A singularity in an unsteady freeconvection boundary layer
Abstract
We consider the evolution of the boundary layer formed by the sudden heating of a horizontal circular cylinder in air, assuming that the Grashof number is large. To begin with the tangential velocity vanishes at the upper generator, from symmetry considerations, but this condition is violated after a finite time and a collision then occurs. The transition between the two types of boundary layers is manifested by a singularity and we elucidate its structure by numerical and analytic studies. It is characterised by a central region in which the inertia forces dominate, the velocity gradient in the tangential direction becomes large and the temperature of the air is almost constant. On either side of this central region the boundary layer is of a more conventional type and formally free of singular behavior. It is claimed that the structure proposed is also relevant to two other unsteady boundarylayer problems, in which singularities dominated by inertia forces have been found to occur.
 Publication:

Quarterly Journal of Mechanics and Applied Mathematics
 Pub Date:
 August 1982
 Bibcode:
 1982QJMAM..35..291S
 Keywords:

 Aerothermodynamics;
 Boundary Layer Stability;
 Free Convection;
 Thermal Boundary Layer;
 Unsteady Flow;
 Circular Cylinders;
 Heat Transfer Coefficients;
 Skin Friction;
 Fluid Mechanics and Heat Transfer