Biot Number⚠ unverified
Physics / Heat Transfer · Compute the Biot number
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| h | h | — | 1.0 | Convective heat transfer coefficient, in watts per square metre-kelvin (W/(m**2*K)) |
| L | L | m | 1.0 | Characteristic length |
| k | k | — | 1.0 | Thermal conductivity of the solid, in watts per metre-kelvin (W/(m*K)) |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Bi | — | Biot number (dimensionless). Returns 0.0 when k is not positive |
The science & history
Understanding the Parameters
- $h$, $L$, $k$ — high $h$ or large $L$ or low $k$ → large Bi (internal gradients matter).
-
Registry unit bug: $h$ and $k$ may be labelled
dimensionless— they are W/(m²·K) and W/(m·K). -
Bi — criterion for lumped vs distributed transient models; distinct from Nu ($hL/k_{\mathrm{fluid}}$).
Derivation (Approaching a Proof)
Conduction resistance $\sim L/(kA)$; convection $\sim 1/(hA)$. Ratio $R_{\mathrm{cond}}/R_{\mathrm{conv}} = hL/k = \mathrm{Bi}$.
History
Named after Jean-Baptiste Biot; central to transient heat-conduction teaching (Heisler charts, etc.).
Related Concepts: Fourier Number, Nusselt Number, Convection Heat Transfer, 1D Steady Conduction
Notes: Registry calculator biot-number (unverified). Solid $k$, not fluid $k$.