Wärmetransportgleichungen

Wärmetransport, or heat transport, is the transfer of thermal energy caused by temperature differences. It occurs within materials and between objects via three mechanisms: conduction, convection, and radiation. The rate and pattern of heat transfer depend on material properties, geometry, boundary conditions, and the presence of interfacial resistance.

In solids, conduction arises from lattice vibrations (phonons) and, in metals, free electrons. Fourier's law describes the conductive heat flux as Q = -k ∇T, where k is the material's thermal conductivity and ∇T is the temperature gradient. Materials with high k are good conductors; those with low k serve as insulators. Anisotropic materials have direction-dependent conductivity.

Convection involves bulk fluid motion transferring heat. It can be natural, driven by buoyancy forces, or forced by pumps or fans. The convective heat transfer rate is commonly written as Q = h A ΔT, with h the heat transfer coefficient, A the surface area, and ΔT a characteristic temperature difference between surface and fluid. The combined effect of conduction within the solid and convection at its surface is often treated with an overall heat transfer coefficient U and Q = U A ΔT_lm.

Radiation transfers energy by electromagnetic waves and does not require a medium. For surfaces, the net radiative heat flux is q = ε σ (T^4 − T_sur^4), where ε is emissivity, σ is the Stefan-Boltzmann constant, and T and T_sur are absolute temperatures. Real surfaces emit and absorb differently across wavelengths, affecting net transfer.

Understanding Wärmetransport is essential in building design, thermal insulation, electronics cooling, energy systems, and chemical processing. At macroscopic scales Fourier's law is typically valid, but at the nanoscale ballistic transport and phonon scattering can dominate, leading to departures from classical models.