Copper pipes 1/2″ from wall. If I spray foam but leave a 4″ gap where the pipes are, will heat loss be negligible or concentrated?

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I imagine heat loss along this strip will be much higher per square inch than if the whole wall was bare.  I’m not saying the wall would be better with no insulation.  I’m wondering if the logic “oh it’s just a thin strip so no worries” would be wrong because the heat will flow faster thru the strip than a generic 4″ high wall space, because the heat won’t be able to flow anywhere else.  If the flow is faster, might it be significant enough to justify spending \$250 (?) to move the pipe / replace it with PEX?

(20 foot wall.  I’m not expecting anyone to do math for me, I’m just giving a sense of the size of gap.)

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Replies

1. | | #1

"heat loss along this strip will be much higher per square inch than if the whole wall was bare"

No. In terms of heat flow, the uninsulated portion of the wall doesn't 'care' what the R value of the other portion of the wall is, unless insulating somehow significantly changed the temperature differential in the room, but that's no longer apples to apples. The equation for heat transfer for a given area is:

q = A · ΔT / R

That uninsulated rectangle has a constant area A, a constant R value, and no real change in temperature differential (ΔT) upon insulating other sections of the wall (most likely), thus heat flow, q, is the same.

You are right in thinking that having that uninsulated rectangle will cause disproportionate heat loss though since it is a thermal bridge.

The R in the above equation can be replaced with it's reciprocal, the U value, and look like this:
q = A · ΔT · U

To calculate the average U value of your wall assembly we use:
Uaverage = (A1 · U1) + (A2 · U2)

Where A is the decimal percent of the given wall area:
A1= insulated area = 0.9 U1= 0.06 (about R 17)
A2= uninsulated area = 0.1 U2=0.5 (R 2)

U=(0.9 · 0.06) + (0.1 · 0.5)= 0.054+0.05=0.104
R = 1/U = 1/0.104 = 9.6

You can see that the 10 percent of wall at R 2 allows close to the same heat loss as the entire other 90 percent of R 17 wall.

Whether this 'matters' is harder to say without more detail and number crunching. A photo or description of where this pipe is located would help. Is it a horizontal pipe in a basement by any chance? If so, how high on the wall? I assume covering it is out due to concerns about freezing?

1. | | #3

Thank you maine_tyler!

Seeing that the heat differential is the same - assuming the temperature in the room will be the same with or without the gap - helped.

The wall height is 6'8" = 80", so 4" = 5%, so
U=(0.95 · 0.06) + (0.05 · 0.5)= 0.057+0.025=0.104
so the heat loss from the gap is not as much as from the rest of the wall, but it certainly is disproportionate.
Actually, since it is indeed a basement wall with horizontal pipes high on the wall, the temperature differential at the top will be higher than the bottom, which is below grade, so the proportion of loss thru the gap vs the rest of the wall will be higher than I just calculated.

There might be some finicky way to reduce the size of the gap, but the PEX sounds worthwhile.

Yes, the gap in insulation would be intended to prevent the pipes from freezing. The copper might move a 1/2", but even that might put too much strain. I'd run the PEX farther away from the wall.

2. Expert Member
| | #2

If you don't want to insulate over the pipes out of concern that they'd freeze, the thing to do is insulate behind them but not in front. The gap in front only has to be as wide as the pipe. With spray foam you can make a shield out of cardboard.

1. | | #5

cardboard - I think that's within my skill set!
Thanks!

1. Expert Member
| | #6

If you're worried you can't get spray foam to fill behind the pipe you could put a 1/2" piece of foam insulation behind the pipe. You could even use that instead of the cardboard for the shield.

3. Expert Member
| | #4

The easiest way to think about this is to remember that heat isn't like water, and has no concept of "pressure". Water will spray out of any little hole or gap it can find, because it can't go anywhere else. Heat doesn't work that way: heat radiates evenly (keeping things simple here) in all directions, similar to how light leaves a light bulb. If you block the light on one side of the light bulb, that doesn't make more light come out the opposite side. You still get the same amount of light out of the opposite side.

The standard way to deal with this is to insulate behind the pipes as DC mentioned. I would add to wrap the pipes with some masking paper, AND make a cardboard barrier. If you don't mask off the pipes, you'll get some overspray on them, which won't hurt anything, but will look crappy.

In terms of heat loss, you'll lose more in the thin spot relative to the rest of the insulated wall, but no more in absolute terms than any part of the wall would lose if insulated to the same lower R value. The extra insulation in the other areas does not make any more heat want to go out through the thin spot, in the same way that your hand on the light bulb doesn't make more light come out the opposite side of the bulb.

