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For laminar-turbulent transition and turbulent flow in pipeline the Nusselt number becomes also depdedant on friction with wall, quantifiable by Darcy friction factor
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{\rm Nu}=\frac{ (f/8) \, ({\rm Re} - 1000) {\rm Pr} }{ 1 + 12.7 \, (f/8)^{1/2} \, ({\rm Pr}^{2/3} -1) } |
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