Abstract
The onset of convection of a nanofluid through a vertical layer of a porous medium confined between impenetrable boundaries is investigated. The flow is driven by a temperature difference across the layer and the motion is described by the continuum model of Neild and Kuznetsov extended to include the Forchheimer component of resistance. The model for the flux of nanoparticles incorporates the effects of Brownian motion and thermophoresis. Conservation of nanoparticles is ensured by demanding that the normal component of the flux of nanoparticles is zero on both vertical impenetrable boundaries. The boundary layer problem has a closed form analytical solution which is compared with the complete numerical solution incorporating boundary layer and streaming flow behaviors. The spatial profiles of velocity, temperature, and the volume fraction of nanoparticles are discussed as these evolve towards their steady-state distributions. The presence of nanoparticles is found to significantly enhance fluid transport.