Convection Heat Transfer⚠ unverified
Physics / Heat Transfer · Convective heat transfer rate (Newton's law of cooling)
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| h | h | W/m^2/K | 10.0 | Convection coefficient |
| A | A | m^2 | 2.0 | Surface area |
| dT | ΔT | K | 20.0 | Temperature difference |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| Q | Q | W | Heat rate |
The science & history
Understanding the Parameters
-
$h$ — from correlations (Nu, Re, Pr) or measurement; free vs forced convection differ by orders of magnitude. Live cards may mislabel $h$ as dimensionless — it is W/(m²·K).
-
$A$ — heat-transfer surface.
- $\Delta T$ — driving temperature difference.
- $Q$ — same units as conduction heat rate; thermal resistance form $R = 1/(hA)$.
Derivation (Approaching a Proof)
Newton’s cooling law is the definition of $h$: $q = h(T_s - T_{\infty})$. Multiplying by area gives $Q = h A \Delta T$. Predicting $h$ from first principles requires solving the energy equation in the boundary layer (Nusselt-number correlations).
History
Newton stated cooling proportional to temperature difference; modern $h$ formalises that for engineering surfaces.
Related Concepts: Nusselt Number, Thermal Resistance Convection, 1D Steady Conduction, Overall Heat Transfer Coefficient
Notes: Registry calculator convection-heat-transfer (unverified). Definition of $h$, not a
correlation for $h$.