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For laminar-turbulent transition and turbulent flow in pipeline the Nusselt number (Nu) becomes also depdedant on friction with wall, quantifiable by Darcy friction factor 

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, and can be estimated through empirical correlation (Gnielinski ):

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Heat Transfer Coefficient (HTC) ] Heat Transfer Coefficient @model ]

Prandtl number (Pr)Dimensionless Heat Transfer Numbers ]


References

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Gnielinski
Gnielinski
Gnielinski, Volker (1975). "Neue Gleichungen für den Wärme- und den Stoffübergang in turbulent durchströmten Rohren und Kanälen". Forsch. Ing.-Wes. 41 (1): 8–16.

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