Amplitude Equation and Heat Transport for Rayleigh–Bénard Convection in Newtonian Liquids with Nanoparticles

Abstract

Rayleigh–Benard convection in liquids with nanoparticles is modelled as a single phase system with liquid properties like density, viscosity, thermal expansion coefficient, heat capacity and thermal conductivity modified by the presence of the nanoparticles. Expressions for the thermophysical properties are chosen from earlier works. The tri-modal Lorenz model is derived under the assumptions of Boussinesq approximation and small-scale convective motions. Ginzburg–Landau equation is arrived at from the generalized Lorenz model. The amplitudes of convective modes required for estimating the heat transport are determined analytically. A table is prepared documenting the actual values of the thermophysical properties of water, ethylene-glycol, engine-oil and glycerine with different nanoparticles, namely copper, copper oxide, titania, silver and alumina, and Nusselt number is calculated. Enhanced thermal conductivity being the reason for the enhancement of heat transport due to the presence of the nanoparticles is shown. Detailed discussion is made on the percentage increase of heat transport in twenty Newtonian nanoliquids compared to that in Newtonian liquids without nanoparticles.