I am trying to model a diffusion process within a laminar flow. I want to plot Sherwood Number across my domain. What i try to do is expressing Sherwood Number as convective flux magnitude/diffusive flux magnitude all over the domain but the results seem to be wrong when compared to correlations. Can anyone suggest me another method to find Sherwood Number in COMSOL?
This is quite difficult, you need to calculate numerically the mass transfer coefficient which by the way depends on what you're looking at. If you do not want to pass through the formal definition and you want tu use fluxes, first of all check that COMSOL calculated fluxes are in agreement with the expected results. Most of time, mesh dependencies are found and this has to be avoided.
Regards
Generally, the Sherwood number is a global quantity linking the molar (or mass) flux ndot (mol/s) transferred at some boundary (say Sb) to the difference between the boundary concentration Cb and a "far from boundary" concentration or input concentration, say Cinf.
You can do that with COMSOL by using Results -> Derived values -> Integration (over surface if 3D, line in 2D). Here select as integrand tds.ntflux_c which is the total molar flux density : you obtain ndot (or ndot per unit-length in 2D).
Now duplicate the last node in Derived values, and now set as integrand tds.ntflux_c/(Cb-Cinf)/Sb, where Sb is the area of boundary : you get k the mass-transfer coefficient (in m/s).
Duplicate again and put this time tds.ntflux_c/(Cb-Cinf)/Sb * L/DAB, where L is a typical length of your problem and DAB the diffusion coefficient, you get (a global) Sh.
This works if Cb is imposed as a constant parameter. You can repeat the computation for various Re for example (not too high however in order to stay in the laminar regime) by making parametric studies, and plot in the end Sh(Re).
The "interesting" Sherwood is generally the global one defined above. If you need a local Sherwood along the boundary, tell me. If you tell us more about your setup, I may refine my answer. On the other hand, I have a couple of example mph-files implementing that if you want.
The advice of Luigi is also relevant : you should check that mass is conserved by computing ndot by two different methods. Both values should match up to some relative tolerance, and this may guide you to find the adequate mesh.
Regards
Olivier Louisnard Thank you Olivier for your guiding answer.
May I ask for the mph-files you mention? I implemented what you suggested and now i get some good values. However, i am still not sure about which boundaries suit best for your description of the formula for Cb and Cinf.
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