Natural convection in a cubical cavity heated from below at low rayleigh numbers

Abstract Natural convection in a cubical cavity heated from below is examined by means of the three-dimensional computation of the time dependent Navier-Stokes and energy transport equations in the range of Rayleigh numbers 3500 ⩽Ra ⩽ 10 000. The Boussinesq approximation has been used to model buoyancy effects on momentum transfer. Four different stable convective structures occur with orientation and flow circulation dictated by the combined effect of the four adiabatic confining lateral walls. Three of these structures are typical single rolls with their axis of rotation or vorticity horizontal and either parallel to two opposite vertical walls, structures S1 and S3, or orientated towards two opposite vertical edges (S2). The fourth structure (S4) is a nearly toroidal roll with the descending motion aligned with the four vertical edges and the single ascending current along the vertical axis of the enclosure. The effect of the Rayleigh number and the type of flow structure on heat transfer rates at the top and bottom plates is also reported. For the single roll-type structures the surface averaged Nusselt number increases with a power of the Rayleigh number that changes within the range studied from 0.7 to 0.4. A similar trend is observed for the toroidal roll but in this case heat transfer rates are 65% lower. The distribution of local heat transfer coefficients at the top and bottom surfaces agrees with the topology of the flow patterns portrayed with the aid of the second invariant of the velocity gradient and the modulus of the cross product of the corresponding velocity and vorticity fields.