| Popis: |
A study of the asymptotic behavior of the heat transfer in laminary boundary layers for large Prandtl Number is presented. The analysis is based on the observation that, for large Prandtl Number, the conduction term in the energy equation must be important only in a region that is very narrow compared with the velocity boundary layer, but that, in that region, both convection and conduction are essential. A transformation (based on the Prandtl Number) of the coordinate normal to the body surface leads to a form of the energy equation in which the appropriate convection and conduction terms can be balanced with respect to their asymptotic dependence on the Prandtl Number, and the behavior of the local heat-transfer coefficient can be deduced immediately. The general method is applied to the well-known problems of forced convection over a body and of the plate thermometer, where it confirms results previously obtained by other methods. The problems of natural convection over a vertical body, of the flow above a rotating disc, and of the Hamel converging channel flow are then treated; new theoretical results are obtained for these cases. |
