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Topic: Third order non-linear boundary value problem
Replies: 7   Last Post: Apr 2, 2014 12:34 PM

 Messages: [ Previous | Next ]
 Torsten Posts: 1,717 Registered: 11/8/10
Re: Third order non-linear boundary value problem
Posted: Mar 28, 2014 9:51 AM

"Rachel " <rachel-dore20@hotmail.com> wrote in message <lh3pjc\$g23\$1@newscl01ah.mathworks.com>...
> Hey Torsten,
>
> Thanks so much for that but I'm really confused I am trying to solve numerically for the velocity profiles of the fluid from the boundary layer equations,
>
> udu/dx+vdu/dy=Udu/dx+nud^2u/dy^2
>
> du/dx+dv/dy=0
>
> (These derivatives are partial apart from the 3rd term in the first equation).
>
> The boundary conditions are du/dy=0(partial) when y=0 and u=0 when y=+-infinity.
>
> I introduced the stream function u=d(stream)/dy and v=-d(stream)/dx (both partials)
>
> where stream function is a similarity solution, stream=x^pf(y/x^q) where eta=f(y/x^q).
>
> Putting the boundary layer equations in terms of the stream function and having found p=1/3 and q=2/3 the equations reduce to f'''+1/3ff''+1/3f'^2 now i thought the boundary conditions changed to f(0)=f''(0)=0 and f'(infinity)=0.
>
> Is there any sense in trying the code with the first set of boundary conditions or would there be a way of solving the PDE's maybe?? I'm clueless with all this.
>
> I solved the ODE analytically using the first set of boundary conditions.
>
> I don't know if this will make much sense to you but it would be great if you could let me know!! Your very good thanks.
>
> Rachel

Is it Blasius' equation you are trying to solve ?
http://en.wikipedia.org/wiki/Blasius_boundary_layer

Best wishes
Torsten.

Date Subject Author
3/27/14 Rachel
3/28/14 Torsten
3/28/14 Rachel
3/28/14 Torsten
3/28/14 Rachel
4/2/14 Rachel
3/28/14 Gene
3/28/14 Rachel