Grashof Number⚠ unverified
Physics / Heat Transfer · Compute the Grashof number
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| g | g | m/s**2 | 1.0 | Gravitational acceleration |
| beta | β | 1/K | 1.0 | Coefficient of thermal expansion |
| dT | dT | K | 1.0 | Temperature difference driving buoyancy |
| L | L | m | 1.0 | Characteristic length |
| nu | ν | m**2/s | 1.0 | Kinematic viscosity of the fluid |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Gr | — | Grashof number (dimensionless). Returns 0.0 when nu is not positive |
The science & history
Understanding the Parameters
- $g\beta\Delta T$ — buoyancy acceleration scale.
- $L^{3}/\nu^{2}$ — geometry and viscosity; large Gr → turbulent free convection more likely.
- Gr — often appears as $\mathrm{Ra} = \mathrm{Gr}\,\mathrm{Pr}$ (Rayleigh number).
Derivation (Approaching a Proof)
From the buoyancy term $g\beta\Delta T$ in the momentum equation, nondimensionalisation with viscous scales produces Gr. It multiplies the free-convection Reynolds-like group.
History
Grashof number is standard in natural-convection correlations (vertical plates, enclosures, etc.).
Related Concepts: Reynolds Number Heat, Prandtl Number, Nusselt Number, Convection Heat Transfer
Notes: Registry calculator grashof-number (unverified). Set physical $g$ if default is 1.