Thanks, so what I surmise from that is helium mixtures remove slightly less heat from the body (166W vs 172W). Is it fair to assume then that for trimix the ratio would fall somewhere in between depending on the amount of helium in the gas?
I believe there no theory to prove here, just simple calculations based on well known parameters
He has higher conductivity than air:
Thermal Conductivity of some common Materials
He has also higher heat capacity than air:
Gases - Specific Heat Capacities and Individual Gas Constants
When breathing both get heated up to same temperature, so we can completely ignore conductivity.
Lots of scuba math below.
one cuft of air weights 0.0807lbs
one cuft of He weights 0.011lbs
one human breath is roughly 1/6th of cuft
Amount of energy required to heat up ~1 lbs of He by 1 degree Kelvin is 2500 Joules. 1 Joule is expending energy of 1 Watt per second.
We are heating up from say 32F to 90F which is 36 K. So total energy to heat up 1lb of He from freezing point to human body temperature is 36 * 2500.
1 lb at normobaric is roughly 90 cuft.
90 cuft is roughly 540 breaths
so to heat up one breath we need 36 * 2500 / 540 Watts total. = 166W.
same calculations for air render = 172 Watts (it has lower heat capacity but each breath weights more)
One breath lasts 15 seconds? 10 seconds? I have seen various estimates of how much radiation human body expels in a second and the lowest I come across was 50W. So not only difference is small, but also it seems that we radiate way more than needed anyways.