On the Validity of the Boussinesq Approximation in a Developing Mixed Convection Boundary Layer

In order to study the effect of the Boussinesq approximation and finding the temperature difference criterion for which it is valid, the fluid flow and heat transfer are studied in a vertical channel. The governing equations are solved considering two approaches namely Boussinesq approximation with constant fluid properties and Favre averaged equations with variable properties for the fluid. Large eddy simulation together with a dynamic subgrid scale model is employed as the numerical method. The working fluid is air and a constant heat flux boundary condition is applied to one of the channel walls while the other wall is kept insulated. The Grashof and Reynolds numbers based on the wall heat flux and the channel width are Gr=9.4middot10⁷ and Re=5080. Since the hot wall temperature is high and the channel walls have a view factor close to unity, radiation is also taken into account and it is shown that about 10% of the heat is transferred via radiation