Simulation of Natural Convection in Concentric Annuli between an Outer Inclined Square Enclosure and an Inner Horizontal Cylinder

Abstract

In this work, the natural convection in a concentric annulus between a cold outer inclined square enclosure and heated inner circular cylinder is simulated for two-dimensional steady state. The Boussinesq approximation was applied to model the buoyancy-driven effect and the governing equations were solved using the time marching approach staggered by body fitted coordinates. The coordinate transformation from the physical domain to the computational domain is set up by an analytical expression. Numerical results for Rayleigh numbers 10 3 , 10 4 , 10 5 and 10 6 , aspect ratios 1.5 , 3.0 and 4.5 for seven different inclination angles for the outer square enclosure 0 o ,- 3 0 o ,- 4 5 o , -60 o ,- 9 0 o ,- 1 3 5 o ,- 1 8 0 o are presented as well. The computed flow and temperature fields were demonstrated in the form of streamlines, isotherms and Nusselt numbers variation. It is found that both the aspect ratio and the Rayleigh number are critical to the patterns of flow and thermal fields. At all Rayleigh numbers angle of inclination has nominal eect on heat transfer. Keywords—natural convection, concentric annulus, square inclined enclosure