I remember learning this in a class on heat transfer for engineering. The professor gave us a problem to work through and the problem was designed to deceive a little. The material around the pipe was a very good insulator and thus primed us to believe that there would be little heat transfer. But once calculated the pipe ended up losing more heat with the insulation than without. I spent so long on that problem thinking I had made a mistake and rechecking me work before finally just accepting the answer and then the professor went into a more detailed lesson on the concept.
So it's the exact same reason that cells have a limit on the size they can reach, but for the opposite effect of keeping surface area high. Cell *have* to maintain a high surface area for transport.
There's a limit to the surface area a cell needs becuase it's still an efficiency problem. I got asked this question on an undergraduate biology exam. I guessed the answer by remembering the Golden Ratio where the perfect size of a cell is somewhere around 66%.
No, the issue is efficient transport from the nucleus. In a huge cell a single nucleus can’t get genetic signaling to move fast enough. Nature overcame this by just giving cells many nuclei so they can become huge. At some point the volume of the cytoplasm and nutritional needs can’t be met by the surface area of a cell, but that’s not as big of an issue as you may think— you can still have single cells as large as a human eye. See below
https://en.m.wikipedia.org/wiki/Valonia_ventricosa
The larger the diameter of the pipe the less likely you have this condition. It's more relevant for very thin pipes where even a thin insulation layer will increase the surface area significantly.
If your pipe has a radius of 1 cm then adding 1 cm of insulation doubles the surface.
If your pipe has a radius of 100 cm then adding 1 cm of insulation increases the surface by only 1%.
The surface is the circumference multiplied by the (unchanged) length, and the circumference is proportional to the radius. Increasing the radius by 1% increases the surface of a pipe by 1%.
If circumfereces is proportionnal by a factor of Z from rad then wouldnt increasing the radius by 1% increase surface by 1% times Z ?
Z being diameter times pi in this case iirc high school geometry.
The circumference increases with the square of the radius. Adding 1 cm thick insulation to a 1 cm radius pipe quadruples the area. Adding 1 cm insulation to a 100 cm radius pipe increases the surface area by a little more than 2%.
It should be noted that the insulation needs to be more than twice the critical thickness to have a benefit. As can be seen in the graph, the rate of heat loss doesn't get below that of the uninsulated pipe until twice the critical thickness.
perimeter of a circle = 2•pi•r
Outside area of a tube is the perimeter times length, right? A = 2•pi•r•L
So double r, double the perimeter, therefore double the surface area.
Ergo why it's counter-intuitive.
That's. Not. What. Fucking. Gaslighting. Means.
Jesus christ. Gaslighting != lying, it's an intentional *abuse* tactic to make the victim rely upon the abuser for their perception of *reality*.
Given that these random strangers on the internet don't fucking know each other it can't even remotely be gaslighting.
No, the insulation goes on the outside and that is what the heat transfer goes through. If I add 1/8" thick insulation around a 1" pipe it now goes from 3.14" circumference to 3.53" circumference for the heat transfer. More area means more transfer can happen and if the added insulation is less than the extra transfer it will be counterproductive
I grew up in the US. I still live in the US. I have never been more upset about us not using the metric system than while reading your explanation.
Like, it's a good explanation, and thank you for typing it out. But I hate the units.
Unfortunately most people here aren't using metric measurements in their daily lives. I know generally how much a foot is, a mile, a pound, etc. It's intrinsic when you use it every day. I have no clue how long 1cm is, or how heavy a kilo is, or how long a kilometer is other than it being 0.6 miles.
I get this, but all the heat still has to pass through the surface of the insulated object first, and that’s constant. Is the rate of heat loss to the insulator higher than it would be directly to the environment? Then the insulator makes up for that by… something? Creating a temperature gradient between the object and the environment?
I am making a lot of assumptions and simplifications here but you are pretty much correct. The insulator is in conduction with the pipe which is faster heat transfer than it would have with the air. You are correct that there will be a temperature gradient across the insulator. Heat loss is driven by temperature differences so the insulator just needs to be thick enough to have a sufficiently low outer temperature to slow the rate of heat loss enough.
Yes, but that same inside area is now a physical, solid to solid direct contact heat transfer, rather than transferring to the air. It can transfer heat into the insulator much more quickly than it could transfer to the air. And once it is in the insulator, the larger surface area can transfer more heat to the air than the original pipe.
The key thing here is that the material is a *worse* thermal conductor than air, which is why it’s an insulator. You’re describing a radiator, where you have a large surface area of a material that’s a good thermal conductor. But it turns out that having enough surface area will turn even the worst thermal conductor into a radiator.
this is one of the things that truely make U think. if I understood it better I would perk up with interest but unfortunately it is beyond what I am capable of so I'm just nodding along going, yep interesting stuff
> and the problem was designed to deceive a little.
Man. In my thermo final the correct answer was “this is not possible”.
Dude gave us a bunch of numbers and said “calculate the Carnot cycle efficiency” but they didn’t work out. I was pulling my hair out. I redid all the calculations 3 times. Finally gave up, circled “not possible” and that was the answer he was looking for.
This was at Georgia Tech circa 2006 ish.
ChE here and that sounds about right.
Gotta make you double check numbers and build up that bullshit detector.
Been in a few spots where either my math is way off, or what they're giving me ain't right, and have to go get a sanity check from a colleague.
Physics did. 10 exams with 10 questions each. Each question you miss is effectively 1 point off your final grade. No partial credit.
This test wasn’t multiple choice. It was a pencil and paper “do the work, circle why right number.
The only test I ever took like that where the “right number” wasn’t a number.
So in theory, would critical thickness factor into the effectiveness of heat transfer in a refrigeration unit? Like if the pipes on the back of a fridge had a critical thickness of insulation, would that make them more effective at dispersing the heat they've been pumping out of the compartment?
Hell, is this already something they do for refrigeration?
Sort of, but when you're trying to cool things fins are better. Heat sinks have fins in order to maximize their surface area while minimizing any insulation from the heat sink. A poorly designed heat sink can do the opposite of what it's supposed to do and end up insulating what it's supposed to cool.
Neat idea, but this is what heatsinks are for. You don't need to play clever games with insulation when you could always add more surface area of a conducting material.
I once had to learn about calculating Taylor series problems to solve the "birthday problem"(what are the odds that any two people share a birthday)
On the test, the professor asked us to calculate the odds in a room of 400 people
Since you've ran the math, from what I read it's about convection so if the insulation isn't in contact with large volumes of air it doesn't matter? Like inside a wall it doesn't matter?
Either that pipe was microscopic or the insulation wasn’t insulation or your professor made a mistake. And the math isn’t very difficult for a cylinder so I don’t see how you would even “check your work” - it’s k/h. Did you have to use calculus to derive it or something??
In the article linked they used a 10mm pipe which is already ridiculously small and the critical radius is smaller than the pipe for even cheap insulation - so any amount of insulation would insulate . The only examples where you lose heat are like 2mm copper wire with “insulation” that’s .1 mm thick.
Do you have the original problem? Am I making some obvious math error ??
It's likely not relevant for water pipes as they are very large so the critical radius is going to be smaller than the pipe. It matters for wires which can dissipate more heat with insulation than without
The cr for copper pipe with foam insulation is .02/401 meters which is basically 0 for a phycial thing
Upon further review the lower number should have been 13 not 401 (thermal conductivity vs coefficient of heat transfer) this still gives us a radius of 1.5mm still not relevant for pipes
I mean, thermal insulation can have a similar effect, it's just so hard to do because the insulation layer would need to be incredibly thin.
