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In this paper, we perform linear and non-linear stability analyses of Rayleigh-Bénard convection in a horizontal layer of water–copper and water–alloy nanoliquids. The corresponding eigen values for the problems involving the two nanoliquids are obtained and compared. The thermophysical properties of nanoliquids have been modelled as a function of the properties of water as base liquid, copper and alloy as nanoparticles. A non-linear analysis is performed using the energy method. The subcritical instability does not exist. As a limiting case the results of water are discussed with results of previous investigations, and a good agreement is found. The effect of nanoparticles is to destabilise the system. The results are depicted graphically.

Linear and non-linear stability analyses of Rayleigh-Bénard convection in water–copper and water–alloy nanoliquids