Evaluation of the Stagnation Point Region Overshoot

Abstract

Stagnation point region overshoot is the augmentation of total heat transfer owing to the presence of insulation at the stagnation point region of an otherwise isothermal body. Evidence summarized by the present work indicates that this paradoxical event can be made to occur. The overshoot is due to the singularly high temperature gradient that is impressed upon the boundary layer just as it arrives at the leading edge of the heated surface after passing over the insulated central portion. The evidence comprises experimental results based on the mass-heat analog using sublimation of naphthalene and on theoretical boundary layer calculations using a method of local similarity. In the experiments, the insulated surfaces were simulated with inert wax, and isothermal regions with active naphthalene. The surfaces were circular disks facing uniform airstreams. The finding was that the total rate of mass transfer would be as much as 10 percent greater than that of a fully active disk if the radius of the central inert region were half the radius of the disk. Put another way, if only the 30-percent annulus at the outer edge of the disk were active, it would transfer mass at the same rate as the completely active disk under the same circumstances of flow. Corresponding results are expected from analogically heated disks operating with Prandtl number near unity and disk Reynolds number ranging from 5000 to 250,000.