Natural Convective Boundary-Layer on Two-Dimensional and Axisymmetric Surfaces in High-Pr Fluids or in Fluid-Saturated Porous Media

TLDR: In this article, the effects of the surface-normal pressure gradient on the temperature profile can be characterized by a single local configuration-parameter which depends on the local geometry and on the Rayleigh number.

Abstract: In natural convective boundary layers on inclined surfaces, the surface-normal component of the buoyancy force induces a pressure gradient across the boundary layer. For the class of flows in which inertial effects are unimportant (including flows at high Prandtl number as well as flow through fluid-saturated porous media), a local nonsimilarity analysis indicates that the effects of the surface-normal pressure gradient on the temperature profile can be characterized by a single local configuration-parameter which depends on the local geometry and on the Rayleigh number. Under Mangler's transformation the reported computational results become applicable to axisymmetric as well as 2-dimensional geometries of arbitrary contour. In contrast to the single-parameter dependence of the temperature profiles, the velocity profiles depend upon 2 local geometric parameters, as illustrated for the example of an inclined flat plate.