Conjugate natural convection in a square enclosure: effect of conduction in one of the vertical walls

Abstract

Steady, laminar, natural convection flow in a square enclosure has been analysed numerically. One vertical wall of the enclosure is thick, with a finite thermal conductivity, while the other three walls are taken to be of zero thickness. The problem is conjugate and the main focus of the study is on examining the effect of conduction in the wall on the natural convection flow in the enclosure. Three separate models to account for the wall conduction are investigated : (i) the complete conjugate case in which conduction in the thick vertical wall is assumed to be fully two-dimensional; (ii) a one-dimensional model in which conduction in the wall is assumed to be in the horizontal direction only; and (iii) a lumped parameter approach which assumes the solid-fluid interface temperature to be uniform. A Boussinesq fluid with Prandtl number of 0.7 (air) and Grashof numbers ranging from 10 3 to 10 7 are considered. For Grashof number > 10 5, the temperature distribution in the wall shows significant two-dimensional effects and the solid-fluid interface temperature is found to be quite non-uniform. This non-uniformity tends to make the flow pattern in the enclosure asymmetric. In the parametric range investigated, all three models predict nearly the same value for the overall heat transfer.