# Heat loss of a cargo container in space

1. Jan 12, 2013

### Prof Null

I'm new here.
I am working on a fictional space commerce system using containers to transport things between planets. The container size is 4x4x8 meters and most often it would be colored but call it grey for the purpose of the question. I don't know what you would make it from, I suppose metal as I can't think what else would survive deep space.

My question is this:
The container starts off on an Earthlike planet at std. temp, then is transported into orbit, then loaded on a Space Container ship. How long would it take for the container to drop in temp to near 4K?

I assume that before they got too cold the cargo ship would pass near a star and spin the ship to "rotissierie" the containers to warm them up - but that only makes the questions grow: I am sure that at some low temperature materials such as plastic and lubricant oils will break down - what would be a fair estimate of the safe minimum temp for such things?
Any help greatly appreciated.

2. Jan 13, 2013

### engnr_arsalan

1) cargo should not be of bare metals.coz metals have high thermal diffusivity so it will absorb as well as radiate energy more quickly. the cargo should be carbon fiber or ceramic like thing..it will provide less heat transfer as well strength..i was reading an article in which they said that the front portion of space shuttle that is black in colour is lined with ceramic type material..coz while entering back in the atmosphere they encounter lots of friction due to which temperature of shuttle surface rises..but lets keep that apart..coming back to your question..it depends upon material as well amount of internal energy of that system to calculate time to reach 4k.so it is hell of a calculation

3. Jan 13, 2013

### CWatters

First you need to know how much thermal energy it contains. That depends on it's initial temperature and thermal mass. The latter would depend on what's in the container. It might be reasonable to assume it's full of water which has a relatively high thermal mass and that would give an estimate for the longest time. Other materials are likely to cool faster as they have less thermal mass.

If the water starts off as a liquid and ends up frozen you need to include the energy due to the phase change as well so there will be three sums...

1) The energy given out as it's temperature falls from say 298K to 273K. Look up "heat capacity" or "specific heat capacity" of water.

2) The energy given out as it freezes. Look up Latent Heat of fusion for water.

3) See 1) but for ice and the range 273K to 4K.

Add them up. Once you know how much energy needs to be lost then you can figure out how long it will take...

If you treat space as a vacuum then there is no heat loss by conduction or convection, only radaition. To work out the radaited losses you need to know a bit about it's surface finnish.

The power loss (energy loss per unit time) at any instant is:

Power = ε σ A ΔT4

where

ΔT is the temperature difference between the space craft and space.

σ = Stefan–Boltzmann constant = 5.670 373(21)×10−8 W·m−2·K−4

A = surface area

ε = The emissivity of the paint..

http://en.wikipedia.org/wiki/Emissivity

Because the temperature isn't constant, nor will the power loss so a bit of maths is required to calculate the time. You may find it takes an infinite time because as the temperature approaches that of space the power loss gets ever smaller. So perhaps work out the time to get within a few degrees of space and call that close enough.

I think I've got all that right -)

No I don't have time to do all the sums :-)

Last edited: Jan 13, 2013
4. Jan 13, 2013

Most people think that cooling should be easy in space, but if you are not much further from the sun than earth your equilibrium temperatures are "earth like". I heard that aluminium heats up considerably, and solar panels equilibrate to about 25°C. Check out this link. It gives you the formulas to calculate the temperature http://www.alternatewars.com/BBOW/Space/Spacecraft_Ext_Temps.htm

5. Jan 13, 2013

### Staff: Mentor

That is an important point - earth is in space as well, and roughly in equilibrium! If you tune the emissivities for visible and infrared light and its orientation in space, you can get any "earth-like" equilibrium temperature you like, as long as the container is roughly 1 AU away from the sun.

To get an estimate for the timescale: Fill it with 60m3 of water, take a perfect black body and perfect thermal conductivity. At 300K, this corresponds to 460W/m2 thermal radiation, for a total of ~75kW. Water has a heat capacity of about 4MJ/(m3K), or 240MJ/K. Without external radiation, this gives a cooling rate of 1.6*10-4/s, or 14K per day. The cooling rate quickly drops if the temperature drops - at 150K, radiation dropped to 1/16, so the cooling rate is just 2K/day (taking into account that ice has just 50% of the heat capacity).

Isolation can reduce any heat exchange with the environment significantly.

6. Jan 14, 2013

### CWatters

I thought the earth would be 20-30C colder if it didn't have an atmosphere? I suppose that's a small difference compared to 293K though.

7. Jan 14, 2013

### sophiecentaur

Thinking about Mercury's wildly differing surface temperatures, 'light and dark sides', it seems that you can choose your temperature to be within a wide range.
A black side facing the Sun and a shiny side facing away will produce a high internal temperature, whilst the reverse will produce a low internal temperature. The only thing that is fixed is the amount of energy falling on the area of your object. This is very important in the design of satellites - particularly TV transmitting satellites, with their multi kW EV panels. It seems that the thermal circuitry in them is as important as the electrical circuitry, with gold foil on the sunny side, dark heat sink panels on the dark side and miles of heat pipe.

8. Jan 14, 2013

### AlexLAV

The more any substance reflects the less it radiates. Metals have high reflectivity in IR spectrum hence they generally are poor thermal radiators. At room temperature emissivity of aluminium is about 0.09, while emissivity of gold is about 0.02-0.04.

9. Jan 14, 2013

### AlexLAV

I think there should not be a problem keeping contents of the container under some moderate temperature, if proper thermal insulation is ensured. The best thermal insulation at low and moderate temperature is vacuum (it is used in vacuum flask).

Suppose the content temperature is about +20 deg. Celsius. If the container is gold-coated it emitts of approxamately 1 kW of total heat power. It is rather high value. One extra layer of golden foil with vacuum gap between it and the container wall leads to the value of total heat sink of about 30 W. Adding one more layer of golden gold with one more vacuum gap leads to the power of total heat radiation down to less than 1 W. If you place some heat source with such thermal power into the container the temperature of the contents will be constant.

10. Jan 16, 2013

### Prof Null

Thankyou AlexLAV, you have been specially helpful. Four layers of gold plate with vacuum in between would be fine - there would be more losses because of the door seams but that must be accepted: I expected that some energy would need to be added to stop things freezing up, this looks more like a good container could make it through a very long trip no problem with only minor energy added.

11. Jan 16, 2013

### sophiecentaur

I am surprised that no one has picked up on my earlier comment that you can actually control the internal temperature by the appropriate use of different emissivities on the sides facing and away from the Sun / star. If you want to stay warm then you can cause the temperature to be high in this way - certainly way out beyond Mars. There's more to it than just going for insulation when you are in or near an Earth-like orbit - and even a lot further away.
It would be only in really deep space that your temperature would be near 4K, on any case.

12. Jan 16, 2013

### Khashishi

The emissivity isn't a single number but a function of wavelength. You can achieve a greenhouse effect by using a paint that is emissive at visible wavelength and reflective at IR wavelength, so you can easily be warmer than the Earth if you need to be, as long as you are near a star.