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Y. Achdou and J. L. Guermond, “Convergence Analysis of a Finite Element Projection Lagrange-Galerkin Method for the Incompressible Navier-Stokes Equations,” SIAM Journal on Numerical Analysis, Vol. 37, No. 3, 2000, pp. 799-826. doi:10.1137/S0036142996313580

has been cited by the following article:

• TITLE: Natural Convection of Water-Based Nanofluids in a Square Enclosure with Non-Uniform Heating of the Bottom Wall

  AUTHORS: Nader Ben-Cheikh, Ali J. Chamkha, Brahim Ben-Beya, Taieb Lili

  KEYWORDS: Natural Convection; Unsteady State; Nanofluids; Solid Volume Fraction; Heat Transfer Enhancement

  JOURNAL NAME: Journal of Modern Physics, Vol.4 No.2, February 5, 2013

  ABSTRACT: In this paper, a numerical study of natural convection in a square enclosure with non-uniform temperature distribution maintained at the bottom wall and filled with nanofluids is carried out using different types of nanoparticles. The remaining walls of the enclosure are kept at a lower temperature. Calculations are performed for Rayleigh numbers in the range 5 × 103 ≤ Ra ≤ 106 and different solid volume fraction of nanoparticles 0 ≤ χ ≤ 0.2. An enhancement in heat transfer rate is observed with the increase of nanoparticles volume fraction for the whole range of Rayleigh numbers. It is also observed that the heat transfer enhancement strongly depends on the type of nanofluids. For Ra = 106, the pure water flow becomes unsteady. It is observed that the increase of the volume fraction of nanoparticles makes the flow return to steady state.