Pressure gradient effect in natural convection boundary layers

Abstract

The high Grashof number laminar natural convection flow around the lower stagnation point of a symmetric bowl- shaped heated body is analyzed. A region is identified where the direct effect on the flow of the component of the buoyancy force tangential to the body surface is comparable to the indirect effect of the component normal to the surface, which acts through the gradient of the nonuniform pressure that it induces in the boundary layer. Analysis of this region provides a description of the evolution of the flow from a pressure-gradient dominated regime to a buoyancy dominated regime. Numerical results are presented for the flows above and below heated power-law body shapes, and the upstream propagation of small perturbations to the stationary flow is discussed. An asymptotic analysis is carried out for the flow below nearly flat horizontal bodies, for which the change from pressure-gradient-driven to buoyancy-driven flow occurs very rapidly in a short region. The influence of body edges located in the region of interest is also discussed.