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natural convection heat transfer coefficient at microscale

natural convection heat transfer coefficient at microscale

natural convection heat transfer coefficient at microscale

(OP)
Hello,
 
I am working on the 3-dimensional model of a heated micro-bridge, as has similarily been discussed in a previous thread (thread569-129689: Heat transfer via air to the substrate) which has unfortunately been closed.

So far, my model includes the substrate (Silicon), the bridge structure (epoxy resin), a heater film on top of the bridge (Aluminium) as well as the surrounding air volume. Additionally, I apply natural convection boundary conditions to the top of the bridge structure.

The actual problem I am experiencing is chosing a suitable heat transfer coefficient h.

I have tried to calculate it using the Nusselt number (h=Nu*k_air/l with l=Area/Perimeter). However, every Nusselt correlation I have found so far refers to makro objects and is therefor valid only at significantly higher Rayleigh numbers (Ra = 2*10e-2 approx. in my case).

I would highly appreciate any hint on how to solve this problem.

Best regards,
Dirk.

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