Gr = gβΔTL³/ν² — ratio of buoyancy to viscous forces in natural convection. Determines whether free convection is laminar or turbulent and is the natural-convection analogue of Re².
Heat Transfer · Natural ConvectionSolve for:
|Twall − T∞| (magnitude, always positive)
Definition:
Gr is the ratio of buoyancy forces to viscous forces. It plays the same role in natural convection that Re² plays in forced convection — it governs whether the flow is laminar or turbulent.
Thermal expansion coefficient β:
Characteristic length L by geometry:
| Geometry | L | Regime boundary |
|---|---|---|
| Vertical plate / wall | plate height H | Gr < 10⁸ laminar, > 10⁹ turbulent |
| Horizontal cylinder | outer diameter D | Ra = Gr × Pr used in correlations |
| Sphere | diameter D | Ra = Gr × Pr used in correlations |
| Horizontal plate (hot) | area / perimeter (A/P) | Ra < 7×10⁴ laminar |
| Enclosed cavity | gap width | Gr based on gap |
Regime thresholds (vertical plate):
Most Nu correlations for natural convection use Ra = Gr × Pr rather than Gr alone, so always compute Ra when using a heat transfer correlation.