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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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Rachel

Posts: 6
Registered: 3/27/14
Re: Third order non-linear boundary value problem
Posted: Mar 28, 2014 8:23 AM
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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



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