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Solution of Blasius Equation Using Shooting

UPDATED: 07/03/2021

This workbook performs a numerical solution of the Blasius equation for flow in a laminar, self-similar, flat plate boundary layer. The Runge-Kutta integration scheme and shooting algorithm used to solve this third-order, non-linear, ordinary differential equation were taken from An Introduction to Computational Fluid Mechanics by C.Y. Chow and embellished with Excel graphics.  Once the value of f'(∞) is close to the desired value (1.0), a half-interval method is used to correct f”(0) until the converged value is found.   Tabulated results from a classical source (Howarth’s results as reported in Schlicting) are included for comparison with the current solution.

animated GIF showing solution of Blasius equation for flow in a self-similar boundary layer by shooting in conjunction with Runge-Kutta integration.
Shooting solution of Blasius Equation for flow in a laminar boundary layer. Shows f, f’ (velocity), and f” (shear) for a sequence of shots. Eventually the outer boundary condition f’ = 1.0 is matched.

 

The “.332” appearing in the correlation for laminar, forced convection on a flat plate follows directly from the value of f”(0) found eventually in the above calculation.

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