Laminar natural convection boundary layers on near-horizontal plates

Abstract

The first order boundary-layer analysis for the laminar natural convection flow over a semi-infinite horizontal or near-horizontal heated plate has been extended to include variable properties effects. Detailed calculations are presented for air and water flows. It is shown further how these calculations can be extended to predict heat transfer rates on plates of rectangular planforms. Because of the lack of sufficiently detailed experimental data, a thorough comparison between the latter and the present calculations has not been possible. However, such comparisons as have been possible are encouraging and a significant improvement on previous theoretical predictions has been achieved. Although higher order corrections have not been discussed in detail, possible matching problems have been investigated briefly. Furthermore, it has been shown that stress work effects in the energy equation and the influence of pressure on density and temperature in the state relation are not only solely higher order effects but are of little significance at such orders.