Black body radiation for cooling in space
Since we all know, not just as Big E. told us, that in space we need no water to cool our systems.
Additionally, we do not have lots of it there. Normally.
So we have to get some nice formula to calculate how fast our space ship can cool down when arriving at the edge of the melting point.
For that physics (more precise: nature) has a nice mechanism called "black body radiation" (which has nothing to do with black holes... not sure about that). With increasing temperature this radiation increases dramatically (best just when your systems become a liquid molten slurry).
Old physicists from Germany (Mr. Stefan and Mr. Boltzmann) found, that following formula holds for hot bodies (not what you think just now), e.g. the cooling power per surface area in W/m^2 (Stefan–Boltzmann law) :
P/A = σ ⋅ T^4
where σ is the Stefan–Boltzmann constant, σ ≈ 5.67⋅10^−8 W m^−2 K^−4
and T the temperature of the surface in unit Kelvin.
So for a given surface area A with unit square meter (m^2) in vacuum (in a cozy, shady spot) with a temperature T in unit K (that is Kelvin), you can easily calculate the cooling power P with unit W (that is Watt, Watts if you like, like Kelvins... I will never get that) like this :
P[W] = 5.67⋅10^−8 ⋅ T[K]^4
or in computer language : P = 5.67e−08 * ( T*T*T*T ) ; // ... just an idea
if you take my advice to do your calculations always in SI (or "metric") units.
A nice little table here for to circumvent the calculation of the fourth power by foot... hand :
Table Black-Body Radiation
When designing your cooling systems it could be useful for the your final heatsink.
Source:
en.wikipedia.org
Since we all know, not just as Big E. told us, that in space we need no water to cool our systems.
Additionally, we do not have lots of it there. Normally.
So we have to get some nice formula to calculate how fast our space ship can cool down when arriving at the edge of the melting point.
For that physics (more precise: nature) has a nice mechanism called "black body radiation" (which has nothing to do with black holes... not sure about that). With increasing temperature this radiation increases dramatically (best just when your systems become a liquid molten slurry).
Old physicists from Germany (Mr. Stefan and Mr. Boltzmann) found, that following formula holds for hot bodies (not what you think just now), e.g. the cooling power per surface area in W/m^2 (Stefan–Boltzmann law) :
P/A = σ ⋅ T^4
where σ is the Stefan–Boltzmann constant, σ ≈ 5.67⋅10^−8 W m^−2 K^−4
and T the temperature of the surface in unit Kelvin.
So for a given surface area A with unit square meter (m^2) in vacuum (in a cozy, shady spot) with a temperature T in unit K (that is Kelvin), you can easily calculate the cooling power P with unit W (that is Watt, Watts if you like, like Kelvins... I will never get that) like this :
P[W] = 5.67⋅10^−8 ⋅ T[K]^4
or in computer language : P = 5.67e−08 * ( T*T*T*T ) ; // ... just an idea
if you take my advice to do your calculations always in SI (or "metric") units.
A nice little table here for to circumvent the calculation of the fourth power by foot... hand :
Table Black-Body Radiation
When designing your cooling systems it could be useful for the your final heatsink.
Source:
Stefan–Boltzmann law - Wikipedia
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