NUMERICAL-ANALYSIS OF NATURAL-CONVECTION OF LOW PRANDTL NUMBER FLUIDS HEATED FROM BELOW

Finite difference calculations were carried out for natural convection in a fluid of low Prandtl number between isothermal, horizontal plates with the higher temperature on the plate below. The motion was postulated to consist of two-dimensional roll cells with a width equal to their height. The computations encompassed Prandtl numbers from 10(-4) to 0.72 and Rayleigh numbers from the critical value for the onset of motion up to 3000. They were repeated for three to sir different grid sizes in order to permit accurate extrapolation of Nu -1 to zero grid size. The computed value of the critical Ra for all values of Pr agreed closely with the theoretical value of 1709. The computed values of Nu for Ra greater than the critical value agreed closely with the prior results of Clever and Busse obtained by the Galerkin method. A correlating equation was derived to represent the new results.