Numerical Study of Natural Convection in a Vertical Porous Annulus with an Internal Heat Source: Effect of Discrete Heating

Abstract

This article reports a numerical study of natural convection in a vertical annulus filled with a fluid-saturated porous medium, and with internal heat generation subject to a discrete heating from the inner wall. The relative importance of discrete heating on natural convection in the porous annulus is examined via the Brinkman-extended Darcy equation. The inner wall of the annulus has a discrete heat source and the outer wall is isothermally cooled at a lower temperature. The top and bottom walls and the unheated portions of the inner wall are kept adiabatic. The governing equations are numerically solved using an implicit finite difference method. A wide range of numerical simulations is conducted to understand the effects of various parameters like heat source length, heat source location, Darcy number, radius ratio, and Rayleigh numbers due to external and internal heating on the flow and heat transfer. The numerical results reveal that the placement of the heater near the middle portion of the inner wall yields the maximum heat transfer and minimum hot spots rather than placing the heater near the top and bottom portions of the inner wall. The heat transfer increases with an increase in the external Rayleigh number and Darcy number, while it decreases with an increase in the internal Rayleigh number, porosity of the porous medium, and the size of the heater. Further, we found that the size and location of the heater has a profound influence on the heat transfer rate and maximum temperature in the annular cavity.

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). The author M. Sankar would like to acknowledge the support and encouragement of the Chairman and Principal of East Point College of Engineering and Technology, Bangalore, India, and Visvesvaraya Technological University, Belgaum for support and encouragement.