Be´nard Instability of Nanofluids

Be`nard instability in nanofluids is investigated in this work. With the combined effects of Brownian motion and thermophoresis of nanoparticles incorporated in natural convection, the critical Rayleigh number governing the transition from laminar to turbulent regime is shown to be 18.11, as compared to 1715.14 in regular fluids. The lower critical value, by as much as two orders of magnitude, reveals that there is heat transfer enhancement by turbulence. This effect is much more significant than the heat transfer enhancement by increased thermal conductivity alone. A nondimensional analysis is performed to extract the dominating parameters governing the turbulence enhancement. Their effects are illustrated along with the characteristic dimension of the Be`nard cells.