NUMERICAL STUDY OF TWO-DIMENSIONAL NATURAL-CONVECTION IN A HORIZONTAL FLUID LAYER HEATED FROM BELOW, BY FINITE-ELEMENT METHOD - INFLUENCE OF PRANDTL NUMBER

Natural convection in a two-dimensional horizontal fluid layer heated from below and cooled from above was computed by a finite-element method using a Galerkin approach. In the case of Pr equals 10 the Nusselt number, obtained by an extrapolation to zero element size, agreed well with the experimental data of Silveston left bracket Forsch, Ing. 24, 59-69(1958) right bracket , for a range of Rayleigh numbers from the critical value up to 25,000. For the Prandtl numbers varying from 0. 001 to 1000, steady-state solutions for convection, heat transfer rates and the critical Rayleigh numbers were computed. A correlating equation for critical Rayleigh number as a function of Prandtl number was proposed. Using the correlating equation of Malkus and Veronis left bracket J. Fluid Mech. 4, 225-260(1958) right bracket , it was possible to compute the heat transfer rate near the critical state, for every Prandtl number higher than 0. 001.