Max internal container temp in sun

[CorbinDallas]

I have had a hard time trying to determine what internal temperature the air will reach inside of a container sitting in the sun. For my example, I will use an insulated shipping container.

Ambient Temp: 50°C
Color of container: White
U-value: 0.2
Max Irradiance intensity: 1120 W/m^2
Container Dimensions: 20ft x 8ft x 10ft

If this container is sitting in the direct sunlight, assuming there is no wind, how hot will it get inside during the day? Eventually, it will get hotter inside the container than the ambient temp due to the solar load, and the ambient temp would actually begin cooling, but that's assuming stead state and t goes to infinite. Any ideas on how I could tackle this?

Thanks

 

[razookm]

To get an accurate result, you will have to carry out a detailed calculation. In such situations, the simplest approach will be to estimate the maximum temperature possible in the container. This is the temperature at which the total radiation from the container to ambient is the same as the radiation from the sun through the exposed area. If the calculated maximum temperature is acceptable, no need to carry out the detailed calculations. But if the result of this calculation is more than acceptable, then one can calculate a more realistic temperature by doing a detailed calculation. This can be done taking credit for transient variation of radiation from sun, mass and heat capacity of the container, initial temperature of the container at the beginning of the day etc. This is a transient calculation and will be difficult to carry out using a spreadsheet even though not impossible. I request other members to suggest software they know of for carrying out such calculations.

 

[CorbinDallas]

How would I go about calculating the max temperature (simple method)?

I would like to be able to do the more detailed approach so any further information or software for that would be great. I have a feeling the internal temp is going to be too high with that first method. It basically just negates the insulation I believe.

 

[IRstuff]

If it were me, I would take the spectral characteristics of the sun and the enclosure to determine the total heat gain, then, using the combination of internal and external convection and radiation, determine the heat loss. The solution to the simultaneous equation will be the internal and surface temperatures that satisfy both constraints.

We know, based on the sad history of kids left in cars, that the internal temperature of a car can easily climb 30F above ambient.

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[razookm]

Simple method is using simple radiation heat transfer calculation using methods provided in any heat transfer textbook.

To explain further, consider the initial condition when the container is at ambient temperature. At this temperature, there is no radiation from the container to the surroundings. After some time, container temperature will start to increase and due to the temperature difference from ambient, there will be radiation heat transfer from the container to the surroundings. The temperature will continue to rise until it reaches a temperature when the radiation from the container to the surroundings is the same as the heat absorbed by the container from sun radiation.

Step-1 Calculate the heat absorbed by container due to sun radiation. Say Q-in

Step-2 Assume a Temperature T-cont and calculate the heat radiated from the container (Q-out) to ambient considering T-ambient = 50 (Refer heat transfer textbook for radiation heat transfer calculation)

Step -3 Repeat step-2 with various temperature till Q-in = Q-out

 

[itsmoked]

Check this:
thread391-464358

Keith Cress
kcress -

http://www.flaminsystems.com

 

[CorbinDallas]

In that thread, how did you come up with the 40°C delta T for the container surface temp? That's what I've been looking to calculate.

 

[LittleInch]

But you say this is an "insulated" container. Insulated with what? it's k factor, what is its thickness?

What units are your U value?

Ambient temp 50C?? Where are you - the middle of the gobi desert?

For what ultimate purpose is this calculation??

The issue is also one of heat ging into the ground, convection from the roof and sides, cooling from at least one side being in the shade or more as the sun moves round.

Too many variables to get anything better than "probably 10 to 20C higher than ambient"

Or put a shade over it.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[CorbinDallas]

Ideally I would just be able to set up the energy balance so that I can change the variables as needed. The 50°C is just a worst-case scenario. This can be a custom design, I can use whatever insulation I want (foam, fiberglass, etc.). One of the insulation I was looking at had an R-value of 6.4 ft2·°F·h/BTU and I was assuming 3"-4" of that (the units for the U Value were just the inverse of that). The container can be painted, so say it's painted white, how do I determine the solar absorptivity or is that just looked up.

My end goal is to have an accurate calculation of how hot I can expect the inside of the container to get in a day. The U value can probably drop, but for now we want to assume 0.2 BTU/ft2·°F·h (one of the walls may not have insulation). Maybe this is going to be too involved to get an accurate estimate.

Based on what Razookm stated above, this is where I'm:

Step-1: Multiply the Irradiance Intensity (1,120 W/m2) by the surface area of the container and by the solar absorbtivity (no idea what this value would be, maybe around 0.5 for white painted corrugated steel?). I'm not sure how I would accurately know how much of the container would be exposed to this since it depends on the angle of the sun. But I would assume 3-4 of the sides would be exposed to this. Once I have this value in watts, I'm not sure how to determine the surface temp of the container.

Step-2: Not sure how to calculate this.

I'm trying to find my old textbooks but haven't had luck. It's been years since college and haven't really been doing this type of engineering since then.

To get the internal temp, would I need to calculate the surface temp of the container then assume conduction through the walls?

 

[LittleInch]

I think so - The white colour will help in terms of heat input and probably temperature. "Black body" temperatures vary a bit but most opt for something about 70 to 80C max.

Try that for starters but note that if the heat power gets higher than the surface heat then it won't happen.

Then once you get heat going through the walls / roof then you can start to think about how much energy does it take to heat up the air inside the container ( assuming it's empty).

But if you're trying to do this over a day, then you need some sort of calculation for temperature / heat input possible from dawn to dusk. That will vary by latitude see

https://www.drroyspencer.com/2019/0...y-night-temperatures-at-different-latitudes/.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[IRstuff]

The basic heat flow network looks like this for temperature. MIL-HDBK-310 has a worst case air temp and solar loading table.

Internal sources surface temp --> internal air temp --> box wall internal surface temp --> box external surface temp --> ambient air temp

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[CorbinDallas]

IRstuff, I read through MIL-HDBK-310, which is where I got the 1120 W/m2. If you look at MIL-STD-310, one of the tables provides a temp of 71°C (160°F) Induced Air Temp for Transit and Storage conditions. Do you have any idea where this value comes from? I don't see anything on where that temp was derived from.

 

[IRstuff]

I presume that "someone" measured the temperature in a warehouse "somewhere" and got 71°C and decided that was "the" storage temperature; but note that this temperature is a passive temperature, i.e., there are no other active sources of heat.

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