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Radiant heating system design or installation mistakes that must be avoided.
This article explains how to avoid some fatal mistakes when installing radiant heat in a concrete floor slab by describing an incompetent radiant heat floor installation along with an explanation of why things went wrong and how to avoid these errors.
The workers in the photograph at page top, where our concrete slab was being poured, were not guilty of a thing. But the contractor who prepared the forms and under-slab insulation placed radiant heat floor tubing too deep in the slab and he omitted proper under-slab insulation.
The result: the owners ultimately had to abandon the entire radiant heated floor system.
Our contractor (Nightmare-works Construction), didn't want to insulate below the radiant-heat floor slab at all, insisting that "Once you get that dirt heated up below your floor your the earth will stay warm and your home will cost almost nothing to heat."
He was dead wrong - a SNAFU that led to complete abandonment of the heating system he installed.
How to avoid some really bad mistakes when installing radiant heat in a concrete floor slab. How our contractor ruined the installation our radiant slab heating system, causing its abandonment. How to place radiant heat tubing at the proper depth in a concrete slab. Building floor slab insulation design advice.
The nonsensical view that one can heat up the soil below an building slab on grade and that the soil would magically stay warm forever was put to the test experts when the author was five years old and the contractor was not even a gleam in his daddy's eye.
During February and March 1948, using a specially built, instrumented structure, Harlan Bareither and other experts and students at the University of Illinois Department of Mechanical Engineering conducted careful tests of various slab on grade floor and insulation designs to map heat loss, temperature, and moisture permeation characteristics of nine types of concrete slab subfloor constructions laid on the ground. 
Previously, the US National Bureau of Standards had already indicated that the heat loss of a concrete slab (floor) on grade (on the ground) is proportional to the perimeter of the building.
Bareither et als. referred to that work, but because the original testing was in warmer conditions (outside temperature had not been below 35°F. for more than three successive days), they recognized the need to test slab-on-grade floors in still colder conditions - in a climate where the ground is frozen during much of the heating season.
The 1948 heat loss research was important in part because it recognized that the rate of heat transfer from the heated building to the outside (earth and surrounding air) would be greater in proportion to the temperature difference between the heated space and the surrounding soils.
Photo: the radiant heat system that we had to abandon because of improper radiant heat tubing placement (too deep) and improper insulation below the slab (incomplete) includes the Thermolec B10-U electric boiler capable of providing 34,120 BTUH, circulator pumps, expansion tank, and radiant heat controls shown here as well as the entire tubing system. [Click to enlarge any image]
One exception to the general order of priorities of where to insulate in buildings (given at HEAT LOSS PREVENTION PRIORITIES) concerns homes built with slab-on-grade construction, particularly homes which have used radiant heat in the floor slab.
The contractor (Nightmare-Works Construction) for a small cabin in the North combined being opinionated and a bully with dismal ignorance of how to construct a properly insulated radiant floor slab. (See SLAB LOG CABIN SIDING for cabin photos and other comments).
Not only did the owners have to battle with the bully to put insulation under the entire slab (he thought that Mother Earth would be warming the home from "ground heat" (which is below 40 °F in winter there).
Owners also lost a battle to have the contractor install proper insulation around the slab perimeter with a frost wall before the floor was poured (he insisted on a floating slab with no inside-perimeter insulation plan).
Worst of all, the contractor also pushed the radiant heat tubing so deep into the concrete (ranging from 7" deep to more than 18" deep) that the entire radiant heat system was not useable at all. Running the radiant heat pushed heat faster into the ground than it did up into the building, even with foam insulation under the slab. We had to abandon the (expensive) radiant floor system and install alternate heating.
Details about this radiant floor slab heat failure and and research on its cause are provided below.
Also see SLAB INSULATION, PASSIVE SOLAR for a discussion of proper insulation below a heated floor slab.
Don't permit your contractor to make the (many) mistakes this one did. Insist that radiant heating in a poured concrete slab have these attributes:
After reviewing photographs taken during installation of the radiant heat floor slab described above, here's what we wrote to the owner and to the contractor:
I am doubtful that we can successfully and economically heat the cabin with radiant in floor heating as the current system is designed and installed, and it is unfortunately the case that the cost-to-cure is prohibitive as the slab would need to be completely replaced with one using proper insulation and tubing placement.
The bully contractor, who originally estimated the monthly heating cost for this small and otherwise well-insulated building, had said the owners would face winter heating bills of about $30./month based on his prior experience. Stunning heating bills arrived, exceeding $400./month or more than ten times the estimated amount. That's when we began digging into the installation details of this project.
The floor slab and radiant heat tubing had been placed by the contractor while we were unable to attend the jobsite.
When the heating bills were excessive and when the heat, running 24-hours a day for weeks, was unable to raise the interior temperatures above 60 deg .F., the contractor offered to "correct" the problem by installing larger capacity circulator pumps.
The most economical fall back is to install electric baseboard heating or possibly hydronic heating using the existing electric boiler which was installed to pump heated water through the radiant tubing in the concrete floor.
Meanwhile we shut down this unfortunate radiant slab heat system, installed a few portable electric heaters, and given the tight, well-insulated construction, we found we can keep the little cabin comfortable for a fraction of the cost of heating the earth underneath our floor with the contractor's heating installation.
