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As kinetic energy is not stored or recycled, large quantities of heat have to be evacuated in a short period of time when aircraft abort their takeoff or land:
B777 brake test, Youtube
Which approximate quantity of energy is transferred to the brakes in a rejected takeoff for heavy aircraft, e.g. Boeing 777 or Airbus A380? What are the typical systems used to cool brakes on these heavy aircraft? Is cooled air or liquid used, or just ram air?
The order of magnitude of brake energy after a rejected takeoff (RTO) for a very heavy aircraft is 1 GJ, or 100 MJ per wheel brake.
Aircraft brakes are cooled with ambient air, either through passive airflow or (optionally) through forced air ventilation.
Cutaway drawings of A380 wheel and brake (Source)
Takeoff speed for heavy aircraft is about 150 knots or 280 km/h. The maximum speed to reject takeoff ($V_1$) depends on the plane, the load, the wind, and the condition of the runway. Let's assume 150 knots for the sake of a rough energy estimation.
The maximum energy that could be transferred to the brakes is more or less the kinetic energy of the plane at takeoff speed: $$E_\rm{kinetic} = \frac{1}{2}mv^2 $$
The actual energy dissipation will be increased by
and decreased by
Neither A380 nor B777 have brakes in the nose gear. (Actually very few heavy aircraft have braked nose wheels. See: Are there any aircraft with a nose wheel braking system?)
The maximum takeoff weight (MTOW) of the A380 is 575 t, and its main gear has 20 wheels. 16 main wheels have brakes and 4 main wheels do not. (See Why do some A380 main wheels have no brakes?)
$$E_\rm{TO,max} = 0.5\cdot 5.75\cdot 10^5\,\rm{kg}\cdot\left(\frac{280}{3.6}\frac{\rm{m}}{\rm{s}}\right)^2 = 1.7\,\rm{GJ}$$
The approximate maximum dissipated energy per wheel brake unit for an A380 after RTO is $$E_{\rm{wheel}} = \frac{1}{16} E_\rm{TO,max} = 110\,\rm{MJ} $$
The MTOW of the heaviest 777 is 352 t, and its main gear has 12 wheels.
$$E_\rm{TO,max} = 0.5\cdot 3.52\cdot 10^5\,\rm{kg}\cdot\left(\frac{280}{3.6}\frac{\rm{m}}{\rm{s}}\right)^2 = 1.1\,\rm{GJ}$$
The approximate maximum dissipated energy per wheel brake unit for a Boeing 777 after RTO is $$E_{\rm{wheel}} = \frac{1}{12} E_\rm{TO,max} = 89\,\rm{MJ} $$
Aircraft which are foreseen to take-off and land frequently may be equipped with electric brake cooling fans (BCF) which extract the interior hot air to the exterior. The BCF are used during ground time to shorten the turn-around time.
As an example, the main wheels of an A318 equipped with electric brake cooling fans:
Interestingly, there is a difference between steel and carbon brake disks. Steel disks wear out faster when hot, whereas carbon disks wear out faster when cold. Therefore it is preferable to reduce the cooling of carbon disk brakes to what is required for the following takeoff (see this answer).
Many (long range) aircraft have no active brake cooling. Passive cooling is caused by
Passive cooling of aircraft brakes follows Newton's law of cooling, which is - in terms of mathematics - an exponential decay (or exponential function with a negative exponent, if you prefer).
It may take many hours of passive cooling to reach the ambient temperature. Also see related question What is the temperature of the brakes after a typical landing?
The source of this graph does not indicate the unit of the x-axis, but minutes seem most plausible. The type of the aircraft under test is also unknown. The information is applicable to a range of Airbus aircraft equipped with carbon disk brakes, from A300 to A380.
External ventilation units exist and may be used whenever necessary. These can be electric, petrol powered,
or supplied by a remote compressor or extractor:
Hot brakes are normally cooled by natural convection, but in extreme cases the fire fighters will cool overheated brakes. Some designs use brake fans. From the linked page:
Brake fans reduce brake cooling times by using wheel mounted electric fans to blow ambient air across the brake and wheel assemblies. Note that the maximum recommended temperature for takeoff as indicated on the instrument panel may have a different value dependent on if the brake fans have been used or not.
Safran brake cooling fan and electric motor (picture source)
According to this page on Airliners.net, the BAe 146 had them, as did PanAm's A310s, but most airlines leave them off to save some weight. Short-haul aircraft make more use of cooling fans: According to this article and video, 90% of A320 use cooling fans. There are also ground-based cooling fans to shorten turn-around times.
The most severe case used in the design is a rejected take-off. Some energy is absorbed by rubbing off the tires, but most ends up in the brake disks. To absorb all this energy, sometimes more disks have to be added in the design phase. The most extreme example is the landing gear of the Tupolev 144 which sported the unusual combination of a high take-off and landing speed and no thrust reversers.
Tupolev Tu-144 landing gear (picture source) Yes, it is this bird!
As always, not all use cases can be foreseen by the designers. The reason why aviation hydraulic fluid must be non-flammable is one case when the heat energy was absorbed by the surrounding structure, with fatal consequences. In this particular case in 1963, a Sud Aviation Caravelle had tried to heat away fog on the runway so they could take off. They did this by taxiing down the runway with considerable thrust and used the brakes to keep the aircraft from accelerating. When the gear was retracted, the brake disks were still glowing red but had little to no air cooling. So the heat dissipated into the aluminium wheel hubs, which became too soft to withstand the tire pressure. Shrapnel from the burst wheels cut hydraulic lines, and the still glowing brake disks ignited the oil which was pumped into the wheel well. The resulting fire destroyed the aircraft.
From the accident report:
Four minutes later witnesses on the ground noticed a whitish trail of smoke on the left side of the aircraft and suddenly a long flame from the left wing-root. Around 0620 hours the aircraft reached an altitude of approximately 2700 m, it then began to lose height, entered a gentle left turn loosing height more rapidly and finally went into a steep dive.
This is why dragging brakes on retractable gears are dangerous: After take-off the wheel and brake is retracted, so air cannot cool it down anymore.
As others have answered, typically brakes are cooled by natural convection. For single-aisle and especially regional aircraft, these are designed to cool to taxi-out temperatures in the time it takes to deboard and reboard the aircraft. For certain aircraft, cooling may be the determining factor in when aircraft depart the gate, which is where temperature management schemes come into play.
Operators have two options when it comes to temperature management. The first is a chart published by the airframer, which is used to estimate the cooling time based on the landing energy and ambient conditions. However, this chart is usually conservative due to uneven heat distribution in brakes, so most operators choose the optional Brake Temperature Monitoring System upgrade. This option uses a temperature sensor called a thermocouple to determine the actual temperature of the brake linings (sometimes called the heatsink). This is integrated with the Engine Indicating and Crew Alerting System (EICAS) so the pilots know when it is acceptable to taxi out.
The consequences of excessive heat in brakes have already been mentioned. After the Sud Aviation incident, the industry introduced fuse plugs into aircraft wheels. These contain a eutectic material which melts and releases tire pressure prior to wheel rupture. Aircraft tires are inflated with nitrogen, the release of which suppresses any fire which might occur.
For those interested in what happens when fuse plugs do not operate properly, here is a video:
