Natural Convective Heat Transfer from a Narrow Isothermal Vertical Flat Plate

Abstract

*† The natural convective heat transfer rate from a vertical isothermal plate 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 rate can be considerably greater than that predicted by these two-dimensional flow results. The heat transfer from a narrow vertical isothermal plate embedded in a plane adiabatic surface, the adiabatic surface being in the same plane as the heated plate, has been considered. 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 was obtained using a commercial finite element method based code, FIDAP. The solution has the Rayleigh number, the dimensionless plate width and the Prandtl number as parameters. Results have been obtained for Rayleigh numbers between 10 2 and 10 8 and for ratios of the plate width to the plate height of between 0.2 and 0.6, attention being restricted to results for a Prandtl number of 0.7. The dimensionless plate width has been found to have a significant influence on the mean heat transfer rate from the plate and an empirical equation for the mean heat transfer rate has been derived.