Solution of the boussinesq equations by the finite element method

A finite element procedure is presented for the calculation of two-dimensional transient convective/conductive heat transfer in a fluid region. The governing equations are expressed in terms of the primitive variables; the flow is assumed to be laminar, and the fluid incompressible within the Boussinesq approximation. Three typical problems are examined: flow through a sudden enlargement, natural convection in rectangular enclosures, and natural convection between horizontal concentric cylinders. An assessment of the characteristics of the flow regime is made in association with varying dimensionless Prandtl and Rayleigh numbers, as well as cavity aspects ratios. The upper limit for the Rayleigh number in the present paper is 10⁷. Wherever possible, the results are compared with existing solutions obtained by other numerical methods.