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I'm interested in personal cooling devices and would like to know if there's a way to make a rough estimate of rate at which you would need to extract heat from the body of an average male walking in weather of say 34 deg C and relative humidity of 90% in order to reduce body temperature to what it would be if walking in the same clothing (say slacks and a T-shirt) at say 24 deg C and RH of 75%. I don't know if there's any kind of model out there or if you have to work it all out from scratch.

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  • $\begingroup$ Lots of info about heat transfer from human bodies, effects of relative humidity etc. I will let you do a search, but one important factor is the temperature difference between the body and the environment, and then core temperature if the body gets too cold. $\endgroup$
    – Solar Mike
    Nov 2, 2021 at 17:08
  • $\begingroup$ I am a runner, have run 29 marathons, and will run again next Sunday at LA marathon. I know how big a difference heat and humidity can make. We all have our own little trricks, I take sea salt and potassium. I produce roughly 90 watts when running and burn around 4500 calories during 26.3 miles. $\endgroup$
    – kamran
    Nov 2, 2021 at 17:13

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The implicit goal appears to be to keep the temperature of the object (the human body) constant independent of changes in the external conditions (clothing, air temperature, wind speed, humidity). The simplest model is a lumped approach.

Let's assume the body is always warmer than the surroundings. The heat extracted by the surroundings is

$$\dot{q}_{x,s} = U A \Delta T$$

where $\dot{q}_{x,s}$ is the heat removed by the surroundings (W), $U$ is the effective heat transfer coefficient of the external surroundings (W/m$^2$ K), $A$ is the area of the object (m$^2$), and $\Delta T$ is the temperature difference between the object and surroundings (K). The person produces $\dot{q}_p$ heat depending on the effort. Finally, your cooling device extracts $\dot{q}_D$ heat. The vector sum is zero.

$$0 = - U A\ (T_o - T_s) + \dot{q}_p - \dot{q}_D $$

Your problem reduces to one of determining $\dot{q}_p$ and $U$ for different conditions. You could start with a constant "resting" heat production value $\dot{q}_{p,o}$. Start also with estimated values for the overall convection heat transfer coefficient for a "naked" object sitting in different air conditions (humidity, wind speed). This will give you a ballpark on what you need for $\dot{q}_D$ for a naked person resting in different air conditions. Add clothes by increasing $U$. Add walking to running effort by increasing $\dot{q}_p$.

This ignores radiation. Radiation can be added back as an additional term in the energy balance as desired.

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