Why does moving air feel cold?

Question

I'm taking a thermodynamics class and had the following question. I was going to ask my professor directly, but it seems like a stupid question with a simple answer, so I thought I'd try my luck here in fear of embarrassment.

When air flows through a pipe, its stagnation enthalpy doesn't change. For a calorically perfect gas, we have that the enthalpy varies linearly with the temperature.

$$h_0 = \text{constant}= h + \frac12u^2$$ $$h = c_pT$$

Let's look at air. Air has a specific heat at constant pressure of $1000\ \mathrm{\frac{J}{kg\cdot K}}$. Room temperature air is about $300 \text{ K}$. Wind speeds are usually below $15\ \mathrm{\frac{m}{s}}$.

Rewriting our equations, we can say:

$$c_p T_0 = c_pT + \frac12u^2$$ $$1000\ \mathrm{\frac{J}{kg \cdot K}} \cdot 300 \text{ K} = 1000\ \mathrm{\frac{J}{kg \cdot K}} \cdot T + \frac12(15\ \mathrm{\frac{m}{s}})^2$$ $$300000 \frac{J}{kg} = 1000T\ \mathrm{\frac{J}{kg}} + 112.5\ \mathrm{\frac{J}{kg}}$$ $$T = 299.9 \text{ K}$$

So, moderate wind speeds don't change the temperature at all. Why, then, does moving air outside feel significantly colder than stagnant air?

Answer 1

There are a couple reasons. First of all, it's important to note that the sensation of warmth or coolness is only indirectly related to temperature. The receptors in your skin that deal with temperature are mainly sensitive to heat transfer and changes in temperature, not so much absolute temperature values. For example, here's an interesting excerpt from the EB article on thermoreception:

Cold receptors respond to sudden cooling with a transient increase in discharge frequency (called the dynamic response) that is directly related to the prior temperature and the magnitude and rate of the temperature decrease. If the cooler temperature is maintained, the discharge frequency adapts to a frequency of static discharge that is directly related to the cooler temperature.

So the sensation of coolness has to do with how quickly heat is being transferred away from the skin. Heat transfer occurs in three modes: radiation, conduction and convection. It's that last one that's important, because convection relies on motion; with no motion, there's only radiation and conduction. Air is a pretty good insulator, making conduction less effective; and it's transparent across a wide spectrum, meaning there's no significant radiative heat exchange. And your skin has many tiny hairs (and perhaps larger hairs, depending on the person) that work against any minor convective flows, as from a draft or small disturbance.

Basically, in the absence of convection (moving air), your skin will locally warm the air right around itself, and that air won't be very quickly replaced by cooler air. As it warms, it conducts even less heat away from your skin (because the smaller temperature differential is a weaker driver).

But the much more significant factor in most cases is probably increased evaporative cooling. Just as that layer of air around your skin conducts heat and is warmed by your skin, it also evaporates moisture and becomes more humid. (Your skin can always lose some amount of moisture to dry air, even if you don't feel sweaty.) Just as heat transfer will be reduced as the air warms up and approaches your body temperature, so too will evaporation be reduced as the air immediately surrounding your body gets slightly more humid. But when the air is moving, it gets much more effective at evaporating moisture from your skin. You can read about the mechanism of perspiration for some more background.

In both cases, the moving air acts relatively more like a constant-energy sink because as your body contributes heat energy and/or moisture, those higher-energy molecules move away from the interface with your skin and are replaced by more cool, dry air. From an analytical perspective, if the air is moving quickly enough you don't have to account for it getting warmer or more humid over time as it exchanges heat and moisture with your skin.

As this comment points out, it's important to recognize that while perspiration is specifically a cooling mechanism, convection works both ways; if the surrounding air is warmer than your skin, a breeze will make it feel even hotter. If you're really interested in this topic, UC Berkeley's Center for the Built Environment has a neat thermal comfort tool that you can play with, which goes into much more detail as far as individual and environmental variables.

Answer 2

The air feeling cold is really your skin being cooled by forced convection and evaporation of sweat.
With no air movement a boundary layer of hotter air forms over the skin and so because of the smaller temperature difference the rate of heat loss decreases.
Moving air over the skin disrupts this boundary later allowing unheated air to be in contact with the skin thus increasing the rate of heat loss and so the skin cools more. Evaporation is a change of state which requires latent heat which is provided by skin which thus cools more. See wind chill and for the "opposite" effect heat index.

Answer 3

In still air, the main heat transfer mechanisms are diffusion and natural convection. If an object is at a higher temperature than the still air, heat will flow from the object to the air. In essence, the air immediately surrounding the object would be at a higher temperature than just the air itself.

In moving air, you also have diffusion and natural and forced convection as heat transfer mechanisms. Forced convection works to remove the heated air in the immediate vicinity around that object (due to diffusion) and supply more air at the original temperature of the air more rapidly than the other mechanisms.