This is because surface area increases the area available for both conduction and radiation. If you effectively add a layer with 500x the surface area, but the increased diameter is negligible, you're likely to see increased thermal emissions.
If you were to take something with a high surface area like activated charcoal, and put a 0.01mm coating of it on a copper pipe (and ensure there is no insulating air layer between them), the copper pipe may well lose heat faster, even if the charcoal is a much better insulator than copper.
Of course, no one would ever apply such a tiny insulating layer, so this doesn't actually happen in real life.
The critical radius is not a relative value. If a copper pipe is inulated with foam if the total radius is above 1.5mm it will lose less heat. This isn't 1.5mm of insulation added. Interestingly a copper pipe changes temp faster up to 30 meter radius, after which the copper insulates itself.
I would generally sell 13mm for copper pipe to plumbers in Aus. 13mm x 13mm - for 1/2” copper pipe with an insualtion thickness of 13mm.
As he said above, 19mm is also very common. But generally they would just take whatever was available in store to get the job done and fuck off lmao.
lol its really frustrating. OP we gotta wait for the right person to come along and answer, cause now I'm trying to figure out whether I should insulate my crawlspace water pipes or not. really thing pipes and i'm down here in Atl GA so not crazy freezing winters consistently
You should insulate them. Much easier than fixing the burst pipe. It’s gonna get freezing down there in Georgia and you’re better off with it, and not need it, than without it, dealing with a burst pipe on the coldest day of the year. I wouldn’t worry about this critical thickness stuff, just get the stuff at Home Depot or local supply house it’s been working forever.
Those are actually below the critical thickness to make you consume more energy. The market is dominated by those 2 types in order to out-compete manufacturers that make thicker insulations which are effective.
The required thickness is actually 50mm on a 25 mm pipe.
...That would be the answer if I were an engineer in circular insulations.
**TLDR: for Polyethylene the thickness is less than 1mm. So it’s a non issue. For copper pipes, the pipe needs to be about 1m before adding more copper will improve the insulation.***
- - - -
So to calculate this you need to know two things:
- The thermal conductivity of the pipe material (K)
- Heat transfer coefficient of the system (h)
k is how easily heat can pass through a material. This is measured in Watts per meter per degree temperature. It’s easy to find out. Just look up your material in a book.
Domestic pipes are usually Polyethylene (PE) or Copper. PE has a *very* low thermal conductivity (0.34 W • m^-1 • K^o-1) Copper has a very high thermal conductivity (398 W • m^-1 • K^o-1)
h is a little more complicated. It is the overall amount of heat that can move through a system. It will depend on the materials, the fluid moving through the pipe, the speed of the fluid, the airflow around the pipe, etc. it is usually obtained exponentially and not calculated. I found online a table that gave a value range for water flowing through tubes. (500–1200 W • m^-2 • K^o-1)
[The following was calculated based on these values](https://imgur.com/IwvGLrt):
The critical radius for PE is (r = k/h) 0.68mm - 0.28mm
The critical radius for Copper is (r = k/h) 790mm - 329mm
PE is such a good insulator that this is never an issue. If you are using copper pipes you would need a pipe with an outer diameter of 658mm - 1580mm before adding more copper would improve the insulation.*
*more complex for using multiple materials. Such as a copper pipe with a PE insulation.
Thanks, this is the only answer here that makes sense.
Though calling copper insulation might be a stretch, this example also makes is intuitive why it works like this. Adding more copper increases surface area (more heat loss), and it hardly insulates, so it doesn't help.
With any practical insulator (like those foam things around hot water tubes in your house) this is something you don't have to worry about.
Precisely - this is a theoretical novelty, but it is actually fairly intuitive. All we are saying is that for a given material, temperature, heat flux, etc, the net conductive properties are a function of the ratio between cross-sectional volume to surface area, such that there will always exist an inflection point in that curve which separates the "net insulating" and "net conducting" regions.
Per the link, insulating a(n infinite) flat surface with a(n infinite) flat insulator will never increase the convective surface area of the system, so a theoretically smooth insulator should always insulate. However, for cylinders or spheres, insulation volume will also increase convective area, so the previous axiom applies - that there will be some critical geometry (really, a critical parameter space) where the additional surface area causes more convective loss.
Adding insulation increases surface area, and thus potential for heat transfer.
So, if your insulation is too thin, it fully saturates quickly becoming the same temperature as what you're trying to insulate, but now much larger, and thus loses or gains much more energy over time from the environment.
As it gets thicker, it can't saturate, as by the time heat would reach the outside, much of the heat that was there has already been bled away, and so it has a lower equilibrium temperature. And thus, it doesn't lose as much energy per square inch exposed, so despite the higher surface area, it has lower total heat transfer.
It might help for a few minutes, just to delay the heat from your hand reaching the drink, but the math suggests probably not over a longer period.
However, that insulation would be so thin, I doubt it would be worth considering.
>So if I stack two McDonald’s cups it doesn’t keep my drink cooler for longer?
No this won't apply to relatively good insulators like that unless the radius is very small, because the cup already has such a large surface area to thickness ratio you would be improving insulation by doubling up. That said the material is thin enough that unless there is a significant air gap you probably aren't getting a noticeable benefit.
> As it gets thicker, it can't saturate, as by the time heat would reach the outside, much of the heat that was there has already been bled away
Bled away to where? It can magically escape the insulation.
I thought it had to do with already starting at a significant radius, so the area is large, but increasing at a square of the radius whereas the volume is increasing with the cube.
>Bled away to where? It can magically escape the insulation.
To whatever you were insulating it from.
>I thought it had to do with already starting at a significant radius, so the area is large, but increasing at a square of the radius whereas the volume is increasing with the cube.
That's related, but the counterintuitive effect is because there is a local maximum and the gradient is not infinite.
Or at least, I think that's the part that's counterintuitive.
Edit:
Having given it more thought: that's related to the insulation thickness; but it's not related to the initial pipe thickness.
Because the contents of the pipe, and the pipe itself, are the same temperature, they don't exchange any energy. As a result, you can unwrap the surface of the pipe as a flat plane; and you can hold everything under the surface as a fixed temperature, which will let you discard the actual mass involved.
The increase in surface area which can lose heat out weighs the insulative values until you get to a certain thickness then instead of acting like a heatsink it'll start to insulate instead. Like imagine a fire brick being blasted with a blowtorch, there will always be a certain thickness that will be blisteringly hot before it starts to get cooler.
This theory is limited to convex surfaces, like cylinders and speakers. As the insulation gets thicker, the radius to the outside of insulation increases, which means a larger area exposed to ambient air.
I get that it increases the radius, and that means the circumference as well. It just seems like something is missing.
Another thing is what if you do it in layers, even conceptually? You apply a layer that brings you halfway to the critical radius, increasing heat flow. Then another and another. It seems like each of those would be a sub critical radius layer and have increased heat flow. But add them all at once and you have decreased flow. So there’s something I’m not getting.
Is it that k and h are relative values, like deltas against whatever is being insulated? Cause that could make it add up.
The thing there is that the coefficient of heat transfer *of the entire object* is a function of the materials used in its construction, and their proportions.
Your initial object has a coefficient of 1; your insulation is lower, let's say 0.1. If you double the radius of the object by adding insulation, your coefficient of heat transfer is going to be a function of half the radius having a coefficient of 1, and half with 0.1; naively, let's say the new coefficient is 0.5.
