Free-convection Flow through a Two-dimensional Box with Openings on opposite Walls

Free-convection flow through a two-dimensional rectangular box having openings at opposite corners on the vertical walls is investigated numerically, using a commercial Computational Fluid Dynamics (CFD) software package. Convection is induced when the box's ceiling or its floor is imposed with a temperature that is different to that of the ambient fluid, while all other walls are insulated. The fluid here is air near standard conditions, with a molecular Prandtl number of 0.707. Computation is performed for a range of Rayleigh-number values, up to about 2.7×10. Chien's turbulence model of low-Reynoldsnumber K-ε is used. When convection is induced by a cold roof or a hot floor, higher flow rate and heat transfer occur. However the resultant flow and temperature variation are more confined to the wall regions, while the rest of the box is relatively much less affected. All this is in contrast to when convection is due to a hot roof or a cold floor. NOMENCLATURE Cμ turbulence-model constant K turbulent kinetic energy m fluid’s mass flow rate through the box uτ friction velocity = (τw/ρ) 2 V velocity magnitude y non-dimensional distance from closest wall = δ/(ν/uτ) δ distance from closest wall α (molecular) thermal diffusivity = k / (ρ cp) β thermal expansion coefficient ε turbulent kinetic energy’s dissipation rate κ Karman constant ν (molecular) kinematic viscosity τw wall shear stress Subscripts a: ambient fluid t: turbulent