Numerical Study of Natural Convection in Vertical Enclosures using a Novel Non-Boussinesq Algorithm

Abstract

This article applies a novel non-Boussinesq numerical algorithm to solve the free-convection problem in a wide range of thin to thick vertical cavities subject to different side-wall temperatures. In this regard, the compressible flow equations are solved using a primitive incompressible method. No Boussinesq approximation and low Mach number consideration are included in the formulation. To implement the compressibility effect, the density field is calculated via the equation of state for gas. The temperature gradient is suitably varied to generate different low to high thermobuoyant fields, where the Boussinesq approximation may or may not be valid. Contrary to published works on the thin vertical cavity problem, the thin cavity is studied over a wide range of temperature gradients. The results are presented for different length-to-height ratios varying from 0.1 to 1.0. The present results are in full qualitative and quantitative agreement with those available in the literature. The quantitative comparisons show that the conduction mechanism is dominant at lower length-to-height ratios if and only if the Rayleigh number is sufficiently low. It is shown that the current formulations provide more reliable solutions than those of past works.

This work was partially supported by the research center of Sharif University of Technology.

Notes

^a Constant-property case.

^b Variable-property case.