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heat transfer in ultra-thin membrane

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I had trouble with meshing.
When I used pre-defined mesh, it kept gave me warnings if I chose 'extra coarse'. I went ahead and ran simulations anyways, but it gave me error saying that the computation did not converge.
Then I user-defined mesh size (minimum=2um). It did compute but the result looked weird.

The membrane thickness is 600 nano meters but the size of the membrane is 300 microns.

I would have attached my model file but it was too big.

What do you think I could do to overcome this problem?

Many thanks!

Minmin

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