Natural convection heat transfer in the annulus between horizontal circular cylinders

Abstract

In this research natural convection heat transfer in the annulus between two horizontal cylinders has been studied. The bipolar cylindrical coordinates are used for the eccentric annulus whereas the polar cylindrical coordinates are adopted for the concentric case. The Navier-Stokes equations based on the Boussinesq approximation are solved numerically using finite difference method and successive overrelaxation procedures. Calculations have been made for three different Rayleigh numbers and a number of different eccentricity while the Prandtl number and the diameter ratio of the cylinders are fixed at 0.7 and 2.6, respectively. The overall result of the calculations for the concentric annulus is in good agreement with the data published in the literature. For the eccentric case the temperature distribution is well predicted in comparison with the experimental data reported by Kuehn and Goldstein (1978). It is found that the heat transfer coefficients at the upper eccentricity, $ε_v= \frac{2}{3}$, are lower by 3 to 8% than those of concentric case, while are higher by 5 to 12% for the lower eccentricity $ε_v=\frac{-2}{3}$. These values slightly disagree with the experimental data but the qualitative trends are well coincident. $ε_v=\frac{-2}{3}$, These values slightly disagree with the experimental data but the qualitative trends are well coincident.