Natural convection in an annulus between two isothermal concentric square ducts

This paper is focused on steady-state, laminar, two-dimensional natural convection in an annulus between two isothermal concentric square ducts. Stream function-vorticity formulation was applied and control volume integration solution technique is adopted in this study. Solutions are obtained up to Rayleigh number of 106. Three different dimension ratios, L∗, namely 15, 310, and 35, are considered. The effects of dimension ratio and Rayleigh number on the flow structure and heat transfer are investigated. The results show that dimension ratio and Rayleigh number have a profound influence on the temperature and flow field. As the dimension ratio is increased (decreasing the gap between squares), a multiple cell solution is developed between the upper sides of the square ducts. The transition to the multiple cell solution depends on the Rayleigh number, Ra and dimension ratio L∗.The results of heat transfer are also presented and comparisons with earlier experimental results are made.