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Calculating air temperature change in a closed system

Calculating air temperature change in a closed system

Calculating air temperature change in a closed system

I'm working with a client and I need to calculate the change in temperature of an enclosed volume. I know the volume, ambient temperature, and heat added to the system (in BTUs). Can someone point me to the correct equation(s) to calculate the increase in temperature? What information am I missing?

Once I know that, can I calculate what size fan (in CFM) that I would need to keep the temperature below a certain value?

Thank you in advance. I appreciate any help!


RE: Calculating air temperature change in a closed system

This isn't cooling down fruit is it?

You're missing lots of information if this is all you have.

One issue is that this is a transient situation by the sound of it so there is no simple calculation as the heat transfer from ambient to what sounds like a cooler internal mysterious substance will change as the delta T changes. So you need to do a step by step calculation.

Then you need to figure out the heat transfer rate from ambient into this "volume" and whether it behaves as a a homogenous mass or has internal heat transfer going on as well.

Size of a fan?? what temperature is the air?. Basically you need all this information again but now with air blowing through it. the air will increase in heat so that's one issue

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

RE: Calculating air temperature change in a closed system

A picture/labeled sketch is worth a thousand words.

Good Luck,

RE: Calculating air temperature change in a closed system

Okay, I see I may have left out some important details. Thank you for the replies. I'm also sharing what I know without sharing exact values so as not to cloud the issue.

It's a container with some electrical equipment inside that produces a certain amount of heat (in BTU). The container has louvers to which I will attach fans to replace the inside hot air with the cooler outside air, so the mysterious substance is just air.

Note that I'm not looking for any values or for anyone to tell me what size fan I need. I was just hoping for some help knowing what equations I would need so I can go dig up the information that I'm missing.

I'd thought of using Q=m*c*dT, but I wasn't sure how to relate BTU to this. If this equation is completely irrelevant and there's a better one, I'd love to know.

Even if I could just get pointed in the right direction for the first part, that'd be awesome.

Thank you

RE: Calculating air temperature change in a closed system

Aren't there entire books on this subject? The equations that matter depend on the exact circumstances and knowing a lot more about the conditions than shared here. See https://ahtt.mit.edu for a free text on heat transfer.

RE: Calculating air temperature change in a closed system

Is it a fixed amount of heat (BTU or Joules) or a fixed rate of heat output (BTU/hr or W)? Makes a massive difference.

Then what is temp of incoming air?

What is you max rise of air temp?

Then you can estimate mass of air required to remove the heat by allowing it to heat up, but then also estimate what this would look like in terms of velocity and if that is a reasonable number ( generally a few feet per second coming out the louvres or maybe less. so then you adjust uhntil you get to something reasonable that is a decent velocity, but doesn't get too hot.

Air is pretty "thin" so it doesn't take a lot to heat it up, but does take a lot to remove heat from something.

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

RE: Calculating air temperature change in a closed system

What you have is a very basic HVAC design problem performed by HVAC Engineers all the time. I myself desiged HVAC for an electrical room a few times over the past few years. You need to read up on basic HVAC design. In this case it is design of an electircal room with internal heat gain and during summer also external heat gain from heat flow through floors walls and ceilings. Also heat input from air seeping through doors crack is also considerred.

So in HVAC deisgn you balance the heat input to the space with the heat loss from the space. This balance occurs at a equillibrium temperature where heat input equals heat output. So you got all this heat input into the room from both internal and externally and at a given temperature you have heat exiting the room by equation Q=UA(dT)- equal to the heat entring the room at equillibrium. So U is the heat transfer coefficient of the floors wall and ceiling taken separately and A is their individual areas and dT is a diffrence in temperature between inside and outside. You set this temperature by seting your indoor design temperature.

Usually electric rooms are cooled with HVAC to maintain temperature inside. Sometimes you may be able to use just ventilation if you have air that is sufficiently cool outside to abasorb the heat when it passes through the room and then to outside, but in summer this usually not possible as electrical equipment must be maintained a 104F maximum inside the enclosures so most design temperatures inside an electrical room is about 80F plus or minus.

Although simple for an experience HVAC designer, you really need to know the basics of HVAC design to design a system such as this.

RE: Calculating air temperature change in a closed system

A good HVAC reference book I always use is

Handbook of Air Conditioning System Design, Carrier Air Conditioning 1965. If you understand all of the principle presented there you can design any basic HVAC system.


Note that you have to ge electrical loads from electical equipment manufacturers. The Heat dissipated by any piecre of electrical switchgear or motor starter is only a fraction of the rated load of the equipment. Then there is also a diversity factor applied since some elecrical equipment does not operate when other equimpment operates. This when it get difficult determining the actual cooling loads since you don't wnat to oversize the HVAC equipment and having it cycle on an off.

However these days there are small HVAC inverter duty mini-split units manufactured by Toshiba, Mitsubishi, Carrier etc. that varies the compressor speed and refigerant flow to keep in sinc the the cooling load so it can reduce in cooling capacity as required to meet the load under low load conditions.

RE: Calculating air temperature change in a closed system

Thank you Snickster. I'll dig more into HVAC systems and the equation you shared.

I appreciate it.

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