  Mixed convection above a horizontal disk rotating in a semi-infinite fluid is
examined when the disk is heated so that its temperature varies quadratically
with distance away from its centre. Steady similarity solutions are presented
for a range of values of the two dimensionless parameters, a Prandtl number and
a Grashof number. The results are corroborated by asymptotic analyses
undertaken in the limits of small and large Prandtl number. For finite Prandtl
number, the existence of multiple solutions at fixed Grashof number is
revealed. The similarity structure for steady solutions fails beyond a critical
Grashof number and this is interpreted in terms of a finite-time singularity of
the unsteady form of the governing equations.