James Darling, General Manager of Preferred Heating LLC, in Eagle River, WI commented on this article that the contractor's promise of heating the building for $20. a month was an unreasonable promise not to be relied on - one that could make the article above misleading. We agreed that the description of the failure of this installation needed some clarification, and added the following information that should be considered:
Keep in mind that this was a small new structure (624 sq.ft.) whose construction details, methods, materials were unusually well documented as a project. So the insulation, air tightness, materials, heating details were known.
The building was super insulated, tiny, airtight, with double-glazing throughout, leading to an expected low heating cost. If the owner's actual heating bills for the structure had been even five times what was promised for this building that was occupied only part-time, the owners would have been happy. Heating bills weren't the arm-waving promise of $20 per month, they were not $200. per month. They were more.
In fact, the utility cost to heat this tiny cabin resulted in bills that more than doubled the corresponding costs of the nearby 1960's vintage two story large old, comparatively poorly-insulated house on the same property, exposed to the same conditions. And the exploding heating costs were observed when heating the building well before the coldest part of the heating season.
The effects of putting the tubing deep into the slab created a problem of heat transfer losses to the ground, not just a matter of longer response time to warm the building. Even if money had been no object, the system simply could not heat the building to an acceptable temperature.
The problem with very deep radiant-heat tubing, combined with incomplete insulation, is that even with just 12 to 18" of concrete above the tubing, heat flowed enough into the ground below the building that even with the thermostat set to maximum, and running heat continuously for a week solid, in moderately cold weather (in the 40's in Northern Minnesota where in winter it can drop to 20 deg F below zero)
we never ever could get the indoor temperature above 59 to 60 °F. And this was in a new, small, airtight one-story well-insulated building.
even if we had continuous solid foam insulation under the slab, say R-10 for simplicity, if we have enough inches of concrete above, even though the "R" of concrete is much lower than the insulation, it's the total heat resistance by the total inches that comes into play.
If we have enough thickness of concrete above the tubing (Where 1" to 2" tubing depth is the best design and 6" is considered a lot, in this building we are looking at 18" or more at least in many areas, maybe 24"). With radiant tubing at those depths, the concrete begins to offer not just a lag time in heating (Mr. Darling's point) but also an actual resistance to heat transfer until we begin losing at least some heat into the ground.
The contractor and others tried to improve the system's performance by changing the boiler settings from those set by the manufacturer on its integrated circuit control board, upping the circulator size and capacity, checking flow rate through the system, checking the thermostat controls.
Our photo (left) shows where we found the radiant heat floor tubing when we later broke open a section of the floor slab. Radiant tubing was at the bottom of the slab, in this area more than seven inches down in the concrete, and set atop the foam sub-slab insulation.
Our photo above on this page shows that tubing was in some sections more than 18" deep, and adjacent to a large area where sub-slab insulation was simply omitted by the contractor.
We also measured floor temperatures in different areas of the building, mapping clearly where the radiant heat tubing dropped to the bottom of the footing-portion of the monolithic-slab footings! That deep run, probably combined with the incomplete insulation at the level drop between slab bottom and the integrated footings, were almost certainly the prime cause of the failure of this system to heat the building.
As our reference document(s) below show by calculation and model, ultimately, the heat flow into the ground for tubing really too deep in the slab can be significant, even if there is insulation below all or part of the slab. In the structure described here, not only was some tubing 12 to 18" or even more below the slab top, the insulation below the slab was incomplete, inviting ready heat flow into surrounding soils.
Despite varying opinion by some radiant floor installers, consumers, and installers as well should be wary of ignoring the advice of the radiant heating design experts and heat transfer engineers about tubing depth in radiant floor slabs shown just below.
Worse than too-deep radiant floor heating tubing, in this case, because the contractor put NO insulation at the area of soil where he stepped the slab down to the depth of the monolithic integrated footings, we have heat transfer from some of the tubing through concrete right into the cold soil, not just through concrete up into the room through the ceramic tile floor.
In this egregious error, even worse than putting radiant heat tubing too deep in the slab, insulation was simply omitted where the floating-slab monolithic footings were poured. The R-value of concrete is roughly .08/inch (US DOE). The builder located sections of the radiant tubing so that there was about 6" or less of concrete (in the 12" footing section") between the tubing and the cold soil, giving us a heat transmission path (tubing to soil) of R 0.24 or less.
This is a likely area of heat loss at all four sides of the building: where the slab dropped down to form footings.
As an aside the ceramic tile on the finished floor slab was set in mastic - leaving some air spaces and mastic that is a poor conductor compared with tile set in concrete (optimal) - but we doubt that's nearly as important in the system failure in this case.
Our photo (left) illustrates a successful radiant heat system installation in Minneapolis, MN - a climate similar to that where we had trouble with the Two Harbors system above.
THIS IS NOT OUR SLAB- which is has tubing at 6" deep and along one side where the tubing is deeper, 10-12" or more. We have better insulation but much deeper placement.
Here is a quote from the last page of the article which reports an expert's study of the heat characteristics that change as tubing moves lower than 3/4" from the top of the slab:
QUOTING except for [bracketed comments]
"These results indicate that tube depth does have a nontrivial effect on the thermal performance of a heated floor slab. There is a performance penalty associated with leaving the tubing at the bottom of the slab vs. positioning it near mid-depth of