Variable Property Effects in Laminar Natural Convection in a Square Enclosure

A numerical, finite-difference study has been carried out to determine the effects of variable properties on the temperature and velocity fields and the heat transfer rate in a differentially heated, two-dimensional square enclosure. Calculations have been done for a Rayleigh number range up to 10⁶, and temperature difference ratios θ₀ = (T_H–T_C) / T_C of 0.2, 0.5, 1.0, and 2.0, where T_Hand T_C are the hot and cold wall temperatures, respectively. Specific issues that have been addressed are the limits of validity of the Boussinesq approximation, the proper use of a reference temperature, variable property correlation of the heat transfer rate, and the limits of conduction-dominated regions.