An exact solution of the boundary-layer equations under particular conditions of porous surface suction

Abstract

No hitherto successful attempts except one (by Griffith and Meredith) have been made to provide an exact solution of the boundary-layer equations of motion when there is a continuous normal velocity at the boundary. At the suggestion of Preston a solution is given in this report when this suction velocity is proportional to xpower-1/2, x being the distance along the plate, and there is a constant velocity outside the boundary layer. The solution is merely an extension of the well-known Blasius' solution, and does not contain any new mathematical technique. Being exact, however, it can command a certain interest, since the treatment of the boundary-layer equations with suction through the boundary is very difficult (Thwaites). The solutions of the differential equation below were obtained on the differential analyser, at Manchester University, at present on loan to the Mathematics Division, N.P.L. Acknowledgements are made to the Analyser Group of this Division for providing these solutions, and in particular to E. C. Lloyd, who was concerned in this particular problem.