Effect of internal heat generation/absorption on Rayleigh-Bénard convection in water well-dispersed with nanoparticles or carbon nanotubes

Abstract

Linear and weakly nonlinear stability analyses of Rayleigh-Bénard convection with internal heat generation/absorption in water-based nanoliquids is studied analytically in the paper using the generalized Buongiorno two-phase model. The Boussinesq approximation and small-scale convective motion are assumed to be valid. By considering a minimal-mode Fourier representation, we arrived at an analytically intractable fifth-order, autonomous, generalized Lorenz model. Results on linear stability (direct and pitchfork bifurcations) and subcritical instability (inverse bifurcation) are obtained using the generalized Buongiorno two-phase model. The generalized Lorenz model with quadratic nonlinearities is then reduced to an analytically tractable Ginzburg-Landau equation with cubic nonlinearity. The analytical solution of this equation is used to quantify heat transport in terms of the Nusselt number. The contribution of nanoparticles/nanotubes in advancement of onset of convection and hence in the enhancement of heat transport by water is explained. The results of the enclosure problem are extracted from those of the Rayleigh-Bénard convection problem. Tall, square and shallow enclosures are considered in the study by varying aspect ratio. The study reveals that among the three enclosures, tall enclosure transports maximum heat. The influence of heat generation/absorption is shown to augment/inhibit onset of convection and enhance/diminish heat transport. A mechanism of improving heat-removal in water-based cooling systems through the use of nanoparticles/nanotubes is proposed. Several limiting cases of the study are presented.