[time-nuts] Re: MHM-A1 maser temperature stabilization

[Poul-Henning Kamp]

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Bob Camp writes:

> Ok, but do I need  > 800 L of the stuff ? 

Forget your 250L of water, it is the wrong way to think about this problem!

Here is a calculated example:

   We want to house a HP5065, it dissipates 40 {W}

   We build the box as a cube with sides 0.75 {m}.

   Surface area = 6 * 0.75 {m} * 0.75 {m} = 3.375 {m²}

   Aerated Concrete has a lambda of 0.14 {W/mK}, and thickness 0.05 {m}

   Heat loss ("U value") of wall:  lambda / thickness = 0.14 {W/mK} / 0.05 {m} = 2.8 {W/m²K}

   Multiply by surface area: 3.375 {m²} * 2.8 {W/m²K} = 9.45 {W/K}

   Divide into power dispation: 40 {W} / 9.45 {W/K} = 4.23 {K}

The inside of the box will be 4.23 Kelvin hotter than the outside. 

   The density of Aerated concrete is 540 {kg/m³}

   Volume of walls = 3.375 {m²} * 0.05 {m} = 0.168 {m³}

   Weight of walls = 540 {kg/m³} * 0.168 {m³} = 91 {kg}

Each of the 6 walls weigh around 15 {kg}, that's workable.

   Thermal Capacity of Aerated concrete is 1 {kJ/kgK}

   Thermal Capacity of walls = 91 {kg} * 1 {kJ/kgK} = 91 {kJ/K}

/This/ is the number that matter:  The amount of energy it takes to change the temperature of the walls 1{K}.

If we dive into algebra, we can now calculate how big a 24h temperature
excursion on the outside it takes to meaningfully change the
temperature of the inner walls in the box, but I'll leave that as
an exercise for the reader.

Instead we build the same box, but with 25mm EPS foam board:

   lambda = 0.041 {W/mK} thickness 0.025 {m}

   Heat loss ("U value") = 0.041 {W/mK} / 0.025 {m} = 1.64 {W/m²K}

   Multiply by surface area: 3.375 {m²} * 1.64 {W/m²K} = 5.535 {W/K}

   Divide into power disipation: 40 {W} / 5.535 {W/K} = 7.22 {K}

   Density: 13 {kg/m³}

   Weight of walls: 13 {kg/m³} * 3.375 {m²} * 0.025 {m} = 1.1 {kg}

   Thermal Capacity of (E)PS: 1.3 {kJ/kgK}

   Thermal Capacity of walls = 1.1 {kg} * 1.3 {kJ/kgK} = 1.43 {kJ/K}

QED:

It takes 63 times /more/ energy to change the temperature of the inner
wall in the 50mm Aerated concrete box, than it does for the foam-box.

/That/ is the "thermal impedance" we need to attenuate the diurnal
and random temperature changes.

... and why we need algebra as soon as we introduce time :-/

Note also that the temperature rise almost twice as much in
the foam box than in the Aerated Concrete box.

-- 
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