On the linear convective stability of a TiO ₂ particle–based nanofluid layer heated from below

The linear hydrodynamics of Rayleigh convection in a horizontal nanofluid layer heated from below was studied. The hydrodynamic stability of the fluid layer bounded by two horizontal perfect thermal conducting walls was extended to analyze steady and oscillatory convection, and the role played by thermophoresis. Experimental data of TiO ₂ particle–based nanofluid was used to discuss the stability of the fluid layer. Results on the relationship between thermal and volume faction Rayleigh numbers are used to discuss experiments in nanofluid Rayleigh convection, while the absence of thermophoresis in the model equations was also considered. For this nanofluid, steady convection sets in at critical wavenumber a _c = 3.12, but thermal R _T and nanoparticle volume fraction R _V Rayleigh numbers are given by an implicit relationship. For the onset of oscillatory convection, the wavenumber is also obtained from an implicit equation involving R _T and R _V . Results are discussed in terms of physical dimensionless parameters of the system like the Lewis and Prandtl numbers. This work complements the earlier efforts of Tzou and more recently by Nield and Kuznetsov.