Green Building Forum - Copper or plastic pipe for solar thermal

Copper or plastic pipe for solar thermal

Ed Davies — Thu, 19 Jan 2012 13:06:47 +0000

By my rather crude approximation, a 10mm pipe with 40 mm of insulation at 60 K above ambient would lose 1 K about every 25 seconds. Obviously at more reasonable temperatures it takes a bit longer. Still, ten minutes of cloud....

Copper or plastic pipe for solar thermal

JSHarris — Thu, 19 Jan 2012 13:25:27 +0000

Interesting; seems surprisingly high to me, even for the steep part at the start of the exponential curve. What value of decay constant did you use?

Copper or plastic pipe for solar thermal

Ed Davies — Thu, 19 Jan 2012 14:50:12 +0000

Here's my calculation, all done per metre of pipe:

10 mm O/D, 8.8 mm I/D, 61e-6 mÂ² cross-section.
Density, 1000 kg/mÂ² and SHC 4180 J/kgÂ·K so linear heat capacity 255 J/mÂ·K.

40 mm of insulation with a conductivity of 0.04 W/mÂ·K - wild guess, probably a bit too conductive but also a bit thick. U value 0.04/0.04 = 1 W/mÂ²Â·K.

Crude approximation by ignoring the fact that there's less area on the inside of the insulation than the outside: assume the area of the insulation is the area half way out, radius about 25 mm (half 40 mm plus radius of pipe) so 2Â·PIÂ·r = 0.16 mÂ²/m so heat loss is 0.16 W/mÂ·K.

At 60 K temperature difference heat loss is 9.6 W/m.

(255 J/mÂ·K) / (9.6 W/m) = 26.56 seconds/K

Copper or plastic pipe for solar thermal

JSHarris — Thu, 19 Jan 2012 15:49:02 +0000

The snag I can see there is that the cooling of the pipe when the pump is turned off will follow Newtons Law of Cooling, where the rate of heat loss at any instant is proportional to the temperature differential at that instant. This will give an exponential curve, where as the pipe cools the rate of heat loss drops, so slowing the rate of cooling. To solve the differential equation we need the decay constant, k, which short of going and measuring it experimentally it I'm not sure how to derive.

Copper or plastic pipe for solar thermal

Ed Davies — Thu, 19 Jan 2012 16:39:07 +0000

But we're only looking for rough orders of magnitude.

Anyway, supposing we did want a bit more precision then the maths is probably not too hard but using a computer is even easier:

> function tempLossRate(temp) { return 0.16/255 * temp; }
> var dT = 1.0;
> var t = 0.0;
> for (var temp = 60; temp > 0; temp -= dT) {
... console.log(temp, t);
... t += dT / tempLossRate(temp);
... }
60 0
59 26.562499999999996
58 53.575211864406775
57 81.05366014026885
56 109.01418645605833
55 137.47400788462977
54 166.4512806119025
53 195.96516950079138
52 226.0359242177725
51 256.68496267931096
50 287.93496267931096
49 319.80996267931096
48 352.3354728833926
47 385.5385978833926
46 419.4481723514777
45 454.0949114819125
44 489.5115781485792
43 525.7331690576701
42 562.7971225460423
41 600.7435511174708
40 639.615502336983
39 679.459252336983
38 720.3246369523677
37 762.2654264260518
36 805.3397507503762
35 849.6105840837096
34 895.1462983694239
33 942.0212983694239
32 990.3167529148784
31 1040.1214404148784
30 1091.5327307374591
29 1144.6577307374591
28 1199.6146272891833
27 1256.5342701463262
26 1315.562047924104
25 1376.860124847181
24 1440.610124847181
23 1507.016374847181
22 1576.3098531080504
21 1648.7530349262322
20 1724.6458920690893
19 1804.3333920690893
18 1888.2149710164576
17 1976.7566376831244
16 2070.5066376831246
15 2170.1160126831246
14 2276.3660126831246
13 2390.2052983974104
12 2512.801452243564
11 2645.613952243564
10 2790.5003158799277
9 2949.8753158799277
8 3126.958649213261
7 3326.177399213261
6 3553.8559706418328
5 3819.4809706418328
4 4138.230970641833
3 4536.668470641833
2 5067.918470641833
1 5864.793470641833
7458.543470641833

So it's down to 40 Â°C after 10 minutes, at 20 Â°C after half an hour and 6 Â°C after an hour.

Copper or plastic pipe for solar thermal

JSHarris — Thu, 19 Jan 2012 17:05:59 +0000

Looks reasonable as an approximation, although I'd still like to measure the rate of cooling to get a feel for the value for the decay constant, k in the cooling equation, dT/dt = k.(T1 - T2)

Copper or plastic pipe for solar thermal

Ed Davies — Thu, 19 Jan 2012 17:20:34 +0000

Doesn't k = 0.16/255 = 0.000627 K/(sÂ·K) = 0.000627 sâ»Â¹ ?

Copper or plastic pipe for solar thermal

JSHarris — Thu, 19 Jan 2012 17:34:20 +0000

Posted By: Ed DaviesDoesn't k = 0.16/255 = 0.000627 K/(sÂ·K) = 0.000627 sâ»Â¹ ?

Yes, possibly, but the reasons I'd like to do a measurement to confirm it are that the U value of the insulation will vary with temperature a bit (the range is outside that where we can presume it's reasonably constant, I think) and the copper pipe will add a small bit of thermal capacity. It's probably a moot point, anyway, as there are undoubtedly much big sources of performance variation in any given system.

I remember calculating the rate of heat loss for a cup of tea years ago (trying to demonstrate that putting the milk in first kept the tea hotter for longer to resolve a small domestic disagreement) only to find that the actual rate of cooling when I did the experiment (two identical mugs filled with hot water one with milk, the other without, and a data logger hooked up to two temperature probes) was quite a lot different in practice to that predicted.

