A Theoretical Study on Natural Convection in a Concentric Vertical Annulus

Abstract

The research include a theoretical study of natural laminar study convection heat transfer in a vertical annuls, the surfaces were at constant temperature and the inner cylinder temperature is higher than the outer cylinder temperature. The air used as a working fluid in the annulus. Rayleigh Number was( 71 Ra 5 10 4 ) and the radius ratio were (1.7, 2.0 and 2.3). Alternating direct implicit method (ADI) was used to solve the governing equations numerically, the governing equations were transformed into vorticity-stream function formula then transformed into algebraic equations using finite difference method. The results were declared by using contour diagrams which represent streamlines and isotherms also the results were declared by velocity and temperature distribution through the annulus and local Nusselt number along the inner cylinder.It was found in this research that heat transfer by conduction in low Rayleigh Number, also increasing the thermal boundary layer around the inner cylinder as the fluid moves up while the thermal boundary layer on the outer cylinder increases as the fluid moves down.