Analytic solutions of the FalknerSkan equation when beta = 1 and gamma = 0
Abstract
Two types of analytic solution for the FalknerSkan equation are obtained when beta is 1 for the boundary conditions f(0) = gamma, f'(0) = 0, and f'(infinity) = 1. The first type is for the case when gamma is greater than or equal to the square root of 2, and is expressed in terms of exponential and error functions. It is essentially the same as that of Thwaites, but is obtained in a more direct way and present in more conventional notation. The second type is for the case when gamma is in the closed interval from 0 to 2, and is obtained in terms of confluent hypergeometric functions.
 Publication:

SIAM Journal of Applied Mathematics
 Pub Date:
 November 1975
 Bibcode:
 1975SJAM....2..558Y
 Keywords:

 Analytic Functions;
 Asymptotic Methods;
 Boundary Layer Equations;
 Boundary Value Problems;
 FalknerSkan Equation;
 Laminar Boundary Layer;
 Boundary Conditions;
 Exponential Functions;
 Hypergeometric Functions;
 Numerical Integration;
 Potential Flow;
 Skin Friction;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer