Finite element simulation of transient natural convection of low-Prandtl-number fluids in heated cavity

The aim of the present investigation was to study numerically the transient of thermal convection in a square cavity filled with low-Prandtl-number fl uids. The flow is driven by the horizontal temperature gradient between the vertical walls maintained at different temperatures. Two-dimensional equat ions of conservation and Energy are solved using a finite element method an d a fractional step time. The discrete equations systems are solved in the lap of each elementmesh with the aim of verifying the Boussinesq hypothesis locally. To compare our results with the earlier predictions, we have chos en the fluids for Prandtl-numbers 0.001, 0.005 and 0.01 and with Grashof nu mbers up to 1 x 10(7). To predict the steady state solutions with an oscill ary transient period, the results ave reduced in terms of the time series a verage Nusselt-number at the vertical walls, the velocity at the center of the cavity and near right boundary. In addition, the isotherms and the velo city field are produced with the aim of showing the main circulation and pa rticularly the weak circulations at the corners of the cavity.