Thermal instability of nanofluids in natural convection

Thermal (Bénard) instability in nanofluids is investigated in this work. Emphasizing the combined behaviors of Brownian motion and thermophoresis of nanoparticles, the critical Rayleigh number is shown to be lower by one to two orders of magnitude than that for regular fluids. The highly promoted turbulence increases the energy bearing capacity of nanofluids, which could result in higher overall heat transfer coefficient than the increase of the effective thermal conductivity alone. The dominating groups are extracted from the nondimensional analysis. Close form solutions for the Rayleigh number are derived from the method of eigenfunction expansions and the weighted residual method.