Natural convective heat transfer from a recessed narrow vertical flat plate with a uniform heat flux at the surface

Abstract

Paper presented at the 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 1-4 July, 2007.

The natural convective heat transfer rate from a relatively narrow heated vertical plate with a uniform heat flux over its surface has been numerically studied. This heated plate is embedded in a large plane adiabatic surface, the surface of the heated plate being somewhat “below” that of the adiabatic surface, i.e., the heated plate surface is recessed in the adiabatic surface. The main aim of the present work was to study how the recessing of the heated plate into the surface affects the mean heat transfer rate from the plate. It has been assumed that the flow is steady and laminar and that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated by using the Boussinesq approach. It has also been assumed that the flow is symmetrical about the vertical centre-plane of the plate. The solution has been obtained by numerically solving the full three-dimensional form of the governing equations, these equations being written in dimensionless form. The solution was obtained using a commercial finite element method based code, FIDAP. The solution has the Rayleigh number based on the plate height and the surface heat flux, the dimensionless plate width, the dimensionless depth that the heated plate is recessed into the adiabatic surface, and the Prandtl number as parameters. Results have only been obtained for Pr = 0.7. A relatively wide range of values of the other input parameters have been considered and the effects of these parameters on the mean Nusselt number have been determined and used to study the effects that arise due to the plate being recessed and that arise due to the fact that the plate is relatively narrow.