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Calculating cooling energy

Calculating cooling energy

Hello Everyone,

I have come across this rather interesting site in my quest to answer a question which is outside of my normal field. I hope that I can add to the community where I can, but also learn from the wealth of expertise that exists here.

So Normally I am working with materials. Today I would like to solve a problem on heat transfer. At least I think it is heat transfer.

Here is my situation.

I have a corrugated cardboard box with some material inside (solid form block of polymer) the polymer is temperature sensitive. It is in contact with the bottom surface of the box but not the sides or the top.

I would like to transport the box (and contents) by truck. The problem is that it can get very hot in the summer in the back of the truck and I need to keep the box cool.

What I would like to do is: create a mpdel which based on the temperature of the day (assuming the truck is in sunlight) how hot it will get inside the truck and how much heat will get to my substance inside the box and how long it will take.

Eventually I would like to also calculate how much cooling/heat energy I need to take away from the box to keep the contents within a certain temperature range for a given time.

I thought maybe the next steps should be applied:
1, Calculate temp inside the truck
2, Calculate the transfer through the box to the polymer
3, Calculate heat energy to remove to keep the polymer at a certain temp

It has been some time since I carried out anything to do with heat transfer. I would very much appreciate maybe some coaching here from the experts so I can relearn a little some of the theory as well.


RE: Calculating cooling energy

You could brush up with a course in heat transfer and thermodynamics.

RE: Calculating cooling energy

Hello willard3,

Thanks so much for your response. I would be happy to brush up! would you be able to point me in the direction of good online resources?

RE: Calculating cooling energy

MIT has open courseware; Lienhard has online text:

Nevertheless, given the probable duration of the transport, the temperature inside will equilibrate to at least the ambient temperature during the transport. You can tack on 10C for solar load.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!
FAQ731-376: Forum Policies forum1529: Translation Assistance for Engineers

RE: Calculating cooling energy

Step is figure out if you even have a problem that needs solving. What is the allowable max temperature of your product?

Sounds like you want to actively cool a cardboard box inside a truck. Where are you going to put the heat that you take out?

Where are you going to find a power source for your active cooling?

Temperature sensitive products are shipped by truck every day. Don't you think it would be easier to simply ship your box via a temperature controlled truck?

RE: Calculating cooling energy

@IRStuff, Many thanks for the links I will check them this evening.

@MintJulep, Thanks for the initial pointers.

Is there a problem that needs solving? Yes. Max allowable temperature is 27 deg C.

Actively cooling the cardboard box I think is what I want to do. Or prevent the temperature rising over 27 within 3 hrs.

Where am I going to put the heat? good question. back into the truck? I just want to slow down the heating up of the box.

Power source? this will depend on how much heat energy I want to take away, so I wanted to understand this to see if it will be feasible.

Temperature controlled truck is out of the question in this case. The material is kept in a warehouse at around 21, going lower will also affect the product and the cost is to high.

Thanks Guys.

RE: Calculating cooling energy

You could have simply stated that you had something that started at21C and had to be kept under 27C during a 3-hr road trip in your OP, and that would have saved everyone some time.

Passive solution:
> aluminized foil to reflect as much sunlight as possible, but even a sunshade would probably do well, coupled with A LOT of styrofoam. Assume 1 m^3 box, no direct sun, no direct wind, 957 kJ of allowable heating over 3 hr --> 89W. This requires about 4 inches of styrofoam around the block of material to keep the thermal loss under 89W

Active solution:
> passive solution with TE coolers or other active cooling. With 4-in styrofoam, you'd need 89W of cooling to maintain temperature.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!
FAQ731-376: Forum Policies forum1529: Translation Assistance for Engineers

RE: Calculating cooling energy

Operate you truck air conditioning (don't turn it off) and put the package on the passenger seat beside you. No sense spinning your wheel!

RE: Calculating cooling energy

@IRstuff, apologies for not being more precise in the OP and also to everyone else.

The package will be in the rear of the truck so it has no exposure to light (I hope). Passive solution is what I was originally thinking. I also thought that there would be a great deal of Styrofoam needed but I had some trouble in identifying the right formulae to calculate this. If you could point me in the right direction I can try different insulating materials and see if I can get a more compact package.

TE coolers sounds also like an interesting solution.

Thanks for the useful tips so far guys - I really appreciate it.


RE: Calculating cooling energy

You could start by doing a relatively simple analysis.

You know the mass / volume of your liquid. You know the specific heat required to heat a unit of your fluid 1 C

Work out how much heat is required to go from 21 to 27C. divide by 60 x 60 x 3 to get heat power in watts.

Work out the square area of the outside of your fluid container.

Heat flow through insulation can then be worked out assuming some sort of air temp in the truck 9 say 40C and a midpoint of your temp, say 24C to even out the heat flow and away you go.

You might also consider just increasing the mass of fluid by say immersing your fluid storage into say a container 5 times the volume filled with water at 21C?? That would need much less insulation and if you do the calculation about heat transfer from air to a solid (convection) then you might not need any insulation at all.

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

RE: Calculating cooling energy

The calculation can give you the peak load but if you still need to control the cooling effect to match the varying load. That is why you should just use the truck thermostat controlled air conditioning system set to maintain the temperature required.

RE: Calculating cooling energy

The amount of Styrofoam will be dictated by the heat capacity and mass of the polymer. Additionally, the thermal conductivity will limit how much of the heat capacity is accessible, particularly for a relatively short drive. The 4 inches I posited assumed accessing only the first 2 inches from the surface of the block, but I ignored its thermal conductivity.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!
FAQ731-376: Forum Policies forum1529: Translation Assistance for Engineers

RE: Calculating cooling energy

And I have received shipments of temperature sensitive materials that have passive cooling inside the box, ie ice packs. In reality they are a gel that has a freezing/melting point that is a below your critical temperature.
Packing with these inside of a Styrofoam box is what allows the shipment of many products, specialty chocolates being one of them.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, Plymouth Tube

RE: Calculating cooling energy

Hello everyone,

Thanks again for the help so far. After a bit of study I think I may be able to go to the next step.

I guess my first step before calculating how much heat to remove, so I need to calculate the heat going in.

I am thinking heat balance here with the following equations:

Qt = Qrad + Qconv + Qcond

Qcond = kA(dT/dx)

Qconv = hA(dT)

Qrad = aAs(T^4) (T being outside temp)

k=thermal conductivity
dT=change in temp
h=heat transfer coefficient
s=Stefan Boltzman constant

Thanks in advance for any feedback

RE: Calculating cooling energy

Your radiative term is going to be astronomical. That term should look like T14-T24 where T1>T2 and both in oR or oK depending of course on your choice of units.


RE: Calculating cooling energy

Go outside with a thermometer and MEASURE the air temperature of a closed truck in the parking lot at 12:00, 2:00 pm, and 4:00 pm on a sunny day.

Do not do anything else until you've done that. Stop playing with equations until you KNOW the truck air temperature. It will be the maximum your product will heat up to.

A standard grocery store "reefer" uses an EXTERNAL motor and cooler to cool the air being recycled from the trailer to the refrigerator by an external A/C unit driven by the truck motor/electrical. Thus, the cooler does not add heat inside the cooled volume at all. The air around the product is maintained cold for the food, and thus the circulating air is well below ALL of the other temperatures: The wall is hottoer, the insulation is hotter, the inner wall is hotter, and the product case (your cardboard box wrapped with foil and insulation foam) is hotter than the circulating air.

But, what is the mass of the product? How often is it shipped the three hour drive? How often are delays and problems occurring en route?

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