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Student Support Forum: 'Third-order, non-linear ODE with integral BC' topicStudent Support Forum > General > Archives > "Third-order, non-linear ODE with integral BC"

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Servillo
03/25/12 11:49pm

I have a third-order, non-linear ODE that I want to solve that represents flow in between two inclined plates.

f'''[theta]+2*Ren*a^2*f[theta]*f'[theta]+4*a^2*f'[theta]==0

'Ren' and 'a' are constants that can be arbitrarily defined.

I can specify boundary conditions in the middle of the flow ( f'[theta]==0 ) and and the edge of the plate ( f[theta]==0 ), but it's the third constraint that gets me when I try to use NDSolve.

In order to maintain that the mass flow rate is identical at every radial location, I have an integral constraint of

1/(2*a)==Integral[f[1],{theta,0,1}]

I have my notebook attached to show what little work I've done with this. If it isn't already obvious, I don't really know how to work with some of the finer points of NDSolve, which I'm sure would help greatly with this problem.

Attachment: inclinedplateflow.nb, URL: ,

Subject (listing for 'Third-order, non-linear ODE with integral BC')
Author Date Posted
Third-order, non-linear ODE with integral BC Servillo 03/25/12 11:49pm
Re: Third-order, non-linear ODE with integral BC toen 03/31/12 01:56am
Re: Re: Third-order, non-linear ODE with integr... Servillo 03/31/12 10:39pm
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