Mathematical model of Heat Transfer Coefficient between inner surface of the pipe and moving fluid:

(1)	$\begin{array}{l}\displaystyle U = \frac{\lambda}{d} \, {\rm Nu}\end{array}$

where

$\begin{array}{l}\lambda\end{array}$	thermal conductivity of flowing fluid
$\begin{array}{l}d\end{array}$	inner pipe diameter
$\begin{array}{l}\rm Nu\end{array}$	dimensionless Nusselt number (Nu)

The Nusselt number (Nu) correlations are:

Stagnant fluid

Natural Convection

Forced Convection

McAdams

(2)	$\begin{array}{l}\displaystyle {\rm Nu}=3.6568\end{array}$

(3)	$\begin{array}{l}\displaystyle \mbox{Nu}_D= \left[ 0.825 + \frac{0.387 \, \mbox{Ra}_D^{1/6}}{ \left[ 1+ (0.492/\mbox{Pr})^{9/16} \right]^{8/27}} \right]^2\end{array}$

(4)	$\begin{array}{l}\displaystyle {\rm Nu}=0.023 \cdot \mbox{Re}_D^{0.8} \cdot \mbox{Pr}^{0.4}\cdot \left( \frac{\mu}{\mu_w} \right)^{0.14}\end{array}$

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See also