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The recovery temperature, is the temperature a moving fluid reaches at the surface of a solid boundary where the flow has zero velocity due to the no-slip condition. It differs from the bulk freestream temperature due to aerodynamic heating in the boundary layer, as the viscous friction causes the fluid to approach (but not reach) the stagnation temperature. The recovery temperature is sometimes referred to as the adiabatic wall temperature, as it is also the temperature the wall will reach in the event it is adiabatic.

The recovery temperature is related to the fluid temperature and Mach number by the following relation: :


 * $$T_r = T \left[ 1 +\frac{\gamma - 1}{2} \; Ma^2 \; r \right] $$

where:


 * $$T_r =\,$$ recovery temperature


 * $$T =\,$$ fluid (static) temperature


 * $$\gamma =\,$$ ratio of specific heats


 * $$Ma =\,$$ Mach number


 * $$r =\,$$ recovery factor

From the above, it can be shown that the recovery temperature is equal to the stagnation temperature when the recovy factor is unity.

Film Cooling
In the context of film cooling, the recovery temperature is typically defined only for the uncooled case, in contrast to the adiabatic wall temperature which accounts for the effect of the cooling flow.

Aircraft
Aerodynamic heating is a concern for supersonic and hypersonic aircraft. The Concorde dealt with the increased heat loads at its leading edges by the use of high temperature materials and the design of heat sinks into the aircraft structure at the leading edges. Higher speed aircraft such as the SR-71 deal with the issue by the use of insulating material and material selection on the exterior of the vehicles. Some designs for hypersonic missiles would employ liquid cooling of the leading edges (usually the fuel en route to the engine).

Reentry vehicles
Aerodynamic heating is also a topic of concern in reentry vehicles. The heating induced by the very high speeds of reentry of greater than Mach 20 is sufficient to destroy the structure of the vehicle. The early space capsules such as those on Mercury, Gemini, and Apollo were given blunt shapes to produce a stand-off bow shock. As a result most of the heat is dissipated to surrounding air without transferring through the vehicle structure. Additionally, these vehicles had ablative material that sublimates into a gas at high temperature. The act of sublimation absorbs the thermal energy from the aerodynamic heating and erodes the material away as opposed to heating the capsule. The surface of the heat shield for the Mercury spacecraft had a coating of aluminum with glassfiber in many layers. As the temperature rose to 2,000 °F (1,100 °C) the layers would evaporate and take the heat with it. The spacecraft would become hot but not harmfully so. The Space Shuttle used insulating tiles on its lower surface to absorb and radiate heat while preventing conduction to the aluminum airframe. The compromise of the heat shield during liftoff of Space Shuttle Columbia contributed to its destruction upon reentry.