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

作者：Liao, SJ^*

来源：Journal of Fluid Mechanics, 1999, 385: 101-128.

DOI：10.1017/S0022112099004292

• Semi infinite flat plate
• Two dimensional viscous flow

We apply a new kind of analytic technique, namely the homotopy analysis method (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 under the boundary conditions f(0) = f'(0) = 0, f'( infinity) = 1. This analytic solution is uniformly valid in the whole region 0 less than or equal to eta < infinity. For Blasius' (1908) flow (alpha = 1/2, beta = 0), this solution converges to Howarth's (1938) numerical result and gives a purely analytic 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 results 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 solutions indeed possess the property that f' --> 1 exponentially as eta --> infinity. This verifies the validity of the homotopy analysis method and shows the potential possibility of applying it to some unsolved viscous flow problems in fluid mechanics.

• 单位
  上海交通大学