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

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Posts: 1,717
Registered: 11/8/10
Re: Third order non-linear boundary value problem
Posted: Mar 28, 2014 9:51 AM
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"Rachel " <> wrote in message <lh3pjc$g23$>...
> 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 ?

Best wishes

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