Rayleigh Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Rayleigh Number

Rayleigh number ( \(Ra\) ) (dimensionless number) and a modified Grashof number used for natural convection calculations.

Rayleigh Number FORMULA

\(Ra = \frac{\rho g  \alpha_c  \Delta T L^3}{\mu  \alpha}\)          \( Rayleigh \; number  \;=\;  \frac{ fluid \; density \;\;x\;\;   gravitational \; acceleration  \;\;x\;\;  thermal \; expansion \; coefficient  \;\;x\;\;  temperature \; differential  \;\;x\;\;  length^3}{  absolute \; viscosity  \;\;x\;\;  thermal \; diffusivity   }\)

Where:

\(Ra\) = Rayleigh number

\(\rho\) (Greek symbol rho) = fluid density

\(g\) = gravitational acceleration

\(\alpha_c\) (Greek symbol alpha) = thermal expansion coefficient

\(\Delta T\) = temperature differential

\(l\) = length

\(\mu\) (Greek symbol mu) = absolute viscosity

\(\alpha\) (Greek symbol alpha) = thermal diffusivity

 

Tags: Equations for Force