The feeling of cold is the result of the environment removing heat energy from your body, not the temperature difference between your body and the environment. In general, the difference in temperature (98.6F and 70F) is the driving force for this heat transfer so we associate the feeling of cold with the temperature difference, but there is another factor involved.
The “film coefficient” between your skin and the environment affects the amount of heat that leaves your body over time, for any given temperature difference. As it has been previously stated, the film coefficient between skin and water is much higher than skin and air, resulting in more heat transferred from your body to the environment.
While it is not quite the same, you can see a similar difference in the heat transfer coefficient numbers for a heat exchanger (an industrial device). These numbers are for the overall heat transfer coefficient, which includes the film coefficient, but also includes some other factors. Still, they illustrate the difference between air and water.
Air -> Cast Iron -> Air = 1.0
Water -> Cast Iron -> Water = 40 – 50
So for the heat exchanger, wetted surfaces transfer heat at approximately 50 times the rate.
Your skin probably does not have this exact multiple of 50, but it will be a significant difference that increases heat energy transferring out of your body to the environment, resulting in you feeling cold.
[https://www.engineeringtoolbox.com/overall-heat-transfer-coefficients-d_284.html](https://www.engineeringtoolbox.com/overall-heat-transfer-coefficients-d_284.html)
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