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Blasius Equation Program

  1. Nov 10, 2009 #1
    1. The problem statement, all variables and given/known data

    I am trying to write an excel spreadsheet to show the f, f', f'', and f''' for [tex]\eta[/tex] = 0 - 8.8 and I just wanted to check my formulas if someone wouldn't mind as my results are slightly off from the tables in my fluid mechanics book


    2. Relevant equations

    Equation:

    [tex] f''' + \frac {1}{2} f f''' = 0 [/tex]

    Boundary Conditions:

    [tex] f(0) = f'(0) = 0 [/tex]

    [tex] f'(\eta \rightarrow \infty) = 1 [/tex]

    [tex] \Delta\eta = 0.2 [/tex]

    Initial

    [tex] f_{i2} = f_{i1} + \Delta\eta * \frac {f'_{i1} + f'_{k1}} {2} [/tex]

    [tex] f'_{i2} = f'_{i1} + \Delta\eta * \frac {f''_{i1} + f''_{k1}} {2} [/tex]

    [tex] f''_{i2} = f''_{i1} + \Delta\eta * \frac {f'''_{i1} + f'''_{k1}} {2} [/tex]

    [tex] f'''_{i2} = -\frac {1} {2} f_{i2} * f''_{i2} [/tex]

    Predictor

    [tex] f_{k2} = f_{i2}+ \Delta\eta * f'_{i2}[/tex]

    [tex] f'_{k2} = f'_{i2}+ \Delta\eta * f''_{i2}[/tex]

    [tex] f''_{k2} = f''_{i2}+ \Delta\eta * f'''_{i2}[/tex]

    [tex] f'''_{k2} = -\frac {1} {2} f_{k2} * f''_{k2} [/tex]

    3. The attempt at a solution

    Thanks in advance!

    Just a note, I couldn't get i-1 and k-1 subscripted, so i2, k2 is current and i1, k1 is the previous result. Initial boundary conditions are set at i0, for f, f', f'', and f'''.
     
  2. jcsd
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