Abstract
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 TiO2 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 ac = 3.12, but thermal RT and nanoparticle volume fraction RV Rayleigh numbers are given by an implicit relationship. For the onset of oscillatory convection, the wavenumber is also obtained from an implicit equation involving RT and RV. 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.
Highlights
Heat transfer enhancement by nanofluids has called the attention of researchers since several years ago due to industrial and lab applications.[1,2,3,4] Most of these applications are related to heat transfer enhancement with a number of theoretical[5,6] and experimental results reported
This study focuses on the linear thermal hydrodynamic stability of a nanofluid layer heated from below
The results are given in terms of dimensionless parameters of the system like the thermal and particle volume fraction Rayleigh numbers, the wavenumber, the frequency of oscillation, the Prandtl number, the average particle volume fraction, a reference value for the particle volume fraction, and a set of parameters to represent the double diffusion across the fluid layer
Summary
Heat transfer enhancement by nanofluids has called the attention of researchers since several years ago due to industrial and lab applications.[1,2,3,4] Most of these applications are related to heat transfer enhancement with a number of theoretical[5,6] and experimental results reported. Nanofluids find most of its applications in heat transfer enhancement, Wong and De Leon[4] envisaged some other interesting applications in biomedicine and food. Rayleigh convection phenomenon in nanofluids has been considered since several years ago. Buongiorno,[8] for example, made a review on convective heat transport by nanofluids. Tzou[10,11] formulated the problem of Rayleigh convection for fixed temperature
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