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The present study deals with the finite element discretization of nanofluidconvective transport in an enclosure with variable properties. We study theBuongiorno model, which couples the Navier-Stokes equations for the base fluid,an advective-diffusion equation for the heat transfer, and an advectiondominated nanoparticle fraction concentration subject to thermophoresis andBrownian motion forces. We develop an iterative numerical scheme that combinesNewton's method (dedicated to the resolution of the momentum and energyequations) with the transport equation that governs the nanoparticlesconcentration in the enclosure. We show that Stream Upwind Petrov-Galerkinregularization approach is required to solve properly the ill-posed Buongiornotransport model being tackled as a variational problem under mean valueconstraint. Non-trivial numerical computations are reported to show theeffectiveness of our proposed numerical approach in its ability to providereasonably good agreement with the experimental results available in theliterature. The numerical experiments demonstrate that by accounting for onlythe thermophoresis and Brownian motion forces in the concentration transportequation, the model is not able to reproduce the heat transfer impairment dueto the presence of suspended nanoparticles in the base fluid. It reveals,however, the significant role that these two terms play in the vicinity of thehot and cold walls.

Combined Newton-Raphson and Streamlines-Upwind Petrov-Galerkin iterations for nano-particles transport in buoyancy driven flow