# BC's for stream function equation...

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 February 1, 2011, 12:30 BC's for stream function equation... #1 New Member   RAJESH.P Join Date: Feb 2011 Posts: 3 Rep Power: 8 Sponsored Links Sir, I am using stream-function vorticity formulation for flow over a flat plate problem. I am solving these steady state equations by line-by-line algorithm. for that far away from the plate I have to use a mixed derivative boundary condition ie (mixed derivative of psi wrt both x and y =0) for stream function equation. But in this case i am not able to tackle this bc using fictitious point method. Please help me if anybody know how to apply this bc...

 February 1, 2011, 16:43 #2 Senior Member   Andrew Join Date: Mar 2009 Location: Washington, DC Posts: 195 Rep Power: 10 you can try v=0 and u=U at that boundary..U is the freestream velocity. Sort of like a symmetry line, but is actually a moving wall ( Fromm 1963 and Fromm and Harlow 1963)

 February 2, 2011, 00:19 #3 New Member   RAJESH.P Join Date: Feb 2011 Posts: 3 Rep Power: 8 Thank you for ur reply But my actual problem is mixed convection heat transfer. So it should give results for both natural and forced convection regimes. For natural convection u and v are zeros. Only possible bc is d^2(psi)/dxdy=0. But I cant apply this Bc directly to discretized stream-function equation.

 February 2, 2011, 00:31 #4 Senior Member   Andrew Join Date: Mar 2009 Location: Washington, DC Posts: 195 Rep Power: 10 how are you getting u and v to be zero?

 February 2, 2011, 00:37 #5 New Member   RAJESH.P Join Date: Feb 2011 Posts: 3 Rep Power: 8 For natural convection occurs due to density change(buoyancy) caused by temperature gradient. therefore far away from the plate this effect is negligible fluid will be at rest both u and v will be zero...

 February 2, 2011, 09:45 #6 Senior Member   Andrew Join Date: Mar 2009 Location: Washington, DC Posts: 195 Rep Power: 10 if you are far enough from the plate free convection should be zero, as you stated and the BC should be driven by the forced convection flow, right? Have you tried to get the flow profile neglecting any free convection?

 Tags boundary condition, stream-function, vorticity

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