Combined Free and Forced Convection of Water Between Horizontal Concentric Cylinders

Abstract

This paper presents a theoretical study of combined free and forced laminar convection of a mass of water confined between two horizontal concentric cylinders with constant surface temperatures and subject to an externally-imposed constant pressure gradient along the axial direction. The governing system of differential equations is solved, within the Boussinesq approximation, by perturbation and finite difference methods, and the solutions are obtained in terms of the various characteristic parameters of the problem. Essentially, it is found that the flow pattern and the wall shear stress in the axial direction are significantly affected by the Prandtl and the Rayleigh numbers. Thus, the axial flow shows a tendency to develop in two or even three jets, depending on the Rayleigh number. The occurrence of the inversion of density, for water at 4°C, was found to modify completely the convective, or secondary flow, but to have little effect on the main, or axial, flow.