The heat loss due to convection and sweat evaporation at the skin is greater than the heating effect due to friction with the air molecules at low velocity.Advertisement Scroll To Keep Reading
Sometimes it may have happened that you stuck your arm out of the window of the car that you were traveling in while on a vacation and felt a comforting, coldness surge through your arm. In-fact, the faster the car goes, the colder it seems.
And on a rather warm day, the coldness is actually quite inexplicable. After-all, when the arm is outside, it collides with the air molecules. This collision is responsible for aerodynamic friction. Shouldn’t friction with the air cause heating, rather than cooling?
Also, why does your arm cool down when traveling at 60 mph (96.5 km/h) while spacecraft traveling at 25,000 mph (40,233 km/h) are equipped with a heat shield to protect from damage caused due to aerodynamic heating?
Before jumping into the crux of the matter, it’s important to understand the basics of friction, collision and heat transfer.
The Science of Heat and Relative Motion
Friction: Thou Shalt Not Move
Imagine that two cardboard boxes are kept over each other. Suddenly, both the boxes are pulled in the opposite directions. It’s slightly difficult to pull those boxes, especially if the sliding surfaces are jagged. This is because there exists a force which tends to resist the relative motion of the boxes opposite to each other.
This force, which resists motion is called friction. It arises due to the interlocking of the jagged surfaces with each other as pushing two interlocked surfaces requires microscopic physical deformations to make way for further movement.
Friction can also be observed within liquid flow. A liquid flows in layers. The bottom layer, in contact with the ground surface, moves the slowest, while the topmost layer moves the fastest. The layers between the top and the bottom move with increasing speeds near the top.
This difference in speeds of layers results in relative motion between them, and thus the development of a force of friction. This force is called viscosity in fluid-dynamics’ terminology. In common parlance, viscous force is also called drag. Similarly, when gases (like air) flow, they also experience a viscous force in an identical mechanism as liquids.
In the motion described above, the common thread is the development of motion resisting force between two relatively moving parallel layers.
Frictional force is a result of two surfaces coming into contact with each (collision) other and moving parallel relative to each other. Thus, some kinetic energy transfer occurs. Some of this kinetic energy gets converted to heat energy. This is responsible for raising the temperature at the interface of the two surfaces. When air strikes a surface, two processes occur.
The first is the stagnation of some air molecules which strike the surface head-on due to the geometry of the surface. The entire kinetic energy of the air molecules is lost and they remain at rest (hence the term ‘stagnation’). This results in an increase of pressure at that region and is called a stagnation point. The amount of heat transferred per unit time, q, at stagnation points is given by:
h = local heat transfer coefficient (mass per unit area per second)
Hst = enthalpy of the fluid layer at stagnation point
Hw = enthalpy of wall (thermodynamic wall is an imaginary surface parallel to direction of fluid flow across which mass transfer doesn’t occur, only energy transfer. In our case, the wall is the solid surface)
Tw =temperature of wall
= radiation factor
The second process is the glancing collision at some angle between air molecules and the surface. The air molecules strike the surface at varying angles, though most of them move parallel to the surface, making a glancing contact and moving away. The kinetic energy of the molecules remains high. The region on the surface where this occurs and is called a low pressure gradient region. The amount of heat transferred per unit time at low pressure gradient regions is given by:
HR = boundary layer recovery enthalpy (boundary is the air layer in contact with the surface. Recovery measures a loss of pressure due to high velocity)
Rest of the terms same as in (i)
Heating effect due to air (aerodynamic heating) is the sum of (i) and (ii).
Wind Chill: Thou shalt Feel the Freeze
The body maintains a core temperature of about 97oF – 99oF (36.1oC – 37.2oC). Except during peak summers, the environmental temperatures remain near 30oC or below, which is colder than the body temperature. The air outside comes into contact with the skin and heat transfer from the body (higher temperature) to the air (lower temperature) occurs. A thin layer of warm air forms near the skin, which provides insulation from further heat loss.
But when air flows, the warm layer is constantly pushed away by incoming colder air. A continuous cycle of heat loss occurs where the body loses heat to the surrounding air, which is pushed away by colder air to be warmed up again. This results in the lowering of skin temperature and a feeling of coldness. This is called wind-chill. Also, if there is sweat on arms, then fast moving air increases the rate of evaporation from the skin, resulting in heat loss.
The faster the air flows, the greater the wind-chill.
The amount of heat transferred per unit time, Q is given by:
h = convection heat transfer coefficient,
A = area exposed to convection,
Thot = temperature of the hotter object,
Tcold = temperature of the colder object
Aerodynamic Heating versus Wind-Chill
Having studied the basics about both, the obvious question which comes to mind is that what happens when these two processes oppose each other. What is the threshold beyond which wind-chill gives way to aerodynamic heating?
As the airspeed increases, the rate of convective heat loss increases, and the body becomes colder. This loss of heat continues at subsonic speeds (speed of vehicle lower than the speed of sound). As the supersonic limit is breached, the heating effect becomes quite dominant and at speed above Mach 2.0 (twice the speed of sound, 1534 m/h = 2469 km/h), heat shields are required to protect from high temperatures (400oF/204oC). There is no universal threshold as such, since the heating effect depends also on the geometry of the vehicle. As a general observation, speeds above Mach 1.0 (1235 km/h or 767 m/h), the heating is significant to cause damage to exposed electrical equipment.
Coming back to the question, yes, it is possible to warm up your arm while moving, but you’d have to be pretty fast to actually cause aerodynamic heating.
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