HEAT TRANSFER AT HIGH PECLET NUMBER IN REGIONS OF CLOSED STREAMLINES

An asymptotic solution is developed for the temperature distribution at high Péclet number in a doubly-connected, laminar, incompressible flow field consisting entirely of closed streamlines. It is shown that, with the exception of a thin thermal layer next to a non-isothermal surface, the temperature is constant along a streamline but that, in contrast to the analogous problem of vorticity transport, this bulk temperature distribution is in general non-uniform. It is also established that the asymptotic expression for the average Nusselt number N ̄u does not contain explicitly the Péclet number Pe irrespective of the thermal and hydrodynamic boundary conditions, a result which is at variance with what is commonly encountered in heat transfer to external flows where, as a rule, N ̄u increases monotonically with increasing Pe. © 1968.