Bill

1. | | #7

I think a water analogy can actually work pretty well if set-up right. The key in my opinion is to avoid flowing analogies like rivers and to think of vessels with level waters. Here it is:

Picture the building envelope as a closed vessel surrounded by a level sea. The water is representative of heat energy. There is water inside the vessel and water outside (the sea) and they have a relative height to one another (delta T). The ability of the vessel walls to pass water (heat) is analogous to R value.

So what we have on a winter day, for example, is a given sea level (outdoor temperature) and a higher inside water level (interior temp). Flow will be from the higher head pressure water inside to out.

But why is the water higher? Because we are pumping water into the vessel to replace what is lost through the vessel walls to the sea below. Typically, we pump water to a given height, meaning the pumping in rate matches the rate of loss.

If we were to increase the water-tightness of the vessel in all but one little area, but we kept our pump-in rate the same as before, the inside water level would rise, i.e. the delta T or 'pressure' would increase. Thus the rate flowing through that little area that wasn't tightened would indeed increase. I think this is why some people have an intuition like the OP's that heat flow will increase in that area. But it assumes a constant pumping rate, when in reality we will reduce our pumping rate to match the reduced water loss in order to maintain a set water level (delta T).

In this analogy we can picture 'tides' of the sea to be like diurnal temperature swings, and then there are of course larger seasonal tides which change whether the water level inside the house is lower or higher than the sea (heating vs cooling).

It's also a nice analogy to visualize that when we better insulate the vessel, we need less pumping action (heat input) to maintain the given water level (inside temperature).

1. Expert Member
| | #8

I can see what you're saying, but I think it's overly complex for a simple analogy. I like water analogies to explain electrical terms like volts/amps/watts (and just did that in a recent thread), where it helps to visualize what's going on. In the case of heat, it's too easy to start thinking about a pressure vessel, where any little hole will result in a sprayed stream, but a big hole is a large volume at a relative trickle of flow rate. That's where people get that "if I plug this up here, it will shoot out over there" idea, and heat doesn't do that.

With your analogy, you have to deal with water levels, so it's more involved. I could see tha analogy with damming a river, where if you assume to build the dam as a series of panels, each panel reduces the flow more, but causes the level of the reservoir to rise. The remaining flow doesn't change as much as you'd think, but you have the complex interaction that the rising water in the reservoir increases the water pressure against the dam, which increases the flow rate through the remaining open areas that have not yet had dam panels inserted. That "increased flow rate due to increased pressure" is not an issue with heat transfer though, so the analogy isn't entirely accurate and can easily mislead people as a result.

Bill

4. | | #9

"but I think it's overly complex"

To each his own, for sure! In my head it is not at all complex, explains the situation nearly perfectly, and is quite elegant. But my description of it certainly lacks eloquence.

"if I plug this up here, it will shoot out over there" idea, and heat doesn't do that."

But with a constant supply, it does and thats what this shows. If using a constant supply, the 'pressure' (delta T) does increase and therfore you will see more flow elsewhere. Your light bulb analogy actually falls short in my opinion because what would happen in terms of heat is that it would build up behind the object blocking it, then more would flow around it than if it weren't there-- assuming a constant wattage bulb.

Changing my analogy to a river is adding tons of complexity and missing the point. I contend my analogy is rather spot on and yours are not, but as stated earlier, to each his own. I guess I'm unclear your aversion to describing heat as having a sort of pressure. What do you call delta T?

1. Expert Member
| | #10

The usual situation is that the indoor temperature is maintained at some constant value, maybe 70*F or so. In such a situation, all areas of an equally well insulated wall lose the same amount of heat (we're assuming a constant outdoor temperature too). If you put extra insulation in one part of the wall, that area loses less heat, but the amount of heat lost everywhere else does not change. The reverse is true for a minimally insulated wall section, which will lose more heat, but will not reduce the amount of heat lost on other areas of the wall. Heat does not "build up" anywhere, because there is no pressure.

I can kinda see what you're trying to say, but I think you're thinking a constant input energy amount, some fixed number of BTUs, rather than a constant temperature. With a constant amount of input BTUs, if you are above the losses of the structure, the temperature will continue to rise inside. All the same things hold true in terms of what insulation does, but now you are varying the rate of rise of the indoor temperature too. That's not the case usually asked about on GBA though.

