Natural Convection in a Vertical Annuli with Discrete Heat Sources

Abstract

In this article, we numerically study natural convection heat transfer in a cylindrical annular cavity with discrete heat sources on the inner wall, whereas the outer wall is isothermally cooled at a lower temperature, and the top wall, the bottom wall, and unheated portions of the inner wall are assumed to be thermally insulated. To investigate the effect of discrete heating on the natural convection heat transfer, at most two heating sources located near the top and bottom walls are considered, and the size and location of these discrete heaters are varied in the enclosure. The governing equations are solved numerically by an implicit finite difference method. The effect of heater placements, heater lengths, aspect ratio, radii ratio, and modified Rayleigh number on the flow and heat transfer in the annuli are analyzed. Our numerical results show that when the size of the heater is smaller, the heat transfer rates are higher. We also found that the heat transfer in the annular cavity increases with radii ratio and modified Rayleigh number, and can be enhanced by placing a heater with the smaller length near the bottom surface.

Acknowledgments

This work was supported by the World Class University (WCU) program through the Korea Science and Engineering Foundation funded by the Ministry of Education, Science and Technology (grant no. R32-2009-000-20021-0). One of the authors (MS) would like to acknowledge the support and encouragement of the Chairman and Principal of East Point College of Engineering and Technology, Bangalore, India. The authors would like to extend their appreciation to the referee for helpful comments which improved the quality of an earlier version of this article.

Notes

The values in the brackets denote the percentage error between the present results and the benchmark solutions.