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.

The effect of density inversion on steady natural convection heat transfer of cold water, between two horizontal concentric cylinders of gap width, L, is studied numerically. Water near its freezing point is characterized by a density maximum at 4°C. Numerical solutions are obtained for cylinders with nonlinear Rayleigh numbers RA ranging from 2 × 103 to 7.6 × 104, a radius ratio 1.75 ≤ ra ≤ 2.6 and an inversion parameter γ, relating the temperature for maximum density with the cavity wall temperatures, between −2 and 2. The results obtained are presented graphically in the form of streamline and isotherm contour plots. The heat transfer characteristics, velocity profiles, and local and overall Nusselt numbers are studied. The results of the present study were found qualitatively valid when compared with an experimental investigation carried out in the past.

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Convective flow and heat transfer of a Boussinesq fluid contained between two horizontal concentric cylinders is investigated under the effects of two driving mechanisms – an externally‐imposed temperature gradient across the annulus, and a uniform internal heat generation. Numerical results for flow field and temperature distribution are obtained in terms of four dimensionless parameters, namely the radius ratio, R, the Prandtl number, Pr, the Rayleigh number, Ra*, and the ratio, S, between the characteristic temperature induced by internal heating and the applied temperature difference between the boundaries. Depending on the value of S, the flow pattern is made up of either one or two vortices in each half cavity, and heat is transferred into or out of the cavity through the hot wall. In particular, for a certain value of the applied temperature difference, the hot wall apparently acts as a thermally‐insulated boundary, the internal heat is completely lost through the cold wall, and the fluid undergoes a transition from a bicellular to a unicellular flow regime.