I got interested in why, at the same temperature, water feels cooler than air. After a google search, I saw that this question got answered here: Why does water feel cooler than air. I understand the answer given there.; however, is there a formula which I could use to calculate the temperature at which the air should feel the same temperature as water? For example, at which temperature should the air feel the same temparature as water at 12ºC?

I myself have tried to get this formula working with Newton's cooling law, but without any results.

Thank you in advance.


It can't be done to any accuracy really here's why.

You need to have the same heat-flow out of the body into the air (insulator) as into the water (conductor). We need to consider both conductive and convective losses through the medium.

At any given temperature, as air is an insulator, the ratio of conductive to convective loss is very much lower than water.

So if the thermal conductive losses are matched when the air/water is stationary, then if there is movement and convective loss occurs the air will convect much, much more energy than the water.

Conversely if the convective heat transfer is equalised, then the water will conduct much more heat energy and the air will feel warmer if it is stationary.

You can always feel the difference.

  • $\begingroup$ So the question: at which temperature should the air feel the same temparature as water at 12ºC? Can simply not be answered? Or, at least, not rigorously? $\endgroup$
    – J doeoeo
    Apr 1 '17 at 22:46
  • $\begingroup$ That's correct. $\endgroup$
    – JMLCarter
    Apr 1 '17 at 22:52
  • $\begingroup$ @JMLCarter And is the convection dominant very quickly then with just a little bit of air movement? Even with the air warmer by 10 degrees? Anyways, I just came back from the beach in a warmer climate, it definitely was one way or the other way, didn't notice a balance (water cooler at 3pm, air about 5 with some wind, or it felt that way) $\endgroup$
    – Bob Bee
    Apr 2 '17 at 0:42
  • $\begingroup$ Windchill effect is detailed here. en.wikipedia.org/wiki/Wind_chill For a light 5mph wind ranging from extremes of 2 to 18$^o$ additional cooling, dpending on ambient temp. Depends on humidity too. Down at the beach at say 28$^o$ it would bring the temperature down to 23$^o$. That said, the dominant effect is the radiative heat from the sun. $\endgroup$
    – JMLCarter
    Apr 2 '17 at 1:08
  • $\begingroup$ Convective coefficients account for the conduction as well as the convection, so as long as you can assume some sort of convection, you shouldn't need to account for conduction, it's already accounted for. If you assume steady state conditions for example, you should be able to find an equivalent air temperature where the heat loss is the same. $\endgroup$
    – JMac
    Jan 7 '20 at 20:11

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