Heat transfer in a large steel box

[BabyHuey06]

If I have a large steel box that is 27ft x 8ft x 8ft and has 7 in thick walls with 4 non-insulated windows each 1ft by 1ft, where does heat escape from inside the box, is it the windows and the walls? So if the inside temperature needs to be 72 F and the outside air is 0 F how much heat would need to be pumped in?

I figured that a lot of the heat would escape through the walls and treated it as heat transfer through conduction, but I am getting an answer of about 39 million BTU/hr and this makes zero sense.

I attached the math I did, but I think my understanding of the situation is where I went wrong. Also I did the math in MathCAD 15 so the units are corrected and handled for me automatically.

 

[jack action]

1. I'm not sure how you've got the 1728 ft² area [2 X (27 X 8 + 8 X 8 + 27 X 8) = 992 ft²];
2. You need to use the temperature difference (72°F - 0°F = 295 K - 255 K = 40 K or ΔT = 72°F / 1.8 °F/K = 40 K), not the inside temperature alone.
3. Remember that steel is about a 1000 times more conductive than air. You took one of the worst insulator you could choose.

 

[BabyHuey06]

1. I'm not sure how you've got the 1728 ft² area [2 X (27 X 8 + 8 X 8 + 27 X 8) = 992 ft²];
2. You need to use the temperature difference (72°F - 0°F = 295 K - 255 K = 40 K or ΔT = 72°F / 1.8 °F/K = 40 K), not the inside temperature alone.
3. Remember that steel is about a 1000 times more conductive than air. You took one of the worst insulator you could choose.

Oh woops, sorry I was messing around with some of the numbers and must of accidentally took a snap shot of the wrong one. Thanks for catching that, but going back with the corrected numbers I am getting about 1 x 10^5. Now you said that steel is like 1000 times more conductive, which means that 1 x 10^5 should make sense?

I am only asking because I am interning with an engineering company and this was a task I was given. I didn't want to ask for help, but I had too, and they are thinking of going with a 15-17,000, BTU/hr heater. That is much less than what I have. Would you happen to know why? I'd rather not ask them though, because I don't want to look like an idiot, given that it was a pretty easy task, but I haven't taken my heat transfer course yet and only have basic knowledge in thermodynamics.

 

[jack action]

I'm no expert on heat transfer, but it looks like you are making some sort of building. I live in Canada, so from personal experience, I know a thing or two about heating them. Here are some rules of thumbs I know (found similar one on the Internet, not sure of the source):

1) For an Old/Uninsulated home: Use 12.5 Watts per square foot of floor space
2) For a typical pre 1980 home with some insulation: Use 10 Watts per square foot of floor space
3) For a post 1980 home with decent insulation: Use 8 Watts per square foot of floor space
4) For a modern highly insulated post 2000 home: Use 6 Watts per square foot of floor space

So for an 8' X 27' (216 ft²) building, Worst case scenario is 2700 W (9200 BTU/h). Problem is, this is for a house that is insulated with «plain air» (inside and outside rows of wood boards on a wood armature, usually 4" wide). #2 is for the same house, but with insulation added within the walls (not that much difference) and #3 is usually with a 6" wide armature (and insulation) instead. Insulation in the roof is usually a lot thicker.

But you say you have 7" thick steel walls. Like I said, steel conducts 1000 times more heat than air (even compared to wood it is about 200 times more), so that would surely make a big difference in the heat needed.

But do you really have 7" thick steel walls? Building a 27'X8'X8' box would require about 2 000 000 $US of steel and weight about 1 000 000 lb (about the maximum weight of a fully loaded Boieng 747-8) . Just checkin'.

 

[BabyHuey06]

I'm no expert on heat transfer, but it looks like you are making some sort of building. I live in Canada, so from personal experience, I know a thing or two about heating them. Here are some rules of thumbs I know (found similar one on the Internet, not sure of the source):
So for an 8' X 27' (216 ft²) building, Worst case scenario is 2700 W (9200 BTU/h). Problem is, this is for a house that is insulated with «plain air» (inside and outside rows of wood boards on a wood armature, usually 4" wide). #2 is for the same house, but with insulation added within the walls (not that much difference) and #3 is usually with a 6" wide armature (and insulation) instead. Insulation in the roof is usually a lot thicker.

But you say you have 7" thick steel walls. Like I said, steel conducts 1000 times more heat than air (even compared to wood it is about 200 times more), so that would surely make a big difference in the heat needed.

But do you really have 7" thick steel walls? Building a 27'X8'X8' box would require about 2 000 000 $US of steel and weight about 1 000 000 lb (about the maximum weight of a fully loaded Boieng 747-8) . Just checkin'.

Thank you for all the information. And yes I am positive haha. The steel box is actually a 1960's refurbished caboose needed for a freight train that were putting back in service. The walls may be a tiny bit thinner as the as buit specs were pretty old and hard to read.

