Editing Heat transfer coefficient (section)

=== Vertical rectangular enclosure ===
For heat flow between two opposing vertical plates of rectangular enclosures, Catton recommends the following two correlations for smaller aspect ratios.<ref name="Cengel480">{{cite book |last=Çengel |first=Yunus |title=Heat and Mass Transfer |publisher=McGraw-Hill |page=480 |edition=Second}}</ref> The correlations are valid for any value of Prandtl number.

For  <math> 1 <\frac{H}{L} < 2 </math> :

:<math>h \ = \frac{k}{L}0.18 \left(\frac{\mathrm{Pr}}{0.2 + \mathrm{Pr}} \mathrm{Ra}_L \right)^{0.29} \, \quad \mathrm{Ra}_L \mathrm{Pr}/(0.2 + \mathrm{Pr}) > 10^3</math>

where ''H'' is the internal height of the enclosure and ''L'' is the horizontal distance between the two sides of different temperatures.

For  <math> 2 < \frac{H}{L} < 10 </math> :

:<math>h \ = \frac{k}{L}0.22 \left(\frac{\mathrm{Pr}}{0.2 + \mathrm{Pr}} \mathrm{Ra}_L \right)^{0.28} \left(\frac{H}{L} \right)^{-1/4} \, \quad \mathrm{Ra}_L < 10^{10}.</math>

For vertical enclosures with larger aspect ratios, the following two correlations can be used.<ref name="Cengel480" /> For 10 < ''H''/''L'' < 40:

:<math>h \ = \frac{k}{L}0.42 \mathrm{Ra}_L^{1/4} \mathrm{Pr}^{0.012} \left(\frac{H}{L} \right)^{-0.3} \, \quad 1 < \mathrm{Pr} < 2\times10^4, \, \quad 10^4 < \mathrm{Ra}_L < 10^7.</math>

For  <math> 1 < \frac{H}{L} < 40</math> :

:<math>h \ = \frac{k}{L}0.46 \mathrm{Ra}_L^{1/3} \, \quad 1 < \mathrm{Pr} < 20, \, \quad 10^6 < \mathrm{Ra}_L < 10^9.</math>

For all four correlations, fluid properties are evaluated at the average temperature—as opposed to film temperature—<math>(T_1+T_2)/2</math>, where <math>T_1</math> and <math>T_2</math> are the temperatures of the vertical surfaces and <math>T_1 > T_2</math>.