Editing Grashof number (section)

===Heat transfer===
Free convection is caused by a change in density of a fluid due to a temperature change or [[Temperature gradient|gradient]]. Usually the density decreases due to an increase in temperature and causes the fluid to rise. This motion is caused by the [[buoyancy]] force. The major force that resists the motion is the [[Viscosity|viscous]] force. The Grashof number is a way to quantify the opposing forces.<ref name="BirdStewartLightfoot2002">{{cite book|last1=Bird|first1= R. Byron|first2= Warren E.|last2= Stewart|first3= Edwin N.|last3= Lightfoot|title= Transport Phenomena|url=https://archive.org/details/transportphenome00bird_116|url-access=limited|location=New York|publisher= J. Wiley|date= 2002|pages=[https://archive.org/details/transportphenome00bird_116/page/n332 318], 359|edition=2nd|oclc=471520548|isbn=9780471410775}}</ref>

The Grashof number is:

:<math> \mathrm{Gr}_L = \frac{g \beta (T_s - T_\infty ) L^3}{\nu ^2}\, </math> for vertical flat plates
:<math> \mathrm{Gr}_D = \frac{g \beta (T_s - T_\infty ) D^3}{\nu ^2}\, </math> for pipes and bluff bodies

where:
* {{mvar|g}}  is [[gravitational acceleration]] due to Earth
* {{mvar|β}} is the coefficient of volume expansion (equal to approximately {{math|1/''T''}} for [[ideal gas]]es)
* {{mvar|T{{sub|s}}}} is the surface temperature
* {{mvar|T{{sub|∞}}}} is the [[bulk temperature]]
* {{mvar|L}} is the vertical length
* {{mvar|D}} is the diameter
* {{mvar|ν}} is the [[kinematic viscosity]].

The {{mvar|L}} and {{mvar|D}} subscripts indicate the length scale basis for the Grashof number.

The transition to [[turbulent flow]] occurs in the range {{math|10{{sup|8}} < Gr{{sub|''L''}} < 10{{sup|9}}}} for [[natural convection]] from vertical flat plates. At higher Grashof numbers, the [[boundary layer]] is turbulent; at lower Grashof numbers, the boundary layer is laminar, that is, in the range {{math|10{{sup|3}} < Gr{{sub|''L''}} < 10{{sup|6}}}}.