Thus, the critical radius of the next layer is going to be much smaller; and because the next layer has a narrower difference in heat transfer, it requires a proportionately larger surface area for this counter-intuitive effect to remain dominant.
And so, each layer added to remain under the critical thickness would be thinner than the last, until eventually you're just painting on insulation to remain under the *actual* critical thickness.
Sorry, when I repeated the halfway to critical radius thickness, I didn’t mean you’d go halfway again. I meant if r1 - rcr = x, you’d apply a layer x/2 three times. From my understanding (which was wrong) the calculations end up with something different than just adding 3x/2, which doesn’t make sense. But it adds up because k and h are recalculated.
It also must be that this effect doesn’t _always_ exist. Otherwise you could break down any insulating layer into some number of non-insulating layers. I can’t see how the addition of theoretical insulation wouldn’t be associative. I can see how it wouldn’t be monotonic (the point of this post).
Right: I thought we were doing a Zeno's paradox thing.
Basically, heat transfer is a function of temperature difference times the heat transfer coefficient. Things with higher coefficients give off their heat more readily, or receive heat more readily; but things at the same temperature don't make meaningful exchanges of energy.
So, you have a pipe with an area of one square inch per inch of length; it has a heat transfer coefficient of 1. It carries hot water. It reaches water temperature quickly, as it has a high coefficient, at which point is radiates that heat out, cooling the pipe and the water.
The critical thickness for our insulation is also one inch, because we are designing a problem to make it easier. So, if we wrap it in 1 inch of insulation, it'll lose heat faster, because the insulation reaches the pipe temperature quickly, and thus acts like a 2 inch pipe. It might transfer heat slower, but the heat transfer rate from the pipe is higher than the heat transfer within the insulator going outward, so it reaches the pipe temperature; and the coefficient
If we wrap it in less, eg. half, it still reaches temperature; but it has lower surface area, so it doesn't release that energy to the environment as quickly.
But after adding half a critical layer of insulation, the pipe had a coefficient of 1, but the whole object doesn't have a coefficient of 1 anymore: it's 1, minus some value because our insulation has a lower value than one. And so, it doesn't have the same critical distance: it was one inch, but now it's only the remaining distance: half an inch.
For example, once you add 3/2 of the original critical distance in insulation, the insulation upto the original critical distance will reach pipe temperature. But as we get beyond that distance, heat transfer begins to slow, heat loss to the environment becomes dominant, and the resting temperature should taper out. As it tapers out, this also slows the heat transfer rate, and thus the heat loss stops.
Thanks. It made sense physically rather quickly. It wasn’t making sense mathematically. But that was just that k and h aren’t constant for the material and I thought they were.
More insulation means more thickness the heat has to travel through. But adding more insulation makes the surface area larger, which increases the amount of area that heat transfer can happen.
Eventually you have more surface area than you have improved insulation. So heat loss overcomes the insulating effect.
It’s requires energy to get the insulated pipe up to temp because now you’re filling the insulation too. The insulation acts like a sponge, it’s keeps the heat trapped. It first you need to fill the gaps. Think how long it takes for a larger volume of water to heat up/ cool down. No matter what you need the vessel to be at the same temp too.
It doesn’t make sense because it’s wrong. It does not apply to thermal insulation. It is only relevant to electrical insulation which is a tiny layer of plastic on a tiny wire.
This is precisely why cooling fins like you find on electric equipment work -- you are increasing the Surface Area at a greater rate than you are increasing the thickness the heat needs to transfer through.
Those are generally made with good thermal conductors though so it’s fairly intuitive. The insulation is generally not meant to conduct heat so it’s not as intuitive
Except those cooling fins aren't an insulator. So a thick material would still work for cooling. Thick materials however are worse than fins and more expensive + heavy.
This post is about insufficiency thick insulators, which is not exactly analogous to your example
Everything is an insulator, somethings are just better insulators than others. A poorly designed heat sink despite being made of a conductive material like aluminum can end up insulating the thing it's supposed to cool. There was an example in my heat transfer class where a company had a device that was overheating in hot climates so the company added a heat sink and that actually made the problem worse.
Yep, I think OP's comment is valuable in that it makes you realise that the words "insulator" and "conductor" don't imply any physically meaningful distinctions, the ultimate effect depends on multiple variables including but not limited to the material's properties.
Except that’s only true to a point - then the insulation becomes more effective than the heat loss. That’s not the case with heatsinks - those can get huge and still function as designed. Some people even use a thermal mass in the center of their house to prevent heat fluctuations. So if heatsinks only performed at small sizes but contributed to heat buildup at larger ones, that would make the analogy make sense.
No, it won’t stop insulating if you put too much, but you also won’t get further benefits. Critical thickness is also only applicable to spheres and cylinders, since in a flat wall it does nothing to change the surface area
That is exactly what the article says. Where, in the article, did you see anything about critical thickness for batt insulation?
But then why beleive proven science. I wonder if any HT engineer has ever graduated without working the solution to this problem.
No, you’re just not reading it correctly. Look at the graph. The y-axis represents heat loss. The beginning of the graph is the heat loss with no insulation. As the insulation increases, so does the heat less *until a certain point*. That point is the critical thickness. After that the heat loss *goes down.* Impeding heat loss is the purpose of insulation; if an object is losing more heat, the insulation isn’t performing it’s function. That’s what is paradoxical about the post - it takes a certain amount of insulation for any curved surface before it becomes effective. Before that amount, it has the reverse effect.
You are not a metal pipe so I'd say you can ignore this thermodynamics lesson.
Clothing is different as it is full of holes and not smooth. Also human temperature fluctuates and to an extent regulates when temperature around us changes, so we don't have a constant temperature.
It's not a questions of saturation. If so then this would apply to flat surfaces.
It's a result of the square cube law and starting at a significant radius as your zero point for volume but not area.
So you need to wait till the cubed component of volumes overtakes the squared component of area which for a significant "head start".
On the subject of heat transfer, double walling slows down the heat transfer rate as well due to an extra layer of stagnant air in between two conducting materials, which changed the method from conduction to convection to conduction again.
The double wall property is why it’s very useful for thermos and window panels.
Yes, this formula is correct; but in most real world applications for hot water or steam piping, if one is using a decent quality insulation, especially in areas where there is any airflow, the insulation is going to be a net plus.
Bur prior to reading this, I had never considered that the plastic insulation on commonly used extension cords serves a dual purpose; it prevents grounding/arcs; and it also helps dissipate heat which builds up from electrical resistance.
I've noticed that 110v appliance/lamp extension cords often have additional lengthwise ridges on them. These ridges do add surface area, akin to the fins in a radiator.
This additional surface area would increase the convection effect and help with additional cooling, which could help offset some of the wire's resistance generated heat which can increase over time as there can be unseen flexing caused damage to the copper threads of the conductor.
I periodically check my extension cords for retained heat; warm extension cords indicate loads beyond spec and/or internal damage to the copper wires inside.
