Wärmetransports

Wärmetransport, or heat transfer, is the transfer of thermal energy between bodies or within a body due to a temperature difference. It is driven by energy conservation and depends on material properties, geometry, and boundary conditions. The rate of heat transfer is commonly represented by a heat flux or a heat transfer coefficient in practical calculations.

Conduction is the transfer of energy through a material by microscopic collisions and lattice vibrations. In solids and stationary fluids it dominates when there is a temperature gradient. Fourier's law describes the relation between heat flux and the temperature gradient: q" = -k ∂T/∂x, where k is the thermal conductivity. In complex materials, conduction occurs across interfaces and through composite layers, requiring effective properties to model the overall transfer.

Convection involves transport of heat by bulk fluid motion. It can be natural, driven by buoyancy forces, or forced, induced by fans or pumps. The convective heat transfer rate is often written as Q = h A (T_s − T∞), with h being the heat transfer coefficient and A the area. The value of h depends on fluid properties, flow regime, and surface characteristics, and is influenced by the Prandtl and Reynolds numbers.

Radiation transfers energy through electromagnetic waves and requires no medium. The radiative heat flux from a surface is q" = ε σ (T^4 − T_env^4), where ε is emissivity and σ is the Stefan-Boltzmann constant. For two surfaces, view factors and geometry determine the exchange; emissivity and temperature differences govern the net transfer, which becomes dominant at high temperatures or in vacuum.

Applications of Wärmetransport include building insulation, heat exchangers, electronic cooling, and materials processing. Analysis often employs numerical methods such as finite difference or finite element approaches to solve steady-state or transient problems using appropriate boundary and initial conditions.