Unsteady-state laminar heat transfer in a rotating disk: self-similar solution

Unsteady-state laminar convective heat transfer is investigated under conditions of air cooling of a rotating isothermal disk. Group analysis is used to reduce the Navier-Stokes and energy equations to a self-similar form which makes possible their exact solution. Calculations reveal that the Nusselt number in the initial stage of cooling significantly decreases in time; in the second stage of cooling, this number has the same value as that for steady-state conditions. The results of this study may be used to optimize the unsteady-state procedures of experimental determination of the heat-transfer coefficient.