Realistic modelling of the stability of nanofluid layers

Abstract

In this research, a linear stability analysis for the onset of Marangoni convection in a horizontal layer of a nanofluid heated from below is investigated. The model employed for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The lower boundary of the layer is assumed to be a rigid surface at fixed temperature, while the top boundary is assumed to be a non-deformable free surface cooled by convection to an exterior region at a fixed temperature. The boundaries of the layer are assumed to be impenetrable to nanoparticles with their distribution being determined from a conservation condition. The numerical computations are performed using the method of expansion of Chebyshev polynomials. Stability boundaries for Marangoni numbers are obtained for several nanofluids. The new finding in this research is that the physical properties of the nanofluids are not constants. These properties have been developed by several authors for various common nanofluids based on an extensive survey of historical experimental data. It has been shown that the solution to the steady-state problem represents a linear distribution in temperature and an exponential distribution in volume fraction of nanoparticles. The assumption that the physical properties of the nanofluids are not constant but functions of temperature and volume fraction of nanoparticle leads to new results of thermal stability that differ from previous results.