Rayleigh Number Calculator

Calculate the dimensionless group that combines buoyancy, viscous and thermal-diffusion effects in natural convection.

Rayleigh number (Ra)2.272E9Dimensionless · Ra = Gr × Pr
Grashof number3.2E9Buoyancy / viscosity screening group
Prandtl number0.71Momentum / thermal diffusion group

Scope: Rayleigh number is a natural-convection screening group. It is not a universal threshold for convection onset or heat-transfer coefficient: geometry, orientation, boundaries and the selected correlation still control that interpretation.

Method and variables

Ra = Gr × Pr = gβ|ΔT|L3/(να). It can be calculated from known Grashof and Prandtl values, or from gravitational acceleration, thermal expansion, temperature difference, length, kinematic viscosity and thermal diffusivity.

Worked example

With Gr = 3.2 × 109 and Pr = 0.71 for air, Ra is approximately 2.27 × 109.

Important limits

Rayleigh number does not itself determine a heat-transfer coefficient or a universal transition threshold. Enclosure versus external flow, surface orientation, aspect ratio, boundary conditions, radiation and property variation all affect the correlation and interpretation.

References

Related tools

Grashof Number Calculator · Prandtl Number Calculator · Dimensionless Numbers Calculators

Frequently asked questions

How are Rayleigh, Grashof and Prandtl numbers related?
Rayleigh number is Ra = Gr × Pr. It combines buoyancy-versus-viscosity effects with the ratio of momentum to thermal diffusion.

Does one Rayleigh value always mean convection starts?
No. Critical values depend on the geometry, orientation, boundary conditions and problem definition. Use a source appropriate to the actual configuration.

Which fluid properties should I use?
Use a mutually consistent set of properties at an appropriate reference state, often a film temperature for external natural convection.