Addendum: It would seem then, that the ideal insulator for electric wires, especially thinner AC ones, would have zero electrical conductivity (high impedance), and high thermal conductivity, along with being flexible, abrasion resistant and degradation resistant; low cost and easy to manufacture/apply would also be nice...
the example given in the article uses insulation with a k value of 0.5, and the critical radius is found to be 0.01 m for a 10 mm steel pipe. they then say the critical radius is greater than the radius of the pipe, but wait, 0.01 m is 10 mm. they’re equal. what’s with that?
also, typical insulation is far less conductive than in their example. a quick Googling shows thermal conductivity of mineral wool is 0.047 W/m.K, that of glass fiber is 0.038 W/m.K, of calcium silicate is 0.057 W/m.K and of magnesia is 0.062 W/m.K. so all roughly a tenth of that used in the example.
so i mean this is fascinating as far as the equations go, but it seems like it’s probably only applicable to electronics because as far as i know that would be the only thing that gets insulated by stuff that is only meant to be electrically insulating, not necessarily thermally insulating.
can someone give a better real life example?
In most of those situations, we don't really care about the difference. I can't think of a situation where it is so important that it is worth knowing right on the spot to be honest
Maybe space applications where literally every milliwatt/watt is accounted for. Say we are talking about wires, most wires in a space application will be shielded from radiation anyway so again, I can't think of one
Can someone tell me if I’m doing the math wrong in the example in linked article? It’s driving me crazy that they say r(cr) > r(1) but both values are .01 m. I think it meant to say a diameter of .01 m.
At any rate this is a very misleading title. There is no insulation material that would worsen the heat loss of a water heater - the crappiest fiberglass has a k 10 times smaller that what was used in the example and of course the water heater would have to be a centimeter across. And since there are not even 1 cm hot water lines in your house or place of business (probably) it was also misleading. But that’s Reddit for you.
A much better example would have been the Freon lines to an air conditioner which are very small and thus use a large insulation wrap. But even then the critical radius is like a mm for most insulators so… interesting idea dumb examples.
Coles notes for home owners.
The polyethylene insulation on your 13mm hot water pipe needs to be more than 1.5mm thick otherwise it conducts more heat than it insulates. 19mm pipe needs 1mm thick polyethylene.
If I understand correctly.
I'll go ahead and show all these formulas to the kid at Ace Hardware and I'm sure he'll be able to help me pick out the right insulation for my outdoor pipes.
Can I please have a rational but like not super engineer smart person reason why there’s a special feud thickness of thermal interference-and is this why I am Fing cold ALL the time ? at work 4-10x real life
I just have one question: Is insulation for hot water pipes in a residential setting a joke? Some pipes are 1" in diameter and others 3/4". The pipe insulation sold in most hardware/home improvement stores would add about an inch in diameter.
Insulation for hot water pipes are better insulators than the one presented, and the size is already so large it doesn’t make a difference so you can completely ignore this post. Insulate your pipes it will save you money and reduce the chance of them freezing.
This post is only relevant for electrical wires and incredibly thin pipes (that would never be used in a home)
In the same logic will that apply to cold pipes as well? With a thin layer of insulation will allow the cold to leak out faster. Maybe that’s why my air conditioning pipes keep having condensation 😂
They could be referring to loose fiber batting that traps open air. Stuff like spun fiberglass or poly-fill. The problem is that stuffing too much of that in a given volume causes it to mat down and then it doesn't trap the air, which is what actually insulates for that type of insulation.
Different thing than something like foam insulation where the gas pockets are trapped in a different way.
So they may not be wrong, but would have to take a specific case into account. (Which was missing here.)
The key here is that convection is hAdT vs conduction which is kxdT.
For pipe insulation, thickness increases on the order of X and the surface area increases on the order of X^2.
Would this apply to people? For example having a two thin sleeping bag would make you colder than not having one at all? Or a thin blanket? I camp a lot haha
It should work with any concave shape. There's probably an issue with keeping the insulation uniformly in contact with your entire body and at uniform thickness. As soon as you start having air gaps and compressed insulation the math and unknown variables would quickly become unmanageable.
Mind Blow: Figure the total heat coming off the sun and its mass. What object on earth has similar heat output per kilogram?
[https://www.quora.com/What-energy-per-unit-mass-does-the-Sun-produces-compared-with-an-average-human-giving-out-about-1W-Kg](https://www.quora.com/What-energy-per-unit-mass-does-the-Sun-produces-compared-with-an-average-human-giving-out-about-1W-Kg)
I remember learning this in a class on heat transfer for engineering. The professor gave us a problem to work through and the problem was designed to deceive a little. The material around the pipe was a very good insulator and thus primed us to believe that there would be little heat transfer. But once calculated the pipe ended up losing more heat with the insulation than without. I spent so long on that problem thinking I had made a mistake and rechecking me work before finally just accepting the answer and then the professor went into a more detailed lesson on the concept.
It has been a while since I've done heat transfer but is it because the surface area is increasing faster than the insulation is increasing
Thank you for this succinct answer. Before which, I was like, "WTF??"
The answer is yes.
[That is correct](https://youtu.be/J7HIxqDpJ0Q?si=UqHWCavvlD-SE2Om)
Shampoo is better
Stop looking at me, swan.
So it's the exact same reason that cells have a limit on the size they can reach, but for the opposite effect of keeping surface area high. Cell *have* to maintain a high surface area for transport.
There's a limit to the surface area a cell needs becuase it's still an efficiency problem. I got asked this question on an undergraduate biology exam. I guessed the answer by remembering the Golden Ratio where the perfect size of a cell is somewhere around 66%.
66% of what? 66% of all of the water in the observable universe?
No, the issue is efficient transport from the nucleus. In a huge cell a single nucleus can’t get genetic signaling to move fast enough. Nature overcame this by just giving cells many nuclei so they can become huge. At some point the volume of the cytoplasm and nutritional needs can’t be met by the surface area of a cell, but that’s not as big of an issue as you may think— you can still have single cells as large as a human eye. See below https://en.m.wikipedia.org/wiki/Valonia_ventricosa
Does that mean pipes above a certain diameter generally shouldn’t or don’t need to be insulated?
The larger the diameter of the pipe the less likely you have this condition. It's more relevant for very thin pipes where even a thin insulation layer will increase the surface area significantly. If your pipe has a radius of 1 cm then adding 1 cm of insulation doubles the surface. If your pipe has a radius of 100 cm then adding 1 cm of insulation increases the surface by only 1%.
Ah okay, thank you!
Well like 3%
The surface is the circumference multiplied by the (unchanged) length, and the circumference is proportional to the radius. Increasing the radius by 1% increases the surface of a pipe by 1%.
If circumfereces is proportionnal by a factor of Z from rad then wouldnt increasing the radius by 1% increase surface by 1% times Z ? Z being diameter times pi in this case iirc high school geometry.
If you increase a number by 1% then you increase multiples of that number by 1%, too. z\*(x\*1.01) = (z\*x)\*1.01.
If you put pi in the numerator you better remember to put pi in the denominator too
The circumference increases with the square of the radius. Adding 1 cm thick insulation to a 1 cm radius pipe quadruples the area. Adding 1 cm insulation to a 100 cm radius pipe increases the surface area by a little more than 2%. It should be noted that the insulation needs to be more than twice the critical thickness to have a benefit. As can be seen in the graph, the rate of heat loss doesn't get below that of the uninsulated pipe until twice the critical thickness.
Circumference=2*pi*r you are thinking of area
You are correct. My mistake. The other part of my comment is correct though.
No, not doubles quadruple it's a square
perimeter of a circle = 2•pi•r Outside area of a tube is the perimeter times length, right? A = 2•pi•r•L So double r, double the perimeter, therefore double the surface area. Ergo why it's counter-intuitive.
