Abstract
Abstract A linear stability analysis is performed for the onset of Marangoni convection in a horizontal layer of a nanofluid heated from below and affected by rotation. The top boundary of the layer is assumed to be impenetrable to nanoparticles with their distribution being determined from a conservation condition while the bottom boundary is assumed to be a rigid surface with fixed temperature. The motion of the nanoparticles is characterized by the effects of thermophoresis and Brownian diffusion. A modification model is used in which the effects of Brownian diffusion and thermophoresis are taken into consideration by new expressions in the nanoparticle mass flux. Also, material properties of the nanofluid are modelled by non-constant constitutive expressions depending on nanoparticle volume fraction. The steady-state solution is shown to be well approximated by an exponential distribution of the nanoparticle volume fraction. The Chebyshev-Tau method is used to obtain the critical thermal and nanoparticle Marangoni numbers. Different stability boundaries are obtained using the modified model and the rotation.
Highlights
The last decade witnessed great interest in nanofluids due to their wide applications in science and engineering because of their thermal and mechanical properties
The object of the present study is to investigate this problem for layers of distilled water (DW)/alumina and DW/cupric oxide nanofluids using a modified model with material properties which are modelled by non-constant constitutive expressions that depend on nanoparticle volume fraction
This work investigated the linear stability of the onset of Marangoni convection for horizontal layers of DW/ alumina and DW/cupric oxide nanofluids rotated about the x3-axis, heated from below and losing heat from their upper surfaces by convection to a region at constant temperature
Summary
The last decade witnessed great interest in nanofluids due to their wide applications in science and engineering because of their thermal and mechanical properties. Buongiorno [1] proposed a model for convective transport in nanofluids, which combines the effect of Brownian motion and thermophoresis His model is used by many researchers to study the onset of thermal instability of a nanofluid layer. Abdullah et al [20] studied the stability of Marangoni convection in a layer of nanofluid using a modification model of the nanoparticle mass flux in which the effects of Brownian diffusion and thermophoresis are taken into consideration They assumed that material properties of the nanofluid layer such as effective thermal conductivity and effective viscosity are modelled by non-constant constitutive expressions which depend on temperature and nanoparticle volume fraction.
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