Rayleigh number (for a uniform wall heating flux)

Description

In fluid mechanics, the Rayleigh number (Ra) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free convection or natural convection. When the Rayleigh number is below a critical value for that fluid, heat transfer is primarily in the form of conduction; when it exceeds the critical value, heat transfer is primarily in the form of convection.

The Rayleigh number is named after Lord Rayleigh and is defined as the product of the Grashof number, which describes the relationship between buoyancy and viscosity within a fluid, and the Prandtl number, which describes the relationship between momentum diffusivity and thermal diffusivity. Hence the Rayleigh number itself may also be viewed as the ratio of buoyancy and viscosity forces multiplied by the ratio of momentum and thermal diffusivities.

For a uniform wall heating flux, the modified Rayleigh number is defined as shown here.

For most engineering purposes, the Rayleigh number is large, somewhere around 10^6 to 10^8.

Related formulas

Variables

Rax Rayleigh number for characteristic length x (dimensionless)
gStandard gravity
βthermal expansion coefficient (equals to 1/T, for ideal gases, where T is absolute temperature) (1/K)
qouniform surface heat flux (W/m2)
νkinematic viscosity (m2/s)
αthermal diffusivity (m2/s)
κthermal conductivity (W/m*K)
xcharacteristic length (m)