Küppers–Lortz instability in rotating Rayleigh–Bénard convection bounded by rigid/free isothermal boundaries

Manifestation of Küppers–Lortz secondary instability in rotating Rayleigh–Bénard convection in a Newtonian liquid (water) and in homogeneous and heterogeneous nanoliquids is reported for rigid-isothermal and free-isothermal boundaries. Water–alumina and water–alumina–copper are used as representative homogeneous and heterogeneous nanoliquids. Experimental data on thermal conductivity and dynamic viscosity are used and empirical models which represent experimental data faithfully are obtained. In order to study Küppers–Lortz secondary instability an energy-conserving, ninth-order Lorenz model is derived using the minimal mode truncated Fourier–Galerkin expansion. It is shown that the critical Rayleigh number obtained in the case of rotating Rayleigh–Bénard convection in water–alumina–copper and water–alumina nanoliquids is smaller than the value obtained in the case of water, whereas the critical Taylor number obtained in the case of water–alumina–copper and water–alumina nanoliquids is larger than the value obtained in the case of water. Thus, the individual effect of suspending dilute concentrations of homogeneous and heterogeneous nanoparticles in water is to promote formation of the steady, primary instability (longitudinal rolls) and impede the appearance of the Küppers–Lortz instability (intersecting rolls). It is also shown that compared to a homogeneous nanoliquid, a heterogeneous nanoliquid is more pro-primary-instability as well as anti-secondary-instability. Further, it is found that by slightly increasing the volume fraction of alumina nanoparticles in water one can achieve the same effect as that of alumina and copper in water. In order to validate the results on Küppers–Lortz instability, we considered the results on Küppers–Lortz instability in the absence of nanoparticles obtained in the two cases of rigid and free boundaries and compared them with those of previous investigations, and reasonably good agreement is found.