The aim of this paper is to find particular integrals of non-linear differential equations which satisfy certain boundary conditions and tend exponentially to zero at infinity. The equations arise in connexion with the problem of integration of the equations of laminar flow in two dimensions. The paper consists of two parts. In the first part the equation / " '+ / / ' = A ( 1 - /'2) is discussed, where A is generally a known parameter, and the primes denote deviations with respect to the independent variable, x. This is the well-known Falkner & Skan’s (1930) equation. It was derived in connexion with the solution of the boundary-layer problem for a particular distribution of the velocity outside the boundary layer. It appears, however, that this equation is of far more fundamental importance in the problem of laminar flow, although, of course, A has a different meaning in the general case than it has in Falkner & Skan’s treatment.
Ferromagnetic Flow of Viscous Fluid in a Slot between Fixed Surfaces of Revolution
