Numerical study of the Boussinesq approach validity for natural convection and surface thermal radiation in an open cavity

Abstract

In this work the validity of the Boussinesq approach for the heat transfer calculations in an open cavity considering natural convection and surface thermal radiation is studied. Numerical calculations were conducted for Rayleigh number (Ra) values in the range of 10$^{4}$ -10$^{6}$. The temperature difference between the hot wall and the bulk fluid ($\Delta $T) was varied between 10 and 100 K, and was represented as a dimensionless temperature difference ($\varphi )$. The deviations for the temperature fields and fluid flow patterns, between variable properties and Boussinesq approach are noticeable for $\varphi $=0.333. For total Nusselt numbers, the results with Boussinesq approach and variable properties, indicates deviations within 0.22 % (Ra=10$^{5}$ and $\varphi $=0.033) and 5 % (Ra=10$^{4}$ and $\varphi $=0.333).