Temperature distribution in generalized von Karman rotating-disk flows

The temperature distribution and heat transfer associated with the generalized flow of an incompressible viscous fluid produced by a rotating infinite disk as studied by von Karman (1921) are investigated. A constant-property energy equation is used to obtain the temperature field by the superimposition of similar temperature profiles of number one greater than the degree of inhomogeneity scaled by powers of the radial coordinate. Solutions for the temperature distribution are obtained as functions of Prandtl number and the ratio between the angular speed of the fluid at infinity to that of the disk, and numerical examples are presented for the case of a degree of inhomogeneity equal to three. It is found that for these types of similar solutions, the temperature profiles exist only when the fluid at infinity corotates with the disk and at a lower rate. Temperature profiles for an isothermal disk with negligible viscous dissipation and the thermal boundary layer with negligible viscous dissipation are also illustrated.