Scales of free convection around a vertical cylinder

Abstract

The natural scales of the laminar steady-state free convection flow regime surrounding an isothermal vertical cylinder are established. It is shown that nondimensionalizing the momentum and energy equations in terms of the Rayleigh or Boussinesq numbers allows the use of the Prandtl number as a criterion to establish whether the motive buoyancy force is mainly balanced by inertia or by friction. Instead, in the conventional formulation based on the Grashof number, this distinction is not possible.