Natural convection in enclosures with variable fluid properties

Abstract

The generalized integral transform technique (GITT) is an hybrid numerical‐analytical method that has been successfully applied in convection‐diffusion problems, where the original potentials are replaced by eigenexpansion series, and the system of partial differential equations is transformed into a finite system of ordinary differential equations, allowing to obtain an error controlled solution without any kind of grid generation. This paper aims at the application of GITT to the transient version of the classical differentially heated square cavity problem, considering fluid properties as functions of temperature. Comparing results to some previously reported data for constant fluid properties validates the computational procedure. The solution for variable fluid properties with Boussinesq approximation is presented for several values of inclinations, at Rayleigh number of 10³ and a Prandtl number of 0.71, demonstrating GITT capability of capturing circulating cells formation and evolution at a low Rayleigh number. New correlations for leaning angle and aspect ratio are presented.

Citation

de Souza, M., Fortes de Miranda, R. and Araujo Machado, H. (2003), "Natural convection in enclosures with variable fluid properties", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 13 No. 8, pp. 1079-1096. https://doi.org/10.1108/09615530310501966