Abstract
Natural convection of air in a tall rectangular cavity is explored by solutions of the fully compressible transient Navier–Stokes equations in two-dimensional form, without the Boussinesq approximation. A temperature difference is imposed on the two vertical side walls, each isothermal, with the two horizontal boundaries adiabatic. Thermo-physical properties of air, including density, viscosity, thermal conductivity and specific heat, are all variable with temperature. Contrary to the conclusions in most previous numerical studies invoking the Boussinesq approximation, this study finds the instability of the conduction regime to be a traveling wave drifting downward in the cavity. The wave-drift speed is a strong function of the dimensionless wall temperature difference, ε, defined as the temperature difference between the vertical walls divided by twice the mean wall temperature. Wave-drift speeds and wave numbers are calculated over a range of ε less than 0.5 and Rayleigh numbers less than 9000. The dimensionless temperature difference ε is also found to have significant effects on local heat transfer and transient flow structure inside the cavity.
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