 

[Chestermiller]

Thank you for all the information. And yes I am positive haha. The steel box is actually a 1960's refurbished caboose needed for a freight train that were putting back in service. The walls may be a tiny bit thinner as the as buit specs were pretty old and hard to read.

You are leaving out a very important resistance to heat transfer that will limit the rate of heat transfer from the wall of the box to the surrounding air and will result in a higher outside wall temperature than the ambient 0 F. This is the heat transfer resistance in the air boundary layer surrounding the box, as characterized by the convective heat transfer coefficient. I would expect an average heat transfer coefficient on the order of 10 - 100 $\frac{BTU}{hr-ft^2-F}$. This resistance will dominate over the conduction through the wall. Try this range of values and see how it affects your predicted heat load and your predicted outside wall temperature.

Chet

 

[jack action]

I double check and I made a mistake it's 284 000 lb (it was 1 000 000 in³) for a 7" wall. But cabooses sure don't have steel walls that thick. According to this source, the cabin alone weights 38 000 lb (plus 2 axles, 11 000 lb each). Assuming the whole weight of the cabin are the walls, that gives a wall thickness of little less than 1", or 2 half-inch plate with insulation in between (maybe empty space). Assuming half the weight is somewhere else (structure, etc.) that would give 2 quarter-inch plate, which sounds more reasonable.

Anyway, doing this little research, I found the following that might be of interest to you. They restore cabooses and use furnaces that produce between 21 600 and 36 000 BTU (@ 74% efficiency) to heat them (which is slightly bigger than what your co-workers were thinking of using). That would mean you need 22-36 W/ft² which, compared to wooden insulated houses - that doesn't lose much heat from the floor - could look pretty reasonable.

For comparison, they usually use these furnaces for 1000 ft² homes (or 7.8 W/ft², to compare with my previous list).

 

[russ_watters]

The walls can't possibly be solid blocks of steel 7" thick. You need to figure out the actual structure of the walls and if they are insulated. Worst case, they might be plate steel inside and out, with steel tube framing between the plates.

 

[BabyHuey06]

The walls can't possibly be solid blocks of steel 7" thick. You need to figure out the actual structure of the walls and if they are insulated. Worst case, they might be plate steel inside and out, with steel tube framing between the plates.

Your correct, looking closer at the spec sheet it turns out that the full dimension was cutoff and what was left looks like a 7, whether it is hollowed steel or not. I really do not know, I'd have to figure that one out.

I double check and I made a mistake it's 284 000 lb (it was 1 000 000 in³) for a 7" wall. But cabooses sure don't have steel walls that thick. According to this source, the cabin alone weights 38 000 lb (plus 2 axles, 11 000 lb each). Assuming the whole weight of the cabin are the walls, that gives a wall thickness of little less than 1", or 2 half-inch plate with insulation in between (maybe empty space). Assuming half the weight is somewhere else (structure, etc.) that would give 2 quarter-inch plate, which sounds more reasonable.

Anyway, doing this little research, I found the following that might be of interest to you. They restore cabooses and use furnaces that produce between 21 600 and 36 000 BTU (@ 74% efficiency) to heat them (which is slightly bigger than what your co-workers were thinking of using). That would mean you need 22-36 W/ft² which, compared to wooden insulated houses - that doesn't lose much heat from the floor - could look pretty reasonable.

For comparison, they usually use these furnaces for 1000 ft² homes (or 7.8 W/ft², to compare with my previous list).

Thanks again for the great info. I actually borrowed one of my friends old thermo books and that had quite a few useful examples. Following those examples, and messing around with the wall thicknesses, I'm getting answers between 2400 BTU/hr and 100,000 BTU/hr. Just need to figure out the caboose walls to get an exact answer

You are leaving out a very important resistance to heat transfer that will limit the rate of heat transfer from the wall of the box to the surrounding air and will result in a higher outside wall temperature than the ambient 0 F. This is the heat transfer resistance in the air boundary layer surrounding the box, as characterized by the convective heat transfer coefficient. I would expect an average heat transfer coefficient on the order of 10 - 100 $\frac{BTU}{hr-ft^2-F}$. This resistance will dominate over the conduction through the wall. Try this range of values and see how it affects your predicted heat load and your predicted outside wall temperature.

Chet

Like I said I used my friends old thermo book and I can see what your saying about how the heat transfer to the surrounding air is a very big limiting factor. Messing around with different wall thickness and whether they were hollowed or not. I noticed that 1 inch of air inside the wall vs 0 inches or air HUGELY reduces the amount of heat loss

 

[Nidum]

Large steel structures store heat - it might take significant time to actually change the wall temperature very much .

Consider fitting insulation . Many old steel cars were wood lined anyway - alternatively there is now a huge range of modern insulating materials available .

Large steel box closed structures can suffer badly from condensation - you need controlled ventilation and heat sources which do not introduce water vapour to control this problem .