Rayleigh number

Physical key figure
Surname	Rayleigh number
Formula symbol	${\displaystyle {\mathit {Ra}}}$
dimension	dimensionless
definition	${\displaystyle Ra_{l,c}=Gr_{l,c}\cdot Pr={\frac {g\cdot \beta }{\nu ^{2}}}\cdot (T_{s}-T_{\infty })\cdot l^{3}\cdot Pr}$
${\displaystyle g}$ Acceleration due to gravity ${\displaystyle \beta }$ Coefficient of thermal expansion ${\displaystyle \nu }$ kinematic viscosity ${\displaystyle T_{s}}$ characteristic temperature ${\displaystyle T_{\infty }}$ Resting temperature ${\displaystyle l}$ Characteristic length
Named after	John William Strutt, 3rd Baron Rayleigh
scope of application	Heat transfer within fluids

The Rayleigh number (after John William Strutt, 3rd Baron Rayleigh ) is a dimensionless number that describes the character of the heat transfer within a fluid : ${\displaystyle Ra}$

• when the Rayleigh number exceeds a critical value for the fluid, the heat transfer is primarily by convection .
• if it remains below the critical value, the heat transfer is primarily given by conduction .

${\displaystyle Ra_{l,c}=Gr_{l,c}\cdot Pr={\frac {g\cdot \beta }{\nu ^{2}}}\cdot (T_{s}-T_{\infty })\cdot l^{3}\cdot Pr}$

in which

• ${\displaystyle Gr_{l,c}}$= the dimensionless Grashof number
• ${\displaystyle Pr}$= the dimensionless Prandtl number
• ${\displaystyle g}$ = Acceleration due to gravity (e.g. acceleration due to gravity in SI units 9.81  m / s ²)
• ${\displaystyle \beta }$= Coefficient of thermal expansion (in SI units 1 / K)
• ${\displaystyle \nu }$ = kinematic viscosity of the fluid (in SI units m² / s)
• ${\displaystyle T_{s}}$= characteristic temperature (in SI units K )
• ${\displaystyle T_{\infty }}$= Resting temperature (in SI units K)
• ${\displaystyle l}$= characteristic length (in SI units, m)

See also

• Bénard experiment