A correlation theory for two-dimensional natural convective heat transport data for horizontal annuli of arbitrary cross section has been developed and applied to two configurations: (i) concentric circular cylinders and (ii) annuli formed by an inner hexagonal cylinder and an outer circular cylinder. Also embodied in the theory is the capability to predict local as well as mean heat transfer. Thermal boundary conditions of the form T′xm can be accommodated. Data for the Rayleigh number (RaR) varied from 10 to 107, Prandtl number (Pr) varied from 0.7 to 3100, and the aspect ratio (Δ′/r′, maximum annulus gap/minimum radius of inner annulus) varied from 0.5 to 2.0. Even with these large variations, the present correlation theory collapses all the experimental data for the annular geometries to a signle line. The physical problem appears to be completely specified by a single equation when the following is known: thermal boundary condition (i.e., m), the fluid (i.e., Pr), the aspect ratio, the Rayleigh number, and the geometry. This work demonstrates that the present theory is applicable to annuli of arbitrary cross section, and therefore the theory will be extended to include curvature effects and axisymmetric geometry.
Hamiltonian guiding center drift orbit calculation for toroidal plasmas of arbitrary cross section