MODELING OF BUOYANCY-DRIVEN FLOW AND HEAT TRANSFER FOR AIR IN A HORIZONTAL ANNULUS: EFFECTS OF VERTICAL ECCENTRICITY AND TEMPERATURE-DEPENDENT PROPERTIES

Abstract

In this article fluid dynamic and thermal fields are presented for numerical simulations of laminar, steady, two-dimensional buoyancy-driven flows in an annulus between two vertically eccentric pipes using the penalty finite element method. The simulations were accomplished for Rayleigh numbers between 10 3 and 10 5 and radius ratio of 2.6, with various eccentricities. For most of the work, the usual Boussinesq approximation was made. However, in order to demonstrate the effects of temperature-dependent physical properties for natural convection in a concentric annulus, a modified Boussinesq approximation with temperature-dependent viscosity and thermal conductivity has been used. The formulation was based on primitive variables. Numerical results are presented in terms of isotherms, streamlines, and Nusselt numbers. The results are compared with recent publications and excellent agreement has been found. Stable solutions were obtained when the model was modified to incorporate temperature-dependent viscosity and thermal conductivity and applied to the case of a concentric annulus. The varying viscosity had the most effect on the fluid velocity, while the effects of varying thermal conductivity were most noticeable in the temperature profiles and local Nusselt numbers.