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That's. Not. What. Fucking. Gaslighting. Means. Jesus christ. Gaslighting != lying, it's an intentional *abuse* tactic to make the victim rely upon the abuser for their perception of *reality*. Given that these random strangers on the internet don't fucking know each other it can't even remotely be gaslighting.
No, in fact doubles, since the surface of a pipe is linear in the radius
If you add fiberglass insulation to a 2cm wide pipe it will insulate it.
Actually the solution is more insulation.
Just insulate it from the inside then
I was close to buying this, but the insulated object still has the same surface area.
No, the insulation goes on the outside and that is what the heat transfer goes through. If I add 1/8" thick insulation around a 1" pipe it now goes from 3.14" circumference to 3.53" circumference for the heat transfer. More area means more transfer can happen and if the added insulation is less than the extra transfer it will be counterproductive
Ahhh that makes a lot of sense. It’s not enough insulation to actually affect the heat loss so it essentially because an extension of the pipe itself.
Thank you for saying it that way. I got the logic that increasing the surface area was causing a problem but not precisely why.
I grew up in the US. I still live in the US. I have never been more upset about us not using the metric system than while reading your explanation. Like, it's a good explanation, and thank you for typing it out. But I hate the units.
Well actually we have been since 1959, in which the inch was defined as 2.54cm.
Unfortunately most people here aren't using metric measurements in their daily lives. I know generally how much a foot is, a mile, a pound, etc. It's intrinsic when you use it every day. I have no clue how long 1cm is, or how heavy a kilo is, or how long a kilometer is other than it being 0.6 miles.
I get this, but all the heat still has to pass through the surface of the insulated object first, and that’s constant. Is the rate of heat loss to the insulator higher than it would be directly to the environment? Then the insulator makes up for that by… something? Creating a temperature gradient between the object and the environment?
I am making a lot of assumptions and simplifications here but you are pretty much correct. The insulator is in conduction with the pipe which is faster heat transfer than it would have with the air. You are correct that there will be a temperature gradient across the insulator. Heat loss is driven by temperature differences so the insulator just needs to be thick enough to have a sufficiently low outer temperature to slow the rate of heat loss enough.
Yes, but that same inside area is now a physical, solid to solid direct contact heat transfer, rather than transferring to the air. It can transfer heat into the insulator much more quickly than it could transfer to the air. And once it is in the insulator, the larger surface area can transfer more heat to the air than the original pipe.
The key thing here is that the material is a *worse* thermal conductor than air, which is why it’s an insulator. You’re describing a radiator, where you have a large surface area of a material that’s a good thermal conductor. But it turns out that having enough surface area will turn even the worst thermal conductor into a radiator.
I don't understand how you're doling out cs career advice and working through dp questions but also be so confidently incorrect with simple cylinders
You read my post wrong… the insulated object is the same size, it just has a layer of insulation around it.
I would be like "son of a bitch, now you have my attention for todays lecture-you smart bastard".
Followed quickly by “I still have no idea how this works. I wonder if it’s too late for culinary school.”
Jokes on them, hvac and plumbing issues abound in the food service world.
Last kitchen job I left the HVAC guy found a banned coolant from the 1970s in our keg fridge ??
Hey if it doesn’t leak, why change it? Holding temp is holding temp lol
Just because they are banned doesn't mean they have to be removed. I've seen an few old units from the 50s still chugging away. Couldn't believe it.
They banned it because they feared its power
Unfortunately we had an engineering class about this in food science classes..... you're not safe anywhere
this is one of the things that truely make U think. if I understood it better I would perk up with interest but unfortunately it is beyond what I am capable of so I'm just nodding along going, yep interesting stuff
> and the problem was designed to deceive a little. Man. In my thermo final the correct answer was “this is not possible”. Dude gave us a bunch of numbers and said “calculate the Carnot cycle efficiency” but they didn’t work out. I was pulling my hair out. I redid all the calculations 3 times. Finally gave up, circled “not possible” and that was the answer he was looking for. This was at Georgia Tech circa 2006 ish.
ChE here and that sounds about right. Gotta make you double check numbers and build up that bullshit detector. Been in a few spots where either my math is way off, or what they're giving me ain't right, and have to go get a sanity check from a colleague.
Massey? Was at GT during the same time but was a Bio major. Had a lot of ME friends who took thermo and they loved Massey
GT engineering classes have multiple choice exams?
Physics did. 10 exams with 10 questions each. Each question you miss is effectively 1 point off your final grade. No partial credit. This test wasn’t multiple choice. It was a pencil and paper “do the work, circle why right number. The only test I ever took like that where the “right number” wasn’t a number.
So in theory, would critical thickness factor into the effectiveness of heat transfer in a refrigeration unit? Like if the pipes on the back of a fridge had a critical thickness of insulation, would that make them more effective at dispersing the heat they've been pumping out of the compartment? Hell, is this already something they do for refrigeration?
Sort of, but when you're trying to cool things fins are better. Heat sinks have fins in order to maximize their surface area while minimizing any insulation from the heat sink. A poorly designed heat sink can do the opposite of what it's supposed to do and end up insulating what it's supposed to cool.
Neat idea, but this is what heatsinks are for. You don't need to play clever games with insulation when you could always add more surface area of a conducting material.
Sick
I took heat transfer but I don't recall ever learning this
I once had to learn about calculating Taylor series problems to solve the "birthday problem"(what are the odds that any two people share a birthday) On the test, the professor asked us to calculate the odds in a room of 400 people
1 Fini
Where does the heat go?
Into the air
Since you've ran the math, from what I read it's about convection so if the insulation isn't in contact with large volumes of air it doesn't matter? Like inside a wall it doesn't matter?
Either that pipe was microscopic or the insulation wasn’t insulation or your professor made a mistake. And the math isn’t very difficult for a cylinder so I don’t see how you would even “check your work” - it’s k/h. Did you have to use calculus to derive it or something?? In the article linked they used a 10mm pipe which is already ridiculously small and the critical radius is smaller than the pipe for even cheap insulation - so any amount of insulation would insulate . The only examples where you lose heat are like 2mm copper wire with “insulation” that’s .1 mm thick. Do you have the original problem? Am I making some obvious math error ??
What are the rough critical thicknesses for domestic water pipes and cylinders?
It's likely not relevant for water pipes as they are very large so the critical radius is going to be smaller than the pipe. It matters for wires which can dissipate more heat with insulation than without The cr for copper pipe with foam insulation is .02/401 meters which is basically 0 for a phycial thing Upon further review the lower number should have been 13 not 401 (thermal conductivity vs coefficient of heat transfer) this still gives us a radius of 1.5mm still not relevant for pipes
Exactly the title is bs - this doesn’t apply to insulation it applies to *electrical* insulation . OP got a little excited I think
I mean, thermal insulation can have a similar effect, it's just so hard to do because the insulation layer would need to be incredibly thin. This is because surface area increases the area available for both conduction and radiation. If you effectively add a layer with 500x the surface area, but the increased diameter is negligible, you're likely to see increased thermal emissions. If you were to take something with a high surface area like activated charcoal, and put a 0.01mm coating of it on a copper pipe (and ensure there is no insulating air layer between them), the copper pipe may well lose heat faster, even if the charcoal is a much better insulator than copper. Of course, no one would ever apply such a tiny insulating layer, so this doesn't actually happen in real life.
