Effects of Radiation and Cold Wall Temperature Boundary Conditions on Natural Convection in a Vertical Annular Porous Medium

This paper deals with the numerical solution for natural convection in a vertical annular porous medium for various cold wall temperature boundary conditions and radiation parameters. The heat transfer is assumed to take place by convection and radiation. The inner wall (hot wall) of the annulus is maintained at an isothermal temperature while the outer wall (cold wall) is subjected to different temperature conditions. The temperature conditions maintained at the cold wall are evaluated for uniform as well as non uniform temperatures. The fluid is assumed to obey Darcy’s law. The governing partial differential equations are non-dimensionalised and solved by finite element method. The porous medium is discretised with unstructured triangular elements. The effects of radius ratio and Rayleigh number on the Nusselt number and Sherwood number are investigated on the annulus for different temperatures at cold wall. The effects of radiation on flow patterns, temperature distribution and concentration distribution are discussed. The results reveal that the Nusselt number and Sherwood number at cold wall decrease with the increase in radius ratio, whereas they increase with the radius ratio at hot wall for different temperature boundary conditions at the cold wall. Temperature cold wall conditions have pronounced effect on the Nusselt and Sherwood numbers

Keywords:

Radiation , convection , vertical annulus , Numerical method , Porous medium , Heat transfer