energyconduction

Energy conduction is a mode of energy transfer in which energy moves within a material or between bodies in direct contact, driven by gradients in temperature, chemical potential, or electric potential. It is a fundamental mechanism of heat transfer, alongside convection and radiation, and operates across microscopic and macroscopic scales through interactions among particles and charge carriers.

Thermal conduction is the transfer of thermal energy caused by a temperature gradient. In metals, free electrons carry a large portion of the energy, while in insulators and semiconductors lattice vibrations, or phonons, dominate. The rate of conduction is described by Fourier's law: q = -k ∇T, where q is the heat flux, k the thermal conductivity, and ∇T the temperature gradient. The temperature field in a solid evolves by the heat equation, which relates changes in temperature to the divergence of the heat flux and internal sources.

Electrical energy conduction is energy transported by moving charges under an electric field. In conductors, current density J follows Ohm's law J = σE, with σ the electrical conductivity. The rate of electrical energy transfer is P = VI, and in resistive elements P = I^2R. In metals, electronic transport also contributes to thermal conduction, and under certain conditions the Wiedemann–Franz relation links electrical and thermal conductivities.

Materials and applications vary with conduction properties. Low-thermal-conductivity materials act as insulators to reduce heat flow, while high-conductivity materials enable heat removal. At small scales, ballistic transport, interfacial resistances, and nanostructuring can modify effective conduction. Applications include building insulation, electronic device cooling, and thermoelectric energy conversion, where conduction properties are engineered to balance heat and electrical transport.