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What is the link between Reynolds number and heat transfer coef. 1

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Increasing Rn usually corresponds to increasing mass flow. Heat transfer also increases with mass flow.

You might notice some differences at very low Rn when convection heat transfer becomes more dominate than conduction heat transfer.

you must get smarter than the software you're using.
 
In turbulent flow, film coefficients vary as Re^0.8. In laminar flow, what it works out to is that you need the same area irrespective of tube diameter. But exchanger performance is complex- there are a lot of factors at play, and what matters most is which resistances to heat transfer are controlling.
 
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