Sizing of insulation for pipes in unheated floor voids

[Thersites]

Coming to the problem fresh, I imagined that there will be a 'sweet spot' for insulation sizing for each size of pipe and for each ΔT that reflects the law of diminishing returns.

Has anyone already done calculations on heat losses that can validate or refute my approach to this?

Using the formula: Q = 2*(pi)*k*L(T1-T2/[ln(r2/r1)]

Where Q = heatloss, k is thermal conductivity of insulator, L is pipe length, T1 & T2 are ext and internal temps, ln is natural log, and r2 & r1 are outer & inner radii of the insulation. Using 0.038 as k (for Armaflex at 40degC) & for 22mm copper with ΔT70 I get 36W loss per metre with 13mm Armaflex and still 22W with 25mm Armaflex.

This is rather higher than I imagined I would find, even using the best and most expensive pipe insulation available for domestic settings. What do others think? Have I made a methodological or calculation error?

 

[John D v2.0]

Not sure what you're coming at afresh, but Yes it does seem excessive, you could use insulated pipes as a radiator if that were the case.
I'm not sure what the divide by ln of the diameters is but usually conductivity needs multiplying by length which you've done and dividing by the area. The area of 15mm pipe is 2xpix0.015 so you need to divide the whole thing by that, the 2pi seems to be multiplied in your equation.
I'll take your word that the ln thing is finding the relevant average radius in some way.
If you divide your 36w by 4xpi² then you get about 1w which does seem more reasonable.
Finally Delta t of 70c seems a lot unless you're running your heating on full belt or the pipes are run outside. The floor void will be relatively warm even in winter.

 

[endecotp]

Coming to the problem fresh, I imagined that there will be a 'sweet spot' for insulation sizing for each size of pipe and for each ΔT that reflects the law of diminishing returns.

Has anyone already done calculations on heat losses that can validate or refute my approach to this?

Using the formula: Q = 2*(pi)*k*L(T1-T2/[ln(r2/r1)]

Where Q = heatloss, k is thermal conductivity of insulator, L is pipe length, T1 & T2 are ext and internal temps, ln is natural log, and r2 & r1 are outer & inner radii of the insulation. Using 0.038 as k (for Armaflex at 40degC) & for 22mm copper with ΔT70 I get 36W loss per metre with 13mm Armaflex and still 22W with 25mm Armaflex.

This is rather higher than I imagined I would find, even using the best and most expensive pipe insulation available for domestic settings. What do others think? Have I made a methodological or calculation error?

I believe your maths is right though you’re missing a ) after T2.

Your delta T is rather high, where is that from? Don’t have the boiler flow temp higher than it needs to be; lower flow temp also improves the boiler efficiency.

If you hold an insulated pipe how warm do you expect it to feel? I’d say you numbers seem about right.

In many cases the lost heat is not really lost as the pipes are inside your house.

Sometimes people post plumbing photos here and I reply “lag those pipes!’; this is why.

 

[OvertonPlumber]

Kingspan Kooltherm Phenolic Pipe Insulation

 

[Ryler]

What do others think?

If the pipes are within the fabric of the building then heat loss is negligible if they are not insulated.

 

[Thersites]

I believe your maths is right though you’re missing a ) after T2. Your delta T is rather high, where is that from?

Thank you very much endecotp for a thoughtful reply (and for spotting the bracket missed out in transcription!). The high ΔT comes from considering a worst case scenario - zero ambient degrees in the underfloor space and 70degC in the flow. I have sized the emitters for ΔT40 inside the building (flow 70 return 50) which is as large as we can tolerate in our old house which, even though it now has a new warm roof (U1.8), D/G sashes, full GF UF insulation and partial EWI (1/3 external walls) still has a heat loss of 24kW.

I sought validation of the maths partly because the heatloss from the pipes still seemed high even with the thickest (and very expensive) Armaflex available, and because when I played with the calculations in a spreadsheet, it became truly vast as the insulation thickness approached zero. This made me wonder if I had picked the correct equation for the purpose. I've assumed I couldn't run these pipes in the (Steicoflex) UF insulation because I assumed the localised heat would warp the pine floorboards immediately above.

Thanks MrBenchmark for the Kooltherm suggestion - so far, I have seen it only for large pipe diameters, not for 15 & 22mm. I will look again. I imagine a mixed economy of Kooltherm with Armaflex for the bends would be necessary.
And Ryler, the pipes are not within the fabric of the building - they are in the subfloor beneath an insulated suspended GF which we are ventilating as much as possible to keep dry. So I'm treating these as outside pipes.

 

[endecotp]

it became truly vast as the insulation thickness approached zero.

As it approaches zero you need to model the conductivity of the copper and the nearby air to get a useful answer.

I think I would have embedded them in the steicoflex myself. Do you have a lot of wood fibre offcuts?

Insulation Superstore claim to normally stock a 15mm Kingspan product, but it’s not currently available and it’s only 15 mm thick:
https://www.insulationsuperstore.co...ion-lagging-by-kingspan-15mm-x-15mm-x-1m.html

 

[M1957]

Coming to the problem fresh, I imagined that there will be a 'sweet spot' for insulation sizing for each size of pipe and for each ΔT that reflects the law of diminishing returns.

Has anyone already done calculations on heat losses that can validate or refute my approach to this?

Using the formula: Q = 2*(pi)*k*L(T1-T2/[ln(r2/r1)]

Where Q = heatloss, k is thermal conductivity of insulator, L is pipe length, T1 & T2 are ext and internal temps, ln is natural log, and r2 & r1 are outer & inner radii of the insulation. Using 0.038 as k (for Armaflex at 40degC) & for 22mm copper with ΔT70 I get 36W loss per metre with 13mm Armaflex and still 22W with 25mm Armaflex.

This is rather higher than I imagined I would find, even using the best and most expensive pipe insulation available for domestic settings. What do others think? Have I made a methodological or calculation error?

What values are you using for r1 and r2?

If the outer diameter of the pipe is 22 mm then radius r1 = 11 mm.
With an insulation wall thickness of 13 mm, r2 = 11+13 = 24 mm.

Using these values I get 21.4 W/m with the 13 mm insulation (considering only conduction through the insulation).