Unicellular unsteady Rayleigh-Bénard convection in Newtonian liquids and Newtonian nanoliquids occupying enclosures : New findings

Rayleigh-Bénard convection in Newtonian liquids and Newtonian nanoliquids occupying rectangular, square and slender vertical enclosures is studied analytically in the paper using Buongiorno model with supplementary information on thermophysical properties of nanoliquids provided by phenomenological laws and mixture theory. The five-mode Lorenz model is derived under the assumptions of Boussinesq approximation, small-scale convective motions and some slip mechanisms like Brownian diffusion and thermophoresis. Inertia, Magnus effects, liquid drainage, diffusophoresis and gravity settling are neglected. Using multiscale method the analytically intractable Lorenz model of the problem is converted to a tractable Ginzburg-Landau equation the solution of which helps in quantifying the unsteady heat transport. The Ginzburg-Landau model derived directly from the governing equation is shown to be the same as that obtained via the Lorenz model. This point to the equivalence of the two models. Enhancement of heat transport due to the presence of nanoparticles is also clearly explained. Results on nanoliquids are discussed against the backdrop of Newtonian liquids without nanoparticles. Physical explanation is provided for all parameters' effects on onset and heat transport. The results pertaining to single-phase model are recovered as a limiting case of the present study.