A uniformly valid analytic solution of two-dimensional viscous flow over asemi-infinite flat plate

We apply a new kind of analytic technique, namely the homotopy analysis met hod (HAM), to give an explicit, totally analytic, uniformly valid solution of the two-dimensional laminar viscous flow over a semi-infinite flat plate governed by f'''(eta) + alpha f(eta)f "(eta) + beta[1-f'(2)(eta)] = 0 unde r the boundary conditions f(0) = f'(0) = 0, f'(+infinity) = 1. This analyti c solution is uniformly valid in the whole region 0 less than or equal to e ta < +infinity. For Blasius' (1908) flow (alpha = 1/2, beta = 0), this solu tion converges to Howarth's (1938) numerical result and gives a purely anal ytic value f "(0) = 0.332057. For the Falkner-Skan (1931) flow (alpha = 1), it gives the same family of solutions as Hartree's (1937) numerical result s and a related analytic formula for f "(0) when 2 greater than or equal to beta greater than or equal to 0. Also, this analytic solution proves that when -0.1988 less than or equal to beta < 0 Hartree's (1937) family of solu tions indeed possess the property that f' --> 1 exponentially as eta --> +i nfinity. This verifies the validity of the homotopy analysis method and sho ws the potential possibility of applying it to some unsolved viscous flow p roblems in fluid mechanics.