Heat Transfer

Conduction is heat passing through a solid without the solid itself moving. Fourier's law gives the rate as Q/t = kAΔT/d, so it rises with the thermal conductivity of the material and the area, and falls as the wall gets thicker. Metals conduct well because their free electrons carry energy as well as the lattice vibrations do, which is exactly why aluminium is a good heat sink and a poor firewall, and why the ratio k/d is what actually matters rather than either on its own.

Convection is heat carried away by a fluid that is itself moving. Newton's law of cooling gives Q/t = hAΔT, where h is the heat transfer coefficient. The important point is that h is not a property of a material, it is a property of the flow: still air is a poor convector, moving air is far better, and a liquid better still. This is why an air-cooled cylinder needs baffles to force air over the fins, and why cooling drops away sharply when an aircraft is taxiing rather than flying.

Radiation needs no medium at all, and follows the Stefan-Boltzmann law, Q/t = εσA(T_h⁴ − T_c⁴) with temperatures in kelvin. Because of the fourth power it is negligible at room temperature and dominant at high temperature, which is why radiation is what matters around a turbine section or a brake unit but not around a cabin wall. Emissivity ε is a surface property, so a polished metal shield radiates and absorbs very little, and that is precisely why heat shields are polished.

• Try this: In conduction, swap aluminium for glass wool at the same thickness. How many times smaller is the rate, and what does that tell you about firewall and insulation design?
• Try this: Set the hot side to 900 °C and look at the comparison chart. Which mode has taken over, and why does the fourth-power law make that inevitable?
• Try this: In radiation, switch from matt black to polished metal without changing any temperature. Why does a polished heat shield work, and what would happen if it became oxidised in service?