NATURAL CONVECTION IN A HORIZONTAL CONCENTRIC CYLINDRICAL ANNULUS

This numerical study of natural convection flow in a horizontal cylindrical annulus is aimed at establishing the utility of the Galerkin‐spline formulation for natural convection problems. The annulus has isothermal walls and the fluid is of constant material properties except for its density; density variation is incorporated via the Boussinesq approximation. Two formulations are employed, the velocity formulation and the streamfunction formulation. We are able to demonstrate the usefulness of the Galerkin‐spline formulation for the problem and in comparison with published data, show that it leads to greater accuracy than the finite difference method. We also show the streamfunction formulation to be superior computationally to the velocity formulation. We find no bifurcation from the basic state up to 60,000 in Grashof number, even without a priori assumption of symmetry about the vertical plane. This last finding is in sharp contrast to results obtained when porous material fills the annulus.