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In Forced Fluid Convection the 
Nusselt number becomes dependant on Reynolds number 

LaTeX Math Inline
body\rm Re
 and Prandtl number 
LaTeX Math Inline
body\rm Pr
LaTeX Math Inline
body--uriencoded--\mbox%7BNu%7D = f (\mbox%7BRe%7D, \mbox%7BPr%7D)
.



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anchor5CZ08
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{\rm Nu}=3.66 + \frac{ 0.065 \cdot {\rm Re} \cdot {\rm Pr} \cdot {D/L} }{ 1 + 0.04 \cdot ({\rm Re} \cdot {\rm Pr} \cdot {D/L})^{2/3} }




Laminar flow in pipeline



LaTeX Math Block
anchorNu
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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) }


Gnielinski


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

LaTeX Math Inline
bodyf
, and can be estimated through empirical correlation (Gnielinski


 

LaTeX Math Inline
body--uriencoded--0.5\leq \mathrm %7BPr%7D \leq 2000
 and 
LaTeX Math Inline
body--uriencoded--%7B\displaystyle 3000\leq \mathrm %7BRe%7D\leq 5\cdot 10%5e%7B6%7D%7D
.


Image Modified

Churchill–Bernstein correlation 

Churchill–Bernstein 




See also

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Physics / Thermodynamics / Heat Transfer

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