# Heat Transfer - Critical Radius of Insulation

A steel pipe with foam insulation is embedded in a concrete wall. The steel pipe is carrying cold water and therefore gains heat from outside atmosphere. Heat transfers through the concrete wall, foam insulation and then to the pipe. Is it possible to calculate critical radius of insulation for this scenario?

(I understand that the critical radius = k/h can only be applied when the foam insulation is exposed to the atmosphere. We can't use heat transfer coefficient (h value) since convection is not possible between 2 solids (foam and concrete, in this case. In the above scenario, concrete wall becomes a part of the insulation.)

Is there another formula/methodology I can use to calculate critical radius for the above scenario?

sophiecentaur
Gold Member
2020 Award
I did a quick Google with "buried pipe insulation heat loss" and there was an avalanche of hits on those lines. If no one with specific knowledge of this topi replies than that list of hits may help you find what you want. Clearly, it's a very common problem so the info will be out there somewhere, Good luck.

Thevan
Chestermiller
Mentor
Are you considering an infinite ocean of concrete surrounding the pipe? Are you assuming that the pipe is infinitely long, or of finite length compared to the dimensions of the concrete?

russ_watters
Are you considering an infinite ocean of concrete surrounding the pipe? Are you assuming that the pipe is infinitely long, or of finite length compared to the dimensions of the concrete?
I'm going with finite parameters. Below are the parameters, for your reference.

Concrete wall of height 5m, length 4m and thickness 0.25m. The metal pipe is embedded in the wall along the length. Length of pipe is 4m, internal radius 0.02m and outer radius 0.03m. Pipe has insulation of thickness 0.03m. Pipe carries cold drinking water and therefore heat transfer is from the atmosphere to the pipe, through the concrete and insulation. Is it possible to calculate critical radius in this scenario? If yes, how would i go about it?

Thank You.

Chestermiller
Mentor
The simplest approach is to look at a worst case bounding scenario in which the concrete wall is replaced by an annulus of outside diameter 0..25 m and length length 4 m. This will give a little less insulating effect than the actual concrete wall, but will be amenable to analysis with cylindrical symmetry.

The simplest approach is to look at a worst case bounding scenario in which the concrete wall is replaced by an annulus of outside diameter 0..25 m and length length 4 m. This will give a little less insulating effect than the actual concrete wall, but will be amenable to analysis with cylindrical symmetry.

Thank You Chester. On a similar topic, is it possible that critical radius of insulation does not exist in certain scenarios (certain types of cylinder material or insulation)? Or is critical radius applicable for all insulated cylindrical structures in heat transfer?

Chestermiller
Mentor
Thank You Chester. On a similar topic, is it possible that critical radius of insulation does not exist in certain scenarios (certain types of cylinder material or insulation)? Or is critical radius applicable for all insulated cylindrical structures in heat transfer?
I don't know. I would have to look at it on a case-by-case basis.

sophiecentaur
Gold Member
2020 Award
Summary:: Find critical radius of a multilayered (3 layered) cylinder

Is there another formula/methodology I can use to calculate critical radius for the above scenario?
The term 'critical radius', afaik, is specifically used in the context of an insulated pipe in free air and relates to the best choice of insulation thickness when convection occurs. I can't see why the OP wants to use that term outside the remit of that piece of theory. If someone has tried to be helpful by introducing the term into the process the I think they may not have thought about the actual problem.
Replace the term with a fuller description and you get a question like " what are the cooling effects of convection when there is no convection?". Make the thickness of the high insulating material as money and strength will allow. Suitable calculations and also a load of data are available.

russ_watters
Chestermiller
Mentor
The term 'critical radius', afaik, is specifically used in the context of an insulated pipe in free air and relates to the best choice of insulation thickness when convection occurs. I can't see why the OP wants to use that term outside the remit of that piece of theory. If someone has tried to be helpful by introducing the term into the process the I think they may not have thought about the actual problem.
Replace the term with a fuller description and you get a question like " what are the cooling effects of convection when there is no convection?". Make the thickness of the high insulating material as money and strength will allow. Suitable calculations and also a load of data are available.
I think the OP is really asking is whether there is an optimum thickness for the insulation in this situation.

sophiecentaur
Gold Member
2020 Award
I think the OP is really asking is whether there is an optimum thickness for the insulation in this situation.
Oh yes. Definitely and hence my comment. I made another comment higher up about using available data and getting a clue. But no one (me included) explained what the critical radius means or attempted to put the OP right, early on. CR applies only for free convection from the lagged pipe in a 'large enough' duct space and depends only on the area of contact with the air. Otoh, the conductivity depends on the area and the thickness. The 'thickness' of the air layer is assumed to be more or less infinite and that's why there's actually a turning value in the heat loss / insulation radius curve. Layers of different conductivity materials won't have a TV. The best solution there is to use as much of the expensive stuff as you can afford.
The way to approach this sort of problem is to forget equations and use the tables available from organisations who have been doing 'it' for generations. Not good Physics perhaps but, then, nor is trying to use the wrong equation in the first place, for which the OP can't in any way be blamed.

russ_watters
Mentor
Right, but some issues with optimum thickness in this situation:
1. How much flexibility do you have in the diameter of the penetration?
2. Drinking water? Cold domestic water pipes are usually not insulated. What does the code say here?
3. The performance requirement wasn't specified. Maybe it doesn't exist?

sophiecentaur
Gold Member
2020 Award
Drinking water? Cold domestic water pipes are usually not insulated.
Frozen unlagged cold waters pipes are not uncommon in older houses in UK. You can't get away with ignoring that potential problem in a 'harsh' winter.

russ_watters
Mentor
Frozen unlagged cold waters pipes are not uncommon in older houses in UK. You can't get away with ignoring that potential problem in a 'harsh' winter.
Where are these pipes and how do they freeze? In the US, outdoor piping is run below frost lines and indoor piping is....indoors. If there is an elevated house or unheated crawl space, that would need both insulation and heat trace. You can't prevent a domestic water pipe from freezing with insulation alone.

sophiecentaur
Gold Member
2020 Award
Where are these pipes and how do they freeze?
Parts of UK usually get mild enough winters and people can be very sloppy about feeding outside water taps and putting in extra cold pipes without paying attention to insulation.
It's the fault of a maritime climate, I think. Some years, we get no snow and very mild frosts in the South West if England and, with the heating running for a large part of the day, naked pipes are not vulnerable. It's when people leave houses unoccupied . . . . . .

russ_watters
Mentor
Parts of UK usually get mild enough winters and people can be very sloppy about feeding outside water taps and putting in extra cold pipes without paying attention to insulation.
Outside water taps use remote valves with drained through-wall pipes. Sure, if you don't install the right kind it can freeze, but that has nothing to do with insulation; insulation won't help.

sophiecentaur
Gold Member
2020 Award
Outside water taps use remote valves with drained through-wall pipes. Sure, if you don't install the right kind it can freeze, but that has nothing to do with insulation; insulation won't help.
Putting a box of fibreglass insulation on an outside tap is enough to protect a wall mounted tap because of the heat coming out through the walls. But people don't take the problem seriously in the South of England because they mostly get away with it. Cavity wall insulation is still not that popular in UK.