identical nanoparticles in both layers and another with different nanoparticles dispersed in the same base fluid. The effects of depth ratio, Darcy number, Taylor number, and thermal conductivity ratio on system stability are analyzed. The results reveal a bimodal stability curve, indicating complex convection modes. The system shows strong sensitivity to depth ratio and rotational effects. For identical nanoparticles, increasing the Taylor number stabilizes the system, while for aluminum–copper combinations, stability increases as the Taylor number decreases. Higher Darcy numbers delay convection, enhancing stability, whereas larger thermal conductivity ratios shift convection to the upper nanofluid layer. Unlike previous studies limited to single-layer nanofluids or microchannel flows, this work presents new insights into the coupled influence of rotation and interfacial effects, advancing the understanding of stability transitions in rotating nanofluid systems.