Copper or plastic pipe for solar thermal

TimSmall — Thu, 19 Jan 2012 22:21:29 +0000

Posted By: JSHarrisbut the saving is so modest when compared to 15 mm pipe that I doubt it's worth worrying about unduly

It is a small effect overall, but given that (assuming that you've decided to use copper anyway) - the 10mm is both much easier to install than the 15mm and also better performing, why bother with the 15mm?

Copper or plastic pipe for solar thermal

djh — Thu, 19 Jan 2012 23:33:04 +0000

Posted By: Ed Davies13 2390.2052983974104

Impressive precision!

Crude approximation by ignoring the fact that there's less area on the inside of the insulation than the outside

There's a specific formula for the Y-value of pipe insulation (I think they're called Y-values when they are linear rather than U-values for areas). I expect it's on the Navi site somewhere or else google will throw it up. I do remember there are magic values involved ('critical radius').

And Tim, yes!

Copper or plastic pipe for solar thermal

Ed Davies — Fri, 20 Jan 2012 10:34:08 +0000

Posted By: djh
Impressive precision!

Well, yes, I did wonder if +/- 1 microsecond would be good enough.

There's a specific formula for the Y-value of pipe insulation (I think they're called Y-values when they are linear rather than U-values for areas). I expect it's on the Navi site somewhere or else google will throw it up. I do remember there are magic values involved ('critical radius').

Yes, I have seen that somewhere but was just doing a quick and dirty calculation so didn't bother to search. It's a bit magic as I recall as it only needs the ratio of the inner and outer radii, not the absolute values, as the scale cancels with the circumferences if you see what I mean.

Yep, Wikipedia says:

http://en.wikipedia.org/wiki/Pipe_insulation#Heat_flow_calculations_and_R-value

This has some significance here. 20 mm of insulation on a 10 mm pipe will be coming up to twice as effective (from the W/(mÂ·K) point of view) as 20 mm of insulation on a 22 mm pipe.

Copper or plastic pipe for solar thermal

djh — Fri, 20 Jan 2012 13:29:23 +0000

It's even more magic than that. Adding a bit of insulation to a pipe actually makes it lose MORE heat than before. The rate of heat loss increases up to the 'critical radius' and then starts decreasing. Some extra thickness later it gets back to just losing as much heat as the naked pipe and after that more insulation actually does something useful.

http://www.raeng.org.uk/education/diploma/maths/pdf/exemplars_engineering/2_SteamPipe.pdf

(or see p72 of http://web.mit.edu/lienhard/www/ahtt.html)

and just to illustrate what a dodgy place the internet is, have a look at this one, which gets it totally wrong: http://www.reviewpe.com/penotes/heat_t/b5_3.htm and even wikipedia gets it partly wrong http://en.wikipedia.org/wiki/Heat_transfer#Critical_insulation_thickness

Copper or plastic pipe for solar thermal

wookey — Fri, 20 Jan 2012 14:30:56 +0000

That's quite remarkable, and most unintuitive. The maths in that paper had integrals in it which is where I always lose the plot. Why does a small amount of insulation make things worse?

Copper or plastic pipe for solar thermal

JSHarris — Fri, 20 Jan 2012 14:52:37 +0000

Thanks for posting those links. Don't you just love it when you find something like that out? I hadn't for a moment thought about the increase in surface area effect, but having read that I'm now sitting here scratching my head and wondering if dementia is setting in early.............

Copper or plastic pipe for solar thermal

Ed Davies — Fri, 20 Jan 2012 17:24:03 +0000

Posted By: wookeyWhy does a small amount of insulation make things worse?

DJH's last link (Wikipedia) explains it very succinctly.

Copper or plastic pipe for solar thermal

pmusgrove — Fri, 20 Jan 2012 19:03:04 +0000

Fascinating stuff but the good man from Rolls-Royce was interested in steam pipes of radii 60mm. The graph we need to see is that relating to water at about 65C in a pipe of radii 15mm. Has anyone worked those figures through the formula to find out the critical thickness of insulation?

Copper or plastic pipe for solar thermal

wookey — Sun, 22 Jan 2012 23:18:11 +0000

DJH's last link (Wikipedia) explains it very succinctly.

True, but he posted that with the caveat that it's 'partly wrong', so I wasn't sure how correct it was. So the explanation is that surface area increases faster than heat-transfer attenuation to start with. Fair enough. Now DJH needs to say what part is wrong.

Copper or plastic pipe for solar thermal

djh — Mon, 23 Jan 2012 14:13:50 +0000

Posted By: wookeyNow DJH needs to say what part is wrong.

I already did, on the Talk page

The description on this page is wrong.This sentence has the logic reversed "The point where the added resistance of increasing insulation thickness becomes overshadowed by the effect of increased surface area is called the critical insulation thickness." It should read "The point where the added resistance of increasing insulation thickness overcomes the effect of increased surface area is called the critical insulation thickness."

Copper or plastic pipe for solar thermal

crusoe — Mon, 23 Jan 2012 19:59:05 +0000

Pedantic semantics aside, plastic pipe (mlcp) is used in places with as much sun as Mallorca, and has survied several seasons to my knowedge. I've had to add to such systems, and had to use the same material, to avoid ripping out and starting again. But in principle, copper or ss - depending on your ideology - neither has massive advantages - are the materials for the job.

Many panels stop at a max 180C, (30C direct sun, not your usual UK conditions) many have drainback, with oversize storage so temps can't reach stagnation levels, so use of plastic in some parts (return) of a system may be countenanced in future legislation. But to be safe here, for all classes of reader, we're better sticking to metal.