Some of this probably just comes down to stuff I like to say when doing STEM outreach for kids: "people understand things in different ways, so what makes sense to one person might not make sense for another. You always need to find someone who can explain things in a way that works for you."

Bill

1. | | #11

"so what makes sense to one person might not make sense for another."

Yes indeed. Multiple perspectives is key.
I guess I didn't explain myself well. I attempted to qualify several times that pressure builds only if a constant power supply. I thought my original reply to the OP and my analogy with the pump rate all made that clear. If we maintain a set temp (reduce pump-in rate), then the pressure is unchanged and thus there is no change of flow across a given area. The only purpose of exploring this phenomenon further than that is to better understand the system dynamics.

2. | | #14

Alright, I don't want to beat a dead horse, or twist the knife so to speak, but I think I found the point to focus on in this analogy debate. Bill, you say,

"In the case of heat, it's too easy to start thinking about a pressure vessel, where any little hole will result in a sprayed stream, but a big hole is a large volume at a relative trickle of flow rate. That's where people get that "if I plug this up here, it will shoot out over there" idea, and heat doesn't do that."

Ok but you are wrong here. Your problem is that you are applying constant power sources in one case, but not the other. So it's inconsistent. My analogy recognizes that they both behave differently depending on maintaining a constant pressure vs maintaining a constant flow.

When you say water (but not heat) will 'shoot out over there' as a result of a plug, you must be thinking of something like a hose, where if you cover part of the hose end with your thumb, water will indeed 'shoot out' faster from the remaining opening. But the *pressure of the hose is increased* when you partially block the opening because a pump does not supply a constant pressure but rather flow (in simplified terms).

And heat will, as I've stated several times over now, do the same thing if there is a constant flow rather than a constant pressure. But you are right that we don't typically supply our houses with constant flow but rather maintain a constant pressure (temp). (Of course the pressure differential changes as outdoor temps change.) And so these realities are equally true for water/pressure analogies as for heat: we just need to define whether we are talking about a constant pressure or constant flow system. In my water vessel analogy, I make it clear it is a constant pressure system as a result of regulating the flow of the pump to match the vessel losses.

5. | | #12

First, pretty sure I'd move the pipes
Second, as mentioned, slide insulation behind it.

Third, IME most pipe freezing is due to air leaks.
In my house, the pipes to the bathroom sink ran through a poorly insulated outside wall, and in 40 years never burst, but they froze regularly. Since they poked into the room at the corner, I moved the entire inside wall in 1 1/2 inches and spray foamed the lot. There is certainly more foam to the outside of the pipes than to the inside.

6. Expert Member
| | #13

My favorite water/heat/insulation metaphor:
Insulating and air sealing part of a building is like waterproofing part of the hull of a boat.

1. | | #15

That's a fun metaphor! But it seems to half-conflict with Tyler's 1st post and with Bill's 1st post. (I haven't had time to really read their follow-up discussion.)
The metaphor does not imply water will move faster thru the unwaterproofed part than it did before there was any waterproofing, but it does imply that a partial job is pointless, that the outcome will be the same with or without incomplete insulation, so the metaphor is an exaggeration, to the point of being half-wrong, right?

1. Expert Member
| | #16

Mellville2,

It depends. A relatively small low-R hole can negate most of the protective effect of the high-R assembly it is in:
https://www.energyvanguard.com/blog/Attic-Stairs-A-Mind-Blowing-Hole-in-Your-Building-Envelope

1. | | #17

Thanks Malcolm! I read Alison's "Flat or Lumpy" article years ago - and when I tried to find it last year I couldn't, so thanks! Perhaps misread it / mis-remembered it. It got me thinking that if the R-value was increased everywhere except one patch, the heat-flow thru that one patch would increase. (Not negating the overall benefit, but diminishing it.)
His "Attic Stairs..." article is also an excellent read.

2. Expert Member
| | #25

True, but in terms of absolute BTUs lost, you always win with insulation, even if you don’t insulate everything. What changes is the *relative* amount of loss, so if you insulate three or four walls and leave the fourth uninsulated, that uninsulated wall loses a whole lot more BTUs than the insulated walls, but the overall room still loses a whole lot less than it did when ALL the walls were uninsulated.

Air sealing is different: if you leave a huge hole somewhere, your other efforts are much reduced.

I think the biggest difference between Tyler’s analogy and mine are that we’re looking at things slightly differently. I’m looking more at the overall room, in absolute losses, I think he’s looking more at relative losses. I’ll mention that I don’t really take issue with his analogy, I think it’s just from a different viewpoint. It’s good to have discussions like this, because everyone gets to learn more stuff.

