The effect of buoyancy on the boundary layer about a heated horizontal circular cylinder in axial streaming

The boundary-layer flow over a semi-infinite horizontal circular cylinder heated to a constant temperature and immersed in a uniform axial free stream is discussed in five situations corresponding to successively greater displacements from the leading edge. In the first three cases the drift velocity due to buoyancy is assumed small compared to the axial velocity component. Close to the leading edge of the cylinder the techniques of Seban & Bond are extended to include the drift velocity; far from the leading edge the asymptotic series methods of Stewartson, of Glauert & Lighthill, and of Eshghy & Hornbeck are employed to obtain a solution for the drift velocity. In the intermediate zone where the series solutions do not apply the appropriate partial differential equations are solved numerically. Still further downstream than the region where the ‘asymptotic’ solutions hold it is assumed that the boundary-layer flow is primarily convective and that the boundary layer is thin compared with the radius of the cylinder. A series solution is obtained which is valid near the lowest generator of the cylinder. Numerical methods are used to advance this solution upwards around the cylinder by solving the full boundary-layer equations step-by-step.