Editing Convection (section)

===Behavior===
The [[Grashof number]] can be formulated for natural convection occurring due to a [[concentration gradient]], sometimes termed thermo-solutal convection.  In this case, a concentration of hot fluid diffuses into a cold fluid, in much the same way that ink poured into a container of water diffuses to dye the entire space. Then:

:<math> Gr= \frac{g \beta \Delta C L^3}{\nu^2} </math>

Natural convection is highly dependent on the geometry of the hot surface, various correlations exist in order to determine the heat transfer coefficient. 
A general correlation that applies for a variety of geometries is

: <math>Nu = \left[Nu_0^\frac{1}{2} + Ra^ \frac{1}{6} \left(\frac {f_4\left(Pr\right)}{300}\right)^\frac{1}{6} \right]^2 </math>

The value of f<sub>4</sub>(Pr) is calculated using the following formula

: <math>f_4(Pr)= \left[1+ \left ( \frac {0.5}{Pr} \right )^\frac{9}{16} \right]^\frac{-16}{9}</math>

Nu is the [[Nusselt number]] and the values of Nu<sub>0</sub> and the characteristic length used to calculate Re are listed below (see also Discussion):

{| class="wikitable"
|-
! '''Geometry'''
! '''Characteristic length'''
! '''Nu<sub>0</sub>'''
|-
| Inclined plane
| x (Distance along plane)
| 0.68
|-
| Inclined disk
| 9D/11 (D = diameter)
| 0.56
|-
| Vertical cylinder
| x (height of cylinder)
| 0.68
|-
| Cone
| 4x/5 (x = distance along sloping surface)
| 0.54
|-
| Horizontal cylinder
| <math>\pi D/2</math> (D = diameter of cylinder)
| 0.36<math>\pi</math>
|}
'''Warning''': The values indicated for the '''Horizontal cylinder''' are '''wrong'''; see discussion.