Evaluation of reference temperature in the pseudo density model for solving internal natural convection of gases

Abstract

This paper attempts to investigate a numerical solution for internal natural convection in gases. There are two kinds of models used to handle buoyancy force in the internal natural convection problems, the pseudo density difference model and the direct model. It was shown that pseudo-density-difference model is originally a solution for external natural convection. However, when this model is adopted to solve the internal natural convection problem the reference temperature must be treated properly. The advantage of using pseudo-density-difference model is less memory in the computational process issued. The direct model was used to evaluate the appropriate reference temperature for pseudo density difference model. Calculations for air in a two dimensions square cavity, which is bounded by adiabatic horizontal planes and isothermal vertical planes, with temperature difference 10⁻¹ K ≤ ΔT ≤ 2.10² K and Rayleigh numbers 10³ < Ra < 10⁶ were carried out. The conclusion of this research is the pseudo density difference model reveals better results when the average temperature is chosen as the reference temperature.