Steady state two-dimensional mixed convection in rectangular enclosures with heated rectangular elements on the wall

Mixed forced and free convective heat transfer through a rectangular cavity which has a rectangular element on one wall, the face of this element being heated to a uniform temperature, with the opposite wall of the cavity cooled to a uniform lower temperature and with the remaining wall portions adiabatic, has been numerically investigated. Attention has been restricted to the case where the forced flow, which is at the same temperature as the cold wall, enters through the cold vertical wall and also leaves through this wall. The cavity is, in general, inclined to the vertical. Both aiding and opposing forced flow have been considered. The study is based on the use of the two-dimensional Navier-Stokes, energy and continuity equations, the flow being assumed to be steady and laminar. It has also been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy force, this being treated using the Boussinesq approximation. These equations have been written with vorticity, stream function and temperature as variables and the resultant equations have been expressed in dimensionless form. These equations have then been solved using the finite element method. The solutions has, as parameters, the Reynolds number, the Grashof number, the fluid Prandtl number, the aspect ratio of the cavity, the angle of inclination of the cavity, the inlet and outlet duct size, and the aspect ratio of the heated element. A single inlet and outlet dimensionless duct size of 0.4 has been considered and attention has been given to a heated element with an aspect ratio of 2 or 1. Results have only been obtained for a Prandtl number of 0.7. Solutions have been derived for wide range of the remaining dimensionless variables.

An experimental study was undertaken to complement and to qualitatively validate the numerical solution. In the experimental investigation the mixed convection phenomena was observed through the plexiglass wall of an air filled cavity with one wall at room temperature and, in the middle of the opposing wall, a variable heat source mounted on a rectangular element. A small blower circulated air in the cavity over the heated element and with smoke introduced in the inlet of the cavity, photographs of the visualized flow patterns were taken to compare to flow patterns generated from numerical analysis.