Parametric Analysis for Thermal and Fluid Dynamic Management of Natural Convection in a Channel-Chimney System

Abstract

In this paper a parametric analysis of natural convection in air in a channel-chimney system symmetrically heated at uniform heat flux, obtained by means of a numerical simulation, is carried out. The analysed regime is two-dimensional, laminar and steady-state. The numerical procedure employs the full Navier-Stokes and energy equations in terms of the stream function-vorticity approach. Results are presented in terms of wall temperature profiles in order to show the more thermally convenient configurations which correspond to the channel-chimney system with the lowest maximum wall temperature. The analysis is obtained for a Rayleigh number in the range between 102 and 105, for a channel aspect ratio equal to 5, 10 and 20 and the extension and expansion ratios between 1.0 and 4.0. Correlations for dimensionless mass flow rate, maximum wall temperature and average Nusselt number in terms of Rayleigh number, aspect ratio, extension and expansion ratios are presented. Geometric optimal configurations, for assigned Rayleigh number and aspect ratio, are estimated as a function of the extension ratio. For considered Rayleigh number the difference between the highest and the lowest maximum wall temperatures increases increasing the channel aspect ratio. This behaviour is as greater as the extension ratio is. These differences decrease significantly for the highest Rayleigh number value. The optimal expansion ratio values depend strongly on Rayleigh number and extension ratio values and slightly on the aspect ratio.