As clearly shown, the dispersion of a progressively larger amount of particles in mass flux into the base fluid seems to result in two main effects: an increase in N u and a progressive reduction in the nanofluid layer’s stability, with the consequent decrease in the critical Rayleigh number for the onset of convection. using Al 2O 3 + H 2O in cavities differentially heated at the sides. What seems important to point out is that the Nu-Ra data do not lie on a unique interpolation curve, which is what would be expected if the nanofluid should behave as a pure fluid, thus illuminating the two-phase behaviou of the nanofluids due to the Brownian motion and thermophoresis diffusion of the suspended nanoparticles, as already experimentally found by Putra et al. As expected, N u increases for values of R a n above the critical value, R a c, corresponding to the departure from the perfectly conducting solution of a nanofluid static layer with an N u value equal to unity. The more common way to present heat transfer results is the typical dimensionless distributions displayed in Figure 4, where the Nusselt number N u is plotted versus R a n for a square cavity using the average volume fraction as a parameter. However, the experimental measurement of the critical Rayleigh number represents a very difficult task for the extremely long waiting time needed for perturbations for growing and breaking the nanofluid stratification thus, an accurate investigation can be obtained only by means of a theoretical stability analysis, in the case of an indefinite horizontal layer, or in a finite-volume numerical simulation if the nanofluid is confined within a cavity, provided that the effective properties are correctly evaluated and the concentration boundary conditions are properly imposed. On the other hand, when the particle size is smaller than 100 nm, Brownian motion and thermophoresis effects are sufficient to destabilize the layer. suggested that the critical Rayleigh number for the onset of convection of a horizontal colloidal suspension layer heated from below may be strictly related to the size of the suspended particles, whose increase above 100 nm should play a stabilizing effect. A totally different result was found by Rao and Srivastava, who conducted experiments using a rectangular cavity filled with Al 2O 3 + H 2O, in which significant enhancements of the heat transfer coefficient up to 36% were detected with respect to the base fluid.

Moreover, although the extra-buoyancy force consequent to the large density difference existing between the solid and liquid phases should lead to a convection enhancement, they measured a heat transfer rate which decreased as the volume fraction was increased, probably as a result of the increase in the effective dynamic viscosity.

Nanofluid instability due to the aggregation and sedimentation of nanoparticles was observed experimentally by Wen and Ding in a water layer heated from below with the addition of different amounts of TiO 2 nanoparticles.

On the contrary, since the nanofluid actually behaves as a two-phase fluid, the nanoparticle’s motion due to the Brownian diffusion and thermophoresis may induce a concentration gradient which enhances the nanofluid layer’s instability, even if the Rayleigh number does not exceed the critical Rayleigh number R a c for the onset of convection in a pure fluid. This could be reasonable should the nanofluid behave as a single-phase fluid. The common evidence is that the addition of nanoparticles to a base fluid has the effect of increasing the dynamic viscosity of the suspension and, consequently, making the layer more stable.

However, a number of discrepancies can be found mainly due to the different numerical models used, which basically means single-phase or two-phase approaches assuming either physical properties that are variable or constant with temperature. The thermal instability of a horizontal nanofluid layer, confined between rigid boundaries and heated from below, has been the subject of several theoretical and numerical studies, for its importance in particular engineering applications, as the cooling of the micro-electronic devices and the solar collectors.

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