Natural Convective Heat Transfer From a Narrow Isothermal Vertical Flat Plate With a Uniform Heat Flux at the Surface

Abstract

Natural convective flow over a vertical plate with a uniform heat flux over its surface has been numerically studied. When the plate is wide compared to its height the flow can be adequately modeled by assuming two-dimensional flow. However, when the width of the plate is relatively small compared to its height, the heat transfer coefficient can be considerably greater than that predicted by these two-dimensional flow results. The Nusselt number distribution over a narrow vertical plate, with a uniform heat flux at the plate surface, has been numerically determined. This heated plate is embedded in a plane adiabatic surface, the surface of the adiabatic surface being in the same plane as the heated plate. It has been assumed 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 has the Rayleigh number, the dimensionless plate width and the Prandtl number as parameters. Results have been numerically determined for a relatively wide range of Rayleigh numbers and dimensionless plate widths for a Prandtl number of 0.7. The dimensionless plate width has been found to have a significant influence on the mean Nusselt number for the plate when the plate is narrow and the Rayleigh number is low. The conditions under which three dimensional flow effects can be neglected have been deduced and an empirical equation for the mean Nusselt number for narrow plates with a uniform surface heat flux has been derived from the numerical results.