Dimensionless multiplier correcting the Conductive Annulus Heat Transfer Coefficient $\begin{array}{l}U^*\end{array}$ to account for the Natural Thermal Convection effects in the Annulus:

(1)	$\begin{array}{l}\displaystyle U = \epsilon_a \cdot U^* = \epsilon \cdot \frac{ \lambda_a}{d_t \cdot \ln (d_{ci}/d_t) }\end{array}$

The most popular empirical correlations are:

(2)	$\begin{array}{l}\epsilon = \begin{cases} 1, & \mbox{if } \ {\rm Ra} < 10^3 \\ 0.18 \cdot {\rm Ra}^{0.25}, & \mbox{if } \ {\rm Ra} > 10^3 \end{cases}\end{array}$

(3)	$\begin{array}{l}\epsilon = \begin{cases} 1, & \mbox{if } \ {\rm Ra} < 10^3 \\ 0.105 \cdot {\rm Ra}^{0.3}, & \mbox{if } \ 10^3 < {\rm Ra} < 10^6 \\ 0.4 \cdot {\rm Ra}^{0.2}, & \mbox{if } \ {\rm Ra} > 10^6 \end{cases}\end{array}$

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See also