Disk Brake Heat Flux⚠ unverified
Mechanical / Clutches Brakes · Compute the heat flux on a brake disk
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| q | q | W | 1.0 | Heat dissipation rate |
| A | A | m**2 | 1.0 | Swept friction area |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | qflux | W/m**2 | Heat flux, in watts per square metre (W/m**2). Returns 0.0 when ``A`` is not positive |
The science & history
Understanding the Parameters
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Heat dissipation rate $q$ — the braking power converted to heat, the slip power $T\omega$ (Clutch Slip Power) or, for a vehicle, the rate of kinetic-energy loss. It is highest at the start of a hard stop and during sustained descents.
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Swept area $A$ — the annular band on the rotor face that the pads sweep. A larger swept area (bigger rotor, wider band) spreads the same power over more surface, lowering the flux and the peak temperature. This is exactly why performance and heavy-vehicle brakes use large-diameter, vented, or multi-pad rotors — to reduce heat flux, not just to add friction.
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Why flux, not power — the surface temperature and thermal stress scale with the flux, not the total power. A brake overheats locally where the flux is high (hot spots, banding), causing thermal cracking, "brake judder," and localized fade even when the average power seems modest.
Derivation (Approaching a Proof)
Heat flux is, by definition, heat-transfer rate per unit area — the thermal analogue of pressure (force per area):
$$q'' = \frac{q}{A}.$$
Its importance comes from what it drives. In transient heating of the rotor surface, the temperature rise depends on the flux entering the material and its thermal properties. For a semi-infinite solid suddenly subjected to a surface flux $q''$, the surface temperature rises as
$$\Delta T_{\text{surface}}(t) \propto q''\,\sqrt{\frac{t}{k\,\rho\,c}},$$
so the flux, not the total power, sets the surface temperature (with $k$, $\rho$, $c$ the rotor's conductivity, density, and specific heat). Reducing $A$-concentration (raising flux) raises surface temperature for the same total heat — the physical reason brake sizing targets heat flux and swept area. The heat that enters the surface is later rejected by convection and radiation to the air (Brake Thermal Capacity).
Dimensional check. $[q''] = \dfrac{\text{W}}{\text{m}^2} = \text{W/m}^2$. ✓
History and Development
Heat-flux analysis underlies all thermal brake design (Shigley, automotive brake engineering). The move to ventilated, drilled, and larger-diameter rotors, and to cross-drilled/slotted patterns, is fundamentally about managing heat flux and surface temperature. The same flux concept governs any surface heating problem (see Heat Flux).
Related Concepts: Heat Flux, Clutch Slip Power, Disk Clutch Heat Generation, Brake Thermal Capacity, Brake Fade Factor
Notes: Heat flux (W/m²) drives surface temperature and thermal stress — bigger swept area lowers it. $q$ is the braking heat rate (slip power). Surface $\Delta T \propto q''\sqrt{t/(k\rho c)}$.