Student Support Forum: 'Thirdorder, nonlinear ODE with integral BC' topicStudent Support Forum > General > "Thirdorder, nonlinear ODE with integral BC"
Author 
Comment/Response 
Servillo

03/25/12 11:49pm
I have a thirdorder, nonlinear 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: , 

   
 
