NATURAL-CONVECTION IN A CUBICAL CAVITY HEATED FROM BELOW AT LOW RAYLEIGH NUMBERS

Natural convection in a cubical cavity heated from below is examined b y means of the three-dimensional computation of the time dependent Nav ier-Stokes and energy transport equations in the range of Rayleigh num bers 3500 less than or equal to Ra less than or equal to 10 000. The B oussinesq approximation has been used to model buoyancy effects on mom entum transfer. Four different Stable convective structures occur with orientation and flow circulation dictated by the combined effect of t he four adiabatic confining lateral walls. Three of these structures a re typical single rolls with their axis of rotation or vorticity horiz ontal and either parallel to two opposite vertical walls, structures S 1 and S3, or orientated towards two opposite vertical edges (S2). The fourth structure (S4) is a nearly toroidal roll with the descending mo tion aligned with the four vertical edges and the single ascending cur rent along the vertical axis of The enclosure. The effect of the Rayle igh number and the type of flow structure on heal transfer rates at th e top and bottom plates is also reported. For the single roll-type str uctures 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 cas e heat transfer rates are 65% lower. The distribution of local heat tr ansfer coefficients at the top and bottom surfaces agrees with the top ology of the flow patterns portrayed with the aid of the second invari ant of the velocity gradient and the modulus of the cross product of t he corresponding velocity and vorticity fields. Copyright (C) 1996 Els evier Science Ltd.