Numerical Solution of the Onset of Natural Convection in a Rotating Nanofluid Layer Induced by Purely Internal Heating

摘要

AbstractIn this paper, the influence of rotation on the onset of natural convection made by purely internal heating in a horizontal layer of nanofluid is investigated. The boundaries are taken to be rigid-rigid and the normal flux of volumetric fraction of nanoparticles under the thermophoretic effects is supposed to be zero on the boundaries. The model used for nanofluid combines the effects of Brownian motion and thermophoresis. The purely internal heating problem determines that there is no applied temperature difference across the layer and so the external Rayleigh number is no longer applicable. Therefore, here the important parameter is an internal Rayleigh number, one based on the heat source strength. Linear stability theory based upon normal mode technique is used to find the critical internal Rayleigh number. The influence of rotation, the Lewis number, the modified diffusivity ratio and the nanoparticle Rayleigh number on the onset of convection are observed numerically using the higher order Galerkin Method. It is found that the effect of increasing the Lewis number, the modified diffusivity ratio and the nanoparticle Rayleigh number is to hasten the onset of convection, while rotation has a stabilizing effect on the stability of the system.