Heat Transfer
Heat transfer is the exchange of thermal energy between systems, or within a system, driven by temperature differences. It occurs by three mechanisms: conduction (energy passed between neighbouring particles), convection (energy carried by bulk fluid motion) and thermal radiation (energy carried by electromagnetic waves, requiring no medium). Rates are governed respectively by Fourier's law, Newton's law of cooling and the Stefan–Boltzmann law.
Curious
Hold a metal spoon in hot soup and the handle warms by conduction; the soup itself circulates as warm liquid rises, an example of convection; and your face feels warmth from the bowl even without touching it, through infrared radiation. The Sun heats Earth entirely by radiation across empty space.
Controlling heat transfer is central to engineering, from home insulation and cooking to cooling computer chips and protecting spacecraft on re-entry. A vacuum flask works by blocking all three modes: a vacuum stops conduction and convection, and silvered walls reflect radiation.
Exploring
| Mode | Mechanism | Rate law | Needs a medium? |
|---|---|---|---|
| Conduction | Particle collisions, electron and phonon transport | q = −k∇T (Fourier) | Yes |
| Convection | Bulk fluid motion | q = hAΔT (Newton) | Yes (fluid) |
| Radiation | Electromagnetic waves | P = εσAT4 (Stefan–Boltzmann) | No |
Deep Dive
Newton's law of cooling. Newton (1701) proposed that the rate of cooling is proportional to the temperature difference with the surroundings, giving exponential decay. It is a good approximation for forced convection and for small temperature differences; for natural convection the heat-transfer coefficient depends on the temperature difference itself, and for large differences radiation (∝ T4) makes the decay non-exponential.
Thermal resistance. Steady heat flow through layers can be treated like electric current through resistors in series: Rcond = L/(kA), Rconv = 1/(hA), and the total rate is ΔT/ΣR (compare Ohm's Law). Building codes express insulation as U-values or R-values on this basis. The Biot number Bi = hL/k decides whether an object can be treated as having uniform temperature (Bi < 0.1).
Radiation. Real surfaces emit less than a black body by the emissivity ε, which depends on wavelength and surface condition. Kirchhoff's law states that, at equilibrium and each wavelength, emissivity equals absorptivity. Radiative exchange dominates at high temperatures and in vacuum, and is central to Earth's energy balance (see Cosmic Microwave Background for a near-perfect black body).
Concept Relationship Map
Requires: heat, temperature
Enables: conduction, convection, thermal radiation, insulation design
Commonly confused with: “heat rises”
Sources
- Fourier, J. (1822). Théorie analytique de la chaleur. Paris.
- Newton, I. (1701). “Scala graduum caloris.” Philosophical Transactions of the Royal Society, 22, 824–829.
- Incropera, F.P., DeWitt, D.P., Bergman, T.L., Lavine, A.S. (2007). Fundamentals of Heat and Mass Transfer (6th ed.). Wiley.