Temperature Change - Insulated Metal Panels 3

[xez]

Hi Everyone,

Haven't touched anything with heat transfer in over 10 years and I don't think I'm doing this correctly. I'd appreciate it if someone take a look and guide me in the right direction. Not sure whether this is the correct forum or the HVAC/R. Thanks in advance.

We're installing about 5,000 sq ft insulated metal panels on the roof and walls of a building. We will assume a 5,500 cu ft volume. The interior will be a constant 35ºF, exterior assume 100ºF to give us mean 65. R-value of the insulated panels is 47. What will the interior temperature change be in 6 hours of the 35ºF is left unconditioned?

This is what I came up with...

R-47 * 5,000 sq ft = 235,000 BTU/hr through the panels

If 0.018 BTU/HR raises 1 cu ft air 1ºF/hr, then 0.018 BTU/hr raises 5,500 cu ft air (1/5,500)ºF/hr

1 BTU/hr * 5,500 cu ft = (55/5,500)ºF/hr = 0.01ºF/hr

235,000 BTU/hr * 5,500 cuft = (235,000 * 0.01) = 2,350ºF/hr

This seems like a really, really high temperature change. Help please? Thank you!

 

[xez]

Looking back at my numbers, I've made a mistaking in my BTU/hr conversion.

The heat transfer is 6,915 BTU/hr through the insulated panles which in turn will give us 69ºF/hr. Looks more reasonable but it still seems pretty high. Any thoughts? Thanks.

 

[DRWeig]

Hi bcng,

I see you have posted the same question in more than one forum. Please do not do that. The forum policies may be read from the link below my signature. They should all be of interest to you, especially #4.

Please red-flag one of your two posts, or else post a link from one thread to the other so that two threads do not get started. Thanks!

Best to you,

Goober Dave

Haven't see the forum policies? Do so now: Forum Policies

 

[ko99]

Your heat transfer estimate is too high because it assumes delta T is fixed at 65F. It's only 65F initialy then it decreases. You need to estimate a thermal time constant, Tau = mass x Cp / h x Area

Cp = specific heat
h = convective heat transfer coefficient



ko (

http://www.msthermal.com)

 

[MintJulep]

6915 BTU/hr / 5500 ft^3 = 1.25 BTU/(hr ft^3)

.018 BTU/(ft^3 F) / 1.25 BTU/(hr ft^3) = .014 F/hr

 

[xez]

DRWeig: Apologies. I've red flagged my other post.

ko99: Not too familiar with heat transfer. How would I use the thermal time constant in respect to the 6,915 btu/hr?

MintJulep: I believe that would be 0.014 hr/F and 69 F/hr. I've never worked with this type of application before. Is this a normal temperature change?

Thanks everyone.

 

[ko99]

bcng,

6915 btu/hr is the heat flow rate used to estimate the heat transfer coeff: h = heat flow rate/(deltaT x area)

FYI, the concept of a time constant is not limited to heat transfer. The most common example is an R-C circuit.

ko (

http://www.msthermal.com)

 

[Compositepro]

In any freezer or refrigerator the air should be a very small part of the mass that is cold. That is why refrigerators still work even when the door is opened regularly.

 

[xez]

So, heat transfer coefficient = k-factor = 0.0213 btu/(F hr ft^2)

Is the mass I'm supposed to use to calculate the time constant, the mass in the cooler or the mass of the insulation?

Currently, I've calculated using mass of insulation 2.15 pcf density * 6in thick panel * 5,000 sq ft of panel. Cp is approximately 0.346 btu/(lb Fº) for PIR/PUR foams.

This gives me Tau = 17.46 hr? What am I supposed to the time constant now? Better yet, I'm not exactly sure what the time constant is telling me...

 

[ko99]

It's the total mass at the initial temperature (35F). The air mass is probably negligible as was already noted, but the mass of the entire building and it's contents should be estimated since it contributes to slowing the temperature rise.

The temperature rise of the building vs time is an exponential curve, starting at 35F at t=0 and essentially reaching steady state at 5 time constants. From this curve, you can estimate the building temperature rise ant any time:
At tau = 1, the mass will be 63% of the way to 100F
At tau = 3, the mass will be 95% of the way to 100F
At tau = 5, the mass will be 99.99% of the way to 100F

For example, IF tau is 24 hours, 6 hours is 0.25 time constants. I'll leave it to you to work out the mass temp rise at tau = 0.25

ko (

http://www.msthermal.com)

 

[IRstuff]

Your error comes from considering only the conduction of the panels. The mode of heat transfer from the panel to the room is through convection. Likewise, the heat transfer from the ambient air to the panel is also through convection. If you want to get fancy, you'd also assume that the heated air within the building will rise to the ceiling, thereby reducing the heat transfer there. You did not mention solar load, nor radiation, which all affect the heat transfer.

TTFN
faq731-376

 

[ko99]

IRstuff is correct. The thermal resistance should include the full path. I'm embarrased to have missed this. My comments on the transient calculations still apply.

Note that if there's significant solar heating it will dominate the heat flow.

ko (

http://www.msthermal.com)