BTW, we have hawks and snapping turtles here. I have watched the pair of swans on my lake start with either four or five cygnets and they currently are down to just two, which is sad, but that’s nature — nature is brutal. My cat stays indoors, and gets to watch (and dream about) the outdoors through the windows. He got rained on once and trapped in the garage once and no longer has any interest in trying to sneak outdoors.

Bill

1. Expert Member
| | #26

A female duck typically has ten ducklings a year. They start reproducing at one year of age and can live 25 years or more. Imagine what the world would look like if they didn't have high mortality.

2. Expert Member
| | #27

Bill,

"It’s good to have discussions like this, because everyone gets to learn more stuff."

3. | | #28

"I’m looking more at the overall room, in absolute losses, I think he’s looking more at relative losses."

I'm fine to let this lie if desired, but I'm not sure what you mean here. Everything I have said applies to the entire system, i.e. the entire vessel and the heat exchange with its environment.

At this point I'm also not sure if there is a specific analogy or statement of yours that we are comparing this with? The light bulb analogy? I've explained why I think that is inaccurate (and it had nothing to do with relative vs absolute).

It looks to me like we do agree on the fundamental system dynamics. My honest assesment is that my analogy and points were simply not carefully read nor properly understood, but that's half my fault for providing a clunky, overly wordy response, as per usual! :)

2. | | #18

"but it does imply that a partial job is pointless, that the outcome will be the same with or without incomplete insulation, so the metaphor is an exaggeration,"

I think it is a 'point making' metaphor rather than one attempting to be as accurate to reality as possible.

In a house, a pump is needed to maintain the delta T. In the boat analogy, what we really have going on is a slow enough leak that the ship can stay afloat due to a bilge pump ridding the hull of water.

The following two statements can both simultaneously be true:

1) Assuming temperature differential is kept constant between compared situations: adding insulation to one part of a wall has NO EFFECT on the heat loss in other parts of the wall. Again, for a given area, A:
q = A · ΔT · U

Where in that equation is the variable for the U value (or any other value) of the other wall areas? Nowhere.

So there is no increased flow in the uninsulated area from insulating the other parts of the wall.

2) Insulating most of a wall, but leaving a significant thermal bridge (such as the attic hatch example) has an outsized effect on heat loss, which can be seen as 'undermining' the surrounding insulating efforts. This doesn't mean it has an effect on the heat flow of those other area, just that your efforts are undermined unless you take care of that last big thermal bridge.

Allison says this in the article Malcolm linked:
"The reason for this is that, although the attic stairs account for only 1% of the area, the rate that heat flows through them by conduction (per square foot) is 38 times higher than in the insulated part of the attic. In other words, the amount of heat that flows through the 10 sf of attic stairs is the same as what flows through 380 sf of the insulated attic. Wow!"

Consider that if you double the R value for a given area, you halve the heat loss. If you start with an uninsulated attic hatch of say, R-1, you can double that to R-2 and you've halved the heat loss. You can double it again to R-4 and you've halved it again. You can double that to R-8 and you've halved it again! So at a measly R-8 you have doubled, doubled, and doubled (2^3=8) your heat loss for that area.

To reduce the heat loss in the wall that you insulated to R-19 by a factor of 8, you would need R-152.

This is to say that with a big thermal bridge, you have a big arse hole in your boat and while there are still other leaks leaking of their own accord, you can most effectively reduce the water you are taking on by stopping the high flow leaks first.

1. Expert Member
| | #19

maine_tyler,

This discussion prompted me to seal up my cat door with a layer of foam.

1. Expert Member
| | #20

If I did that my cat would shred it by morning.

2. Expert Member
| | #21

DC,

Sadly, Theo was eaten by a cougar last fall.

3. Expert Member
| | #22

I'm sorry for your loss. It's never easy losing a pet.

4. Expert Member
| | #24

DC,

Thanks. One of the things you just have to accept if you live in their territory.

3. Expert Member
| | #23

It's true that insulating one surface is independent of other surfaces. But it's really about air sealing. My observation -- with no hard science to back it up -- is that if part of a house is leaky it doesn't matter how well sealed the rest is.

7. | | #29

To DC, #23,
I suppose if we wanted to try to quantity this, we could look at the air exchange rate and the temperature delta to calculate BTUs lost from the overall leaks. But that may not totally account for the discomfort present when you're sitting in the path of a cold air leak. The house will be full of cold spots.

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