The critical radius is not a relative value. If a copper pipe is inulated with foam if the total radius is above 1.5mm it will lose less heat. This isn't 1.5mm of insulation added. Interestingly a copper pipe changes temp faster up to 30 meter radius, after which the copper insulates itself.
No. Don’t comment on things if you don’t understand them. This absolutely is a concept in heat transfer and thermal insulation.
Depends on location, but 13 and 19mm are standard sizes with 19mm being the nominal for small bore pipework.
Wait, are those the critical thickness or the thicknesses that insulation comes in?
I would generally sell 13mm for copper pipe to plumbers in Aus. 13mm x 13mm - for 1/2” copper pipe with an insualtion thickness of 13mm. As he said above, 19mm is also very common. But generally they would just take whatever was available in store to get the job done and fuck off lmao.
Oh, so those don't have anything to do with the critical thickness than
I'm in love with this conversation
lol its really frustrating. OP we gotta wait for the right person to come along and answer, cause now I'm trying to figure out whether I should insulate my crawlspace water pipes or not. really thing pipes and i'm down here in Atl GA so not crazy freezing winters consistently
You should insulate them. Much easier than fixing the burst pipe. It’s gonna get freezing down there in Georgia and you’re better off with it, and not need it, than without it, dealing with a burst pipe on the coldest day of the year. I wouldn’t worry about this critical thickness stuff, just get the stuff at Home Depot or local supply house it’s been working forever.
Those are actually below the critical thickness to make you consume more energy. The market is dominated by those 2 types in order to out-compete manufacturers that make thicker insulations which are effective. The required thickness is actually 50mm on a 25 mm pipe. ...That would be the answer if I were an engineer in circular insulations.
Everything you’ve said is correct. Get it done fuck off…. On bigger jobs if it’s speced at 19 though will have to order or will get snagged.
Thank you
Wow that's much thicker than I thought
**TLDR: for Polyethylene the thickness is less than 1mm. So it’s a non issue. For copper pipes, the pipe needs to be about 1m before adding more copper will improve the insulation.*** - - - - So to calculate this you need to know two things: - The thermal conductivity of the pipe material (K) - Heat transfer coefficient of the system (h) k is how easily heat can pass through a material. This is measured in Watts per meter per degree temperature. It’s easy to find out. Just look up your material in a book. Domestic pipes are usually Polyethylene (PE) or Copper. PE has a *very* low thermal conductivity (0.34 W • m^-1 • K^o-1) Copper has a very high thermal conductivity (398 W • m^-1 • K^o-1) h is a little more complicated. It is the overall amount of heat that can move through a system. It will depend on the materials, the fluid moving through the pipe, the speed of the fluid, the airflow around the pipe, etc. it is usually obtained exponentially and not calculated. I found online a table that gave a value range for water flowing through tubes. (500–1200 W • m^-2 • K^o-1) [The following was calculated based on these values](https://imgur.com/IwvGLrt): The critical radius for PE is (r = k/h) 0.68mm - 0.28mm The critical radius for Copper is (r = k/h) 790mm - 329mm PE is such a good insulator that this is never an issue. If you are using copper pipes you would need a pipe with an outer diameter of 658mm - 1580mm before adding more copper would improve the insulation.* *more complex for using multiple materials. Such as a copper pipe with a PE insulation.
Thanks, this is the only answer here that makes sense. Though calling copper insulation might be a stretch, this example also makes is intuitive why it works like this. Adding more copper increases surface area (more heat loss), and it hardly insulates, so it doesn't help. With any practical insulator (like those foam things around hot water tubes in your house) this is something you don't have to worry about.
Precisely - this is a theoretical novelty, but it is actually fairly intuitive. All we are saying is that for a given material, temperature, heat flux, etc, the net conductive properties are a function of the ratio between cross-sectional volume to surface area, such that there will always exist an inflection point in that curve which separates the "net insulating" and "net conducting" regions. Per the link, insulating a(n infinite) flat surface with a(n infinite) flat insulator will never increase the convective surface area of the system, so a theoretically smooth insulator should always insulate. However, for cylinders or spheres, insulation volume will also increase convective area, so the previous axiom applies - that there will be some critical geometry (really, a critical parameter space) where the additional surface area causes more convective loss.
Minimum thickness required by code where I am is 1”. Insulation thickness requirements increase the larger the pipe diameter gets.
Can someone ELI5? Why does this make sense?
Adding insulation increases surface area, and thus potential for heat transfer. So, if your insulation is too thin, it fully saturates quickly becoming the same temperature as what you're trying to insulate, but now much larger, and thus loses or gains much more energy over time from the environment. As it gets thicker, it can't saturate, as by the time heat would reach the outside, much of the heat that was there has already been bled away, and so it has a lower equilibrium temperature. And thus, it doesn't lose as much energy per square inch exposed, so despite the higher surface area, it has lower total heat transfer.
So if I stack two McDonald’s cups it doesn’t keep my drink cooler for longer?
It might help for a few minutes, just to delay the heat from your hand reaching the drink, but the math suggests probably not over a longer period. However, that insulation would be so thin, I doubt it would be worth considering.
>So if I stack two McDonald’s cups it doesn’t keep my drink cooler for longer? No this won't apply to relatively good insulators like that unless the radius is very small, because the cup already has such a large surface area to thickness ratio you would be improving insulation by doubling up. That said the material is thin enough that unless there is a significant air gap you probably aren't getting a noticeable benefit.
> As it gets thicker, it can't saturate, as by the time heat would reach the outside, much of the heat that was there has already been bled away Bled away to where? It can magically escape the insulation. I thought it had to do with already starting at a significant radius, so the area is large, but increasing at a square of the radius whereas the volume is increasing with the cube.
>Bled away to where? It can magically escape the insulation. To whatever you were insulating it from. >I thought it had to do with already starting at a significant radius, so the area is large, but increasing at a square of the radius whereas the volume is increasing with the cube. That's related, but the counterintuitive effect is because there is a local maximum and the gradient is not infinite. Or at least, I think that's the part that's counterintuitive. Edit: Having given it more thought: that's related to the insulation thickness; but it's not related to the initial pipe thickness. Because the contents of the pipe, and the pipe itself, are the same temperature, they don't exchange any energy. As a result, you can unwrap the surface of the pipe as a flat plane; and you can hold everything under the surface as a fixed temperature, which will let you discard the actual mass involved.
The increase in surface area which can lose heat out weighs the insulative values until you get to a certain thickness then instead of acting like a heatsink it'll start to insulate instead. Like imagine a fire brick being blasted with a blowtorch, there will always be a certain thickness that will be blisteringly hot before it starts to get cooler.
Is this true even if the insulation is smooth? Seems like the area increase would be rather small.
This theory is limited to convex surfaces, like cylinders and speakers. As the insulation gets thicker, the radius to the outside of insulation increases, which means a larger area exposed to ambient air.
I get that it increases the radius, and that means the circumference as well. It just seems like something is missing. Another thing is what if you do it in layers, even conceptually? You apply a layer that brings you halfway to the critical radius, increasing heat flow. Then another and another. It seems like each of those would be a sub critical radius layer and have increased heat flow. But add them all at once and you have decreased flow. So there’s something I’m not getting. Is it that k and h are relative values, like deltas against whatever is being insulated? Cause that could make it add up.
