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Separating a higher-order ODE into 1st-order ODEs

  1. Sep 17, 2006 #1
    Normally I can do these, and I'm fairly familiar with the equations used here, but for the life of me I can't figure this one out. Here's the question:

    The following equation is the known as Blasius boundary layer equation for the laminar flow over a flat
    plate in similarity variables:

    2f''' + ff'' = 0
    [itex]\eta[/itex] = 0, f' = f = 0
    [itex]\eta[/itex] --> inf, f' --> 1


    [tex]\eta = \frac{y}{x} \sqrt{\frac{U_{\infty}x}{\nu}[/tex]

    [tex]\frac{u}{U_\infty} = f'(\eta)[/tex]

    This'll look familiar to anyone else who knows fluid mechanics, I'm sure. The question requires me to solve this numerically using MATLAB, which I think I can figure out, but the methods we use require a series of 1st order ODES. I can't figure out how to separate this and it's driving me craaaaazy. Every method I try doesn't fit with the given boundary values. I've tried rearranging everything given there but I can't figure it out. Anyone got any ideas?
    Last edited: Sep 17, 2006
  2. jcsd
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