# Field function - Fully developed flow profile for a square micro channel

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 April 8, 2015, 13:24 Field function - Fully developed flow profile for a square micro channel #1 New Member   Join Date: Mar 2013 Location: Ireland Posts: 10 Rep Power: 13 Hi, I was wondering if anybody had a field function defined for fully developed flow in a square channel? I have a field function for a circular channel but i am under pressure with time to create a square one. Any help would be fantastic.

April 8, 2015, 13:44
#2
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Filippo Maria Denaro
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Quote:
 Originally Posted by smorls Hi, I was wondering if anybody had a field function defined for fully developed flow in a square channel? I have a field function for a circular channel but i am under pressure with time to create a square one. Any help would be fantastic.

a laminar fully developed solution can be obtained by simply solving the Poisson equation for the streamwise component with homogeneous Dirichlet BC.s

April 8, 2015, 13:53
#3
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Quote:
 Originally Posted by FMDenaro a laminar fully developed solution can be obtained by simply solving the Poisson equation for the streamwise component with homogeneous Dirichlet BC.s
Thanks for you response
But im sorry to say that i have never heard of homogeneous Dirichlet BC.s before?

Would you be able to expand a little?

 April 8, 2015, 14:20 #4 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,817 Rep Power: 73 it means w=0 on the walls

 April 9, 2015, 09:59 A good reference for laminar solution in rectangular ducts #5 Member   DaveyBaby Join Date: May 2013 Posts: 46 Rep Power: 13 Here is a solution for rectangular ducts, slightly more general. http://web.ornl.gov/info/reports/1951/3445603527379.pdf pages 11-12

April 9, 2015, 11:01
#6
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Filippo Maria Denaro
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Quote:
 Originally Posted by DaveyBaby Here is a solution for rectangular ducts, slightly more general. http://web.ornl.gov/info/reports/1951/3445603527379.pdf pages 11-12

yes, Eq.(5) in the paper is the Poisson equation I wrote above

 Tags field function, fully developed flow, square channel, square inlet