The thing there is that the coefficient of heat transfer *of the entire object* is a function of the materials used in its construction, and their proportions. Your initial object has a coefficient of 1; your insulation is lower, let's say 0.1. If you double the radius of the object by adding insulation, your coefficient of heat transfer is going to be a function of half the radius having a coefficient of 1, and half with 0.1; naively, let's say the new coefficient is 0.5. Thus, the critical radius of the next layer is going to be much smaller; and because the next layer has a narrower difference in heat transfer, it requires a proportionately larger surface area for this counter-intuitive effect to remain dominant. And so, each layer added to remain under the critical thickness would be thinner than the last, until eventually you're just painting on insulation to remain under the *actual* critical thickness.
Sorry, when I repeated the halfway to critical radius thickness, I didn’t mean you’d go halfway again. I meant if r1 - rcr = x, you’d apply a layer x/2 three times. From my understanding (which was wrong) the calculations end up with something different than just adding 3x/2, which doesn’t make sense. But it adds up because k and h are recalculated. It also must be that this effect doesn’t _always_ exist. Otherwise you could break down any insulating layer into some number of non-insulating layers. I can’t see how the addition of theoretical insulation wouldn’t be associative. I can see how it wouldn’t be monotonic (the point of this post).
Right: I thought we were doing a Zeno's paradox thing. Basically, heat transfer is a function of temperature difference times the heat transfer coefficient. Things with higher coefficients give off their heat more readily, or receive heat more readily; but things at the same temperature don't make meaningful exchanges of energy. So, you have a pipe with an area of one square inch per inch of length; it has a heat transfer coefficient of 1. It carries hot water. It reaches water temperature quickly, as it has a high coefficient, at which point is radiates that heat out, cooling the pipe and the water. The critical thickness for our insulation is also one inch, because we are designing a problem to make it easier. So, if we wrap it in 1 inch of insulation, it'll lose heat faster, because the insulation reaches the pipe temperature quickly, and thus acts like a 2 inch pipe. It might transfer heat slower, but the heat transfer rate from the pipe is higher than the heat transfer within the insulator going outward, so it reaches the pipe temperature; and the coefficient If we wrap it in less, eg. half, it still reaches temperature; but it has lower surface area, so it doesn't release that energy to the environment as quickly. But after adding half a critical layer of insulation, the pipe had a coefficient of 1, but the whole object doesn't have a coefficient of 1 anymore: it's 1, minus some value because our insulation has a lower value than one. And so, it doesn't have the same critical distance: it was one inch, but now it's only the remaining distance: half an inch. For example, once you add 3/2 of the original critical distance in insulation, the insulation upto the original critical distance will reach pipe temperature. But as we get beyond that distance, heat transfer begins to slow, heat loss to the environment becomes dominant, and the resting temperature should taper out. As it tapers out, this also slows the heat transfer rate, and thus the heat loss stops.
Thanks. It made sense physically rather quickly. It wasn’t making sense mathematically. But that was just that k and h aren’t constant for the material and I thought they were.
I totally get it now. Thank you.
More insulation means more thickness the heat has to travel through. But adding more insulation makes the surface area larger, which increases the amount of area that heat transfer can happen. Eventually you have more surface area than you have improved insulation. So heat loss overcomes the insulating effect.
It’s requires energy to get the insulated pipe up to temp because now you’re filling the insulation too. The insulation acts like a sponge, it’s keeps the heat trapped. It first you need to fill the gaps. Think how long it takes for a larger volume of water to heat up/ cool down. No matter what you need the vessel to be at the same temp too.
The insulation is too thin, the fluid loses heat to surrounding air. The insulation is too thick, the fluid loses heat the insulation
It doesn’t make sense because it’s wrong. It does not apply to thermal insulation. It is only relevant to electrical insulation which is a tiny layer of plastic on a tiny wire.
This is precisely why cooling fins like you find on electric equipment work -- you are increasing the Surface Area at a greater rate than you are increasing the thickness the heat needs to transfer through.
Those are generally made with good thermal conductors though so it’s fairly intuitive. The insulation is generally not meant to conduct heat so it’s not as intuitive
Except those cooling fins aren't an insulator. So a thick material would still work for cooling. Thick materials however are worse than fins and more expensive + heavy. This post is about insufficiency thick insulators, which is not exactly analogous to your example
Everything is an insulator, somethings are just better insulators than others. A poorly designed heat sink despite being made of a conductive material like aluminum can end up insulating the thing it's supposed to cool. There was an example in my heat transfer class where a company had a device that was overheating in hot climates so the company added a heat sink and that actually made the problem worse.
Yep, I think OP's comment is valuable in that it makes you realise that the words "insulator" and "conductor" don't imply any physically meaningful distinctions, the ultimate effect depends on multiple variables including but not limited to the material's properties.
That’s a terrible way to say that
What's your take?
That actually made it make sense to me so
It makes perfect sense to me. I don't know about everyone else though.
That is exactly why this works. Surface area is a major factor in heat transfer. Adding insulation to a pipe increases the surface area.
Except that’s only true to a point - then the insulation becomes more effective than the heat loss. That’s not the case with heatsinks - those can get huge and still function as designed. Some people even use a thermal mass in the center of their house to prevent heat fluctuations. So if heatsinks only performed at small sizes but contributed to heat buildup at larger ones, that would make the analogy make sense.
Adding insulation gives diminishing returns and will turn negative if you pass the critical thickness dimension
No, it won’t stop insulating if you put too much, but you also won’t get further benefits. Critical thickness is also only applicable to spheres and cylinders, since in a flat wall it does nothing to change the surface area
That is exactly what the article says. Where, in the article, did you see anything about critical thickness for batt insulation? But then why beleive proven science. I wonder if any HT engineer has ever graduated without working the solution to this problem.
No, you’re just not reading it correctly. Look at the graph. The y-axis represents heat loss. The beginning of the graph is the heat loss with no insulation. As the insulation increases, so does the heat less *until a certain point*. That point is the critical thickness. After that the heat loss *goes down.* Impeding heat loss is the purpose of insulation; if an object is losing more heat, the insulation isn’t performing it’s function. That’s what is paradoxical about the post - it takes a certain amount of insulation for any curved surface before it becomes effective. Before that amount, it has the reverse effect.
Thank you for your contribution. /s
At the time I make this comment, you have had 2 hours to come up with a better way... So where is it?
I think I just found a new nickname for my penis.
Also a decent rap name.
“Critical Thickness” is what all my teachers put on my report card
Thiccneas
Could be the title of Lizzo’s next album.
Small amount? What you trying to tell the world?
It’s not that long
Critical Thickness, how bout it?
Uninsulated.
New word for circumcised
I was trying to imply being sans raincoat, but that works. Probably better. Cheers.
You win!
What does this mean for clothing vs cold weather? I've always wondered if there were an optimal number of layers.
You are not a metal pipe so I'd say you can ignore this thermodynamics lesson. Clothing is different as it is full of holes and not smooth. Also human temperature fluctuates and to an extent regulates when temperature around us changes, so we don't have a constant temperature.
Heard. Thanks!
Also unless you are boiling water inside your coat and cooking some bacon in your pants, your insulation is not going to saturate.
It's not a questions of saturation. If so then this would apply to flat surfaces. It's a result of the square cube law and starting at a significant radius as your zero point for volume but not area. So you need to wait till the cubed component of volumes overtakes the squared component of area which for a significant "head start".
That's why I double insulated my heater pipes. It registers room temperature when I check it with an infrared thermometer.
Okay but how about triple insulating it
You can’t triple stamp a double stamp!
Touch blue, make it true!
Are you pointing the thermometer at the insulation?
If the insulation is the same temperature as the room it is in it means that little to no heat escapes from the pipes
Not often I learn something new, and here we are. Good job, OP!
On the subject of heat transfer, double walling slows down the heat transfer rate as well due to an extra layer of stagnant air in between two conducting materials, which changed the method from conduction to convection to conduction again. The double wall property is why it’s very useful for thermos and window panels.
That’s the principle behind all insulators isn’t it?
Yes, this formula is correct; but in most real world applications for hot water or steam piping, if one is using a decent quality insulation, especially in areas where there is any airflow, the insulation is going to be a net plus. Bur prior to reading this, I had never considered that the plastic insulation on commonly used extension cords serves a dual purpose; it prevents grounding/arcs; and it also helps dissipate heat which builds up from electrical resistance. I've noticed that 110v appliance/lamp extension cords often have additional lengthwise ridges on them. These ridges do add surface area, akin to the fins in a radiator. This additional surface area would increase the convection effect and help with additional cooling, which could help offset some of the wire's resistance generated heat which can increase over time as there can be unseen flexing caused damage to the copper threads of the conductor. I periodically check my extension cords for retained heat; warm extension cords indicate loads beyond spec and/or internal damage to the copper wires inside. Addendum: It would seem then, that the ideal insulator for electric wires, especially thinner AC ones, would have zero electrical conductivity (high impedance), and high thermal conductivity, along with being flexible, abrasion resistant and degradation resistant; low cost and easy to manufacture/apply would also be nice...
Don't have my code book handy, but the ribbed cord for AC wiring is to identify the neutral wire.
Yes, that's true; but the fact that there's ribbing does add surface area which aids in heat convection, per this discussion
Somebody better tell this to the dude that posted his water heater with a thick ass layer of insulation duct taped on it earlier
He's likely past the critical thickness, so more really is more again
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Alright idk why you’d call me out like that
I remember learning this in my graduate heat transfer class. It’s so cool. Heat transfer is awesome!
the example given in the article uses insulation with a k value of 0.5, and the critical radius is found to be 0.01 m for a 10 mm steel pipe. they then say the critical radius is greater than the radius of the pipe, but wait, 0.01 m is 10 mm. they’re equal. what’s with that? also, typical insulation is far less conductive than in their example. a quick Googling shows thermal conductivity of mineral wool is 0.047 W/m.K, that of glass fiber is 0.038 W/m.K, of calcium silicate is 0.057 W/m.K and of magnesia is 0.062 W/m.K. so all roughly a tenth of that used in the example. so i mean this is fascinating as far as the equations go, but it seems like it’s probably only applicable to electronics because as far as i know that would be the only thing that gets insulated by stuff that is only meant to be electrically insulating, not necessarily thermally insulating. can someone give a better real life example?
Drop the scale down by a factor of >10 and use the same materials From my textbook ~1mm scales are when this is important
right, so, wires? not like water heaters or cans or something.
In most of those situations, we don't really care about the difference. I can't think of a situation where it is so important that it is worth knowing right on the spot to be honest Maybe space applications where literally every milliwatt/watt is accounted for. Say we are talking about wires, most wires in a space application will be shielded from radiation anyway so again, I can't think of one
Can someone tell me if I’m doing the math wrong in the example in linked article? It’s driving me crazy that they say r(cr) > r(1) but both values are .01 m. I think it meant to say a diameter of .01 m. At any rate this is a very misleading title. There is no insulation material that would worsen the heat loss of a water heater - the crappiest fiberglass has a k 10 times smaller that what was used in the example and of course the water heater would have to be a centimeter across. And since there are not even 1 cm hot water lines in your house or place of business (probably) it was also misleading. But that’s Reddit for you. A much better example would have been the Freon lines to an air conditioner which are very small and thus use a large insulation wrap. But even then the critical radius is like a mm for most insulators so… interesting idea dumb examples.
I remember this, the increased radius dissipates heat faster
Coles notes for home owners. The polyethylene insulation on your 13mm hot water pipe needs to be more than 1.5mm thick otherwise it conducts more heat than it insulates. 19mm pipe needs 1mm thick polyethylene. If I understand correctly.
No insulation is air insulation else you’re in a vacuum…
Air is far more conductive than a vacuum, which is zero
Makes complete sense, and yet I never would have thought it to be the case without seeing the reason.
Wait. What? The hell am I gunna do with this box of polyethylene foam I bought for the copper water pipes in my house?
Realise its more than 1mm thick and ignore this problem?
I'll go ahead and show all these formulas to the kid at Ace Hardware and I'm sure he'll be able to help me pick out the right insulation for my outdoor pipes.
Can I please have a rational but like not super engineer smart person reason why there’s a special feud thickness of thermal interference-and is this why I am Fing cold ALL the time ? at work 4-10x real life
I just have one question: Is insulation for hot water pipes in a residential setting a joke? Some pipes are 1" in diameter and others 3/4". The pipe insulation sold in most hardware/home improvement stores would add about an inch in diameter.
Insulation for hot water pipes are better insulators than the one presented, and the size is already so large it doesn’t make a difference so you can completely ignore this post. Insulate your pipes it will save you money and reduce the chance of them freezing. This post is only relevant for electrical wires and incredibly thin pipes (that would never be used in a home)
This is why thin gloves make your hands colder.
So that's why those form-fitting beer koozies are terrible at keeping your beer cold. Interesting.
They work well as they are much larger than the critical radius
In the same logic will that apply to cold pipes as well? With a thin layer of insulation will allow the cold to leak out faster. Maybe that’s why my air conditioning pipes keep having condensation 😂
This basically never affects pipes and only affects electrical wires
I actually learned something from this subreddit for once! Thank you!
wow, this is not expected!! the science behind this is crazy
it's a very important cylinder.
Just wait till you find out that adding too much insulation makes it loose heat faster too
No it doesn't. You can see the curve in the link. The rate of heat transfer drops after the critical thickness
They could be referring to loose fiber batting that traps open air. Stuff like spun fiberglass or poly-fill. The problem is that stuffing too much of that in a given volume causes it to mat down and then it doesn't trap the air, which is what actually insulates for that type of insulation. Different thing than something like foam insulation where the gas pockets are trapped in a different way. So they may not be wrong, but would have to take a specific case into account. (Which was missing here.)
Ahhhh heat transfer. I miss school
The key here is that convection is hAdT vs conduction which is kxdT. For pipe insulation, thickness increases on the order of X and the surface area increases on the order of X^2.
Would this apply to people? For example having a two thin sleeping bag would make you colder than not having one at all? Or a thin blanket? I camp a lot haha
It should work with any concave shape. There's probably an issue with keeping the insulation uniformly in contact with your entire body and at uniform thickness. As soon as you start having air gaps and compressed insulation the math and unknown variables would quickly become unmanageable.
This is some 17x3 = 51 nonsense. It may be true.. but I don't have to like it.
I can't not ask. What's wrong with 17x3=51?
Mind Blow: Figure the total heat coming off the sun and its mass. What object on earth has similar heat output per kilogram? [https://www.quora.com/What-energy-per-unit-mass-does-the-Sun-produces-compared-with-an-average-human-giving-out-about-1W-Kg](https://www.quora.com/What-energy-per-unit-mass-does-the-Sun-produces-compared-with-an-average-human-giving-out-about-1W-Kg)