Lagging pipes

Many (many) years ago, my old physics teacher told us (though I may have been the only one listening) that lagging pipes to prevent heat loss was a waste of material after a certain point.  This was because the thermal conductivity of the lagging increases (relatively) as its cross-sectional area increases with the radius of the lagging (x the length of the pipe insulated), thus making the "resistance" to heat loss less.  Furthermore, as the surface area of the lagging increases in direct proportion to the radius of the lagging, the heat loss from that surface will increase in similar fashion.  Obviously, it is important to lag pipes, but, what is the ideal thickness of the lagging?
20:04 Sat 19th Feb 2005
 
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OK this one has been bugging me, I'm pretty sure it's wrong but couldn't quite see why.While my thermodynamics is pretty rusty I think I've got it sorted now but I stand to be corrected.

The Energy flow by conduction per second is directly  proportional to the area and the temperature gradient i.e.

2 pi.r l (T1-T2)/r where r is the lagging thickness, l the length of pipe and T1 and T2 the inside and outside temperature respectively.

so the energy flow per second of the lagged pipe *by conduction* is not dependant on the thickness of the lagging.

However the temperature at the surface of the lagging is much reduced due to the larger surface area, and the energy lost by radiation is directly proportional to the surface area (which is directly proportional to the thickness of the lagging) but proportional to the fourth power (ie the square of the square) of the temperature.

As the energy lost by a pipe is mostly by radiation it is highly dependant on the surface temperature and that is why thicker is better. 

I'm grateful to this website for aiding my failing memory

 http://online.cctt.org/physicslab/content/PhyAPB/lessonnotes/thermodynamics/lessonthermodynamics.asp

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I do not think you are right about most heat being lost by radiation, Jake.  You will know that so-called radiators should really be called "convectors" or "convector-heaters".  And isn't the heat loss through radiation proportional to the DIFFERENCE between the fourth power of the absolute temperature of the radiator and the absorber? So when you have the "right" amount of lagging, the temperature of the outside of the lagging will be pretty much the same as the surroundings, so the heat loss through radiation will be pretty small.
-- answer removed --

That's my point if you have more lagging the surface temperature of the lagging is lower, reducing the difference in temperature between the lagged pipe and the environment compared to the unlagged or thinly lagged case.

However as I say I stand to be corrected here, the main thing that worries me is that it seems that lagging doesn't reduce the rate of energy loss between the pipe and the surface of the lagging and that the drop in temperature is only due to the increased surface area that the energy spreads out over - is that right?? 

Fear not, you can all rest easy now... I 'studied' mechanical engineering at the university of hertfordshire and I distinctly remember the conclusion of one of our thermodynamics lectures was that if rc (critical radius) is exceeded, then the lagging becomes less effective.

Unfortunately, this was a third year module, by which time I was quite tired of listening. I don't remember why, but it is definately true! If you want to know the actual answer, speak to Dr Sammi Nasser at the university of hertfordshire. The man is a thermodynamics legend!
If the material used for lagging is an insulated material ,then where is the question of heat loss from the lagged surface? pls let me know

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Does anybody know if it is ok to use pipe lagging on hot water pipes? thanks
Muppit, what took you so long? Thanks for the contact name at U of Herts. I am amazed that you found my two-year-old question and took the trouble to answer it. Thanks again. Bert

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