Abstract
Linear and weakly nonlinear stability analyses of Brinkman–Bénard convection in water with a dilute concentration of single-walled carbon nanotubes (SWCNTs) is studied analytically in the paper. The thermophysical properties of water-SWCNTs nanoliquid and water-SWCNTs nanoliquid-saturated high-porosity medium are calculated using phenomenological relations and the mixture theory. The five-mode Lorenz model is derived under the assumptions of Boussinesq approximation, small-scale convective motion, weak thermophoresis and porous friction. Using the method of multiscales the five-mode Lorenz model is reduced to a cubic Ginzburg–Landau equation the solution of which helps in quantifying the unsteady heat transport. The effects of SWCNTs, porous parameter and viscosity ratio on onset of convection and the heat transport are documented. Results of the unicellular-Brinkman–Bénard convection problem is extracted from those of the multicellular-Brinkman–Bénard convection problem. Three different enclosures are considered in the study and their influence on the onset of convection and the heat transport are compared. The single-phase model which incorporates nanoliquid thermophysical properties is shown to be a limiting case of the model proposed in the present paper.
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