# Nusselt Number

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 January 28, 2016, 04:46 Nusselt Number #1 New Member   Join Date: Jan 2016 Posts: 4 Rep Power: 10 The Nusselt number used by Ansys CFX in default is NU=2/(1+c*Kn) where c is emperical factor of 3.18. My question is how do we calculate Knudsen number Kn ? I am working on a steam flow in convergent divergent nozzle.

January 28, 2016, 05:12
#2
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Glenn Horrocks
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Location: Sydney, Australia
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Quote:
 The Nusselt number used by Ansys CFX in default is NU=2/(1+c*Kn) where c is emperical factor of 3.18.
No it is not. The Nusselt number is usually defined as the ratio of convective heat transfer to conductive heat transfer (https://en.wikipedia.org/wiki/Nusselt_number), usually something like Nu=hL/k. For a Navier Stokes solver h, L and k are flow conditions, an applicable length scale and a material property.

I have no idea where your Nusselt number as a function of Knudsen number came from, but if you wish to use it: The Knudsen number is the ratio of the mean free path of molecules to a relevant length scale (https://en.wikipedia.org/wiki/Knudsen_number). So you need to define those two numbers. You can evaluate mean free path, see https://en.wikipedia.org/wiki/Mean_free_path

 January 28, 2016, 06:52 #3 New Member   Join Date: Jan 2016 Posts: 4 Rep Power: 10 @ghorrocks Thank You for your reply . Well i found that ansys CFX uses this expression as a default and can be found in ansys cfx help http://orange.engr.ucdavis.edu/Docum.../CFX/xthry.pdf under equation 4.280 (page 161/270) I would like to know knudsen number expression in terms of H2Og.Dynamic Viscosity,Pressure H2Ol.Particle Diameter something like this to form an equation and enter the value in fluid defination morphology.

 January 28, 2016, 16:14 #4 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,701 Rep Power: 143 A bit of context for your question would have been nice. The equation you quoted is the underlying equation for the heat transfer and droplet growth in the droplet condensation model. Nusselt number is used many times by CFX with many different definitions. You are going to have to find a relationship for Kn yourself through a literature search. Knudsen number is not a variable used in CFX (to my knowledge), so you are going to have to derive it from flow variables (pressure, temperature etc).

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