Nu = h * Dh / k. A representative k value for a mix of water and air can be found by weighted average of the k for each component using the mass of each component. Dh is the characteristic length of the system, in this case the hydraulic diameter for the pipe (Use the diameter if it's round). h is the convection coefficient in W/m^2K, so unless you're using a h value as an input to the model, you'll have to measure the total heat flux across the pipe wall (q), the surface area of the pipe wall (A), and the difference in temperature between the average temperature of the fluid and the interior wall temperature of the pipe (DT). Then h = q / (A*DT). Filling in the values from the derivation here: http://en.wikipedia.org/wiki/Nusselt_number (Note the temperatures required for this formula) might be helpful if the boundary layer doesn't reach the center of the pipe over the length you're modelling. 

thanks Cornac, I have already obtained h, thus I have to reach a reasonable value of k.

Hi,

I think the best way is to directly calculate the Nusselt number is to use the derivative of temperature in normal direction to the surface. Not familar with COMSOL specifically however most comercial software (eg fluent) alow you to calculate derivatives on surfaces, you need to calculate the normal derivatives of temp and Nu is just a non-dimentionalization of that derivateive, see

http://www.sciencedirect.com/science/article/pii/S001793101200957X

for a difinition around a circular cylinder (external flow).

Sina

Thanks Sina, I can't obtain your paper home, but it seems to hard for me.

With Comsol, I can obtain derivative but I don't know the characteristic length. The pipe is round but the water occupies only a part of the pipe, I think it affects.

In fact, I know local Nusselt because air and water are separated. If I average these two numbers over the interface, would I have the right number?

b

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