Conduction
Thermal conduction is the transfer of heat through a material, without bulk motion, by microscopic processes: collisions between molecules in gases, lattice vibrations (phonons) in solids, and the motion of free electrons in metals. Its rate follows Fourier's law, q = −k∇T, where q is the heat flux and k the thermal conductivity, which ranges from about 0.02 W m−1 K−1 for still air to over 2,000 for diamond.
Curious
Touch metal and wood in the same room: the metal feels colder even though both are at room temperature. Metal conducts heat away from your hand much faster, so your skin cools more. Metals are good conductors because their free electrons carry heat as well as electric current (see Metals).
Poor conductors, or insulators, slow heat flow. Many insulating materials, such as wool, foam and double glazing, work by trapping air, which conducts heat poorly as long as it cannot circulate (see Convection).
Exploring
| Material | Thermal conductivity k (W m−1 K−1, ~300 K) |
|---|---|
| Diamond (natural) | ~2,000–2,200 |
| Copper | ~401 |
| Aluminium | ~237 |
| Stainless steel | ~15 |
| Glass | ~0.8–1.0 |
| Water | ~0.6 |
| Wood (pine, across grain) | ~0.12 |
| Air (still) | ~0.026 |
Deep Dive
Heat equation. Combining Fourier's law with energy conservation gives ∂T/∂t = α∇²T, where the thermal diffusivity α = k/(ρc) sets how fast temperature disturbances spread; a disturbance penetrates a distance of order √(αt) in time t. Fourier developed his series to solve this equation, founding a branch of mathematics (see Waves, Acoustics & Oscillations).
Microscopic picture. Kinetic theory gives k ≈ (1/3)Cvλ for gases, where C is heat capacity per volume, v mean speed and λ mean free path; like viscosity, it is nearly independent of pressure over a wide range (see Kinetic Theory of Gases). In metals, electrons dominate and the Wiedemann–Franz law relates k to electrical conductivity. In insulators, phonons carry heat, limited by scattering from defects, boundaries and other phonons (Umklapp processes; see Brillouin Zone).
Limits of Fourier's law. Fourier's law implies infinite propagation speed and fails at very short length and time scales, as in nanoscale devices and ultrafast laser heating, where ballistic phonon transport and “second sound” (wave-like heat propagation, first observed in superfluid helium) occur. These are active research areas.
Concept Relationship Map
Requires: heat transfer, temperature
Enables: the heat equation, insulation, thermal management
Commonly confused with: how hot or cold a surface feels
Sources
- Fourier, J. (1822). Théorie analytique de la chaleur. Paris.
- Incropera, F.P., DeWitt, D.P., Bergman, T.L., Lavine, A.S. (2007). Fundamentals of Heat and Mass Transfer (6th ed.). Wiley.
- Kittel, C. (2004). Introduction to Solid State Physics (8th ed.). Wiley.