Heat transfer is the movement of thermal energy driven by temperature differences. There are three modes of heat transfer. Conduction transfers heat through a solid by molecular and electronic interactions. Convection transfers heat through the bulk motion of a fluid, either naturally or forced. Radiation transfers energy as electromagnetic waves and does not require a medium.
Each mode is governed by its own law. Fourier's law of conduction states that heat flux is proportional to the negative temperature gradient, \(q = -k(dT/dx)\), where \(k\) is the thermal conductivity of the material. Metals have high \(k\) and are good conductors, while insulators such as foams and ceramics have low \(k\). Newton's law of cooling expresses the convective heat transfer rate as \(Q = hA(T_s - T_{\infty})\), where \(h\) is the convection coefficient that depends on the fluid and the flow conditions. The Stefan-Boltzmann law describes radiation from a black body as \(Q = \sigma \varepsilon A T^4\), where \(\sigma = 5.67 \times 10^{-8}\) W/m²K⁴ and \(\varepsilon\) is the emissivity of the surface.
In practical engineering, multiple resistances often act in series. The overall heat transfer coefficient \(U\) combines conduction, convection, and fouling resistances into a single value, and the heat transfer rate becomes \(Q = UA\Delta T\). For heat exchangers, the log mean temperature difference, \(LMTD = (\Delta T_1 - \Delta T_2)/\ln(\Delta T_1/\Delta T_2)\), provides the appropriate driving temperature difference between the two fluid streams, accounting for the fact that this difference usually varies from one end of the exchanger to the other.