Prandtl Number⚠ unverified
Physics / Heat Transfer · Compute the Prandtl number
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| nu | ν | m**2/s | 1.0 | Kinematic viscosity of the fluid |
| alpha | α | m**2/s | 1.0 | Thermal diffusivity of the fluid |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Pr | — | Prandtl number (dimensionless). Returns 0.0 when alpha is not positive |
The science & history
Understanding the Parameters
- $\nu$, $\alpha$ — both m²/s; Pr is their ratio.
- Pr — appears in forced-convection Nu correlations; relative thickness of velocity vs thermal boundary layers $\sim \mathrm{Pr}^{1/3}$ in many regimes.
Derivation (Approaching a Proof)
From fluid properties: $\mathrm{Pr} = \nu/\alpha = \mu c_p / k$. Nondimensional energy and momentum equations introduce Pr as the coupling parameter.
History
Ludwig Prandtl; Pr is a primary fluid property group in convective heat transfer.
Related Concepts: Reynolds Number Heat, Nusselt Number, Grashof Number, Fourier Number
Notes: Registry calculator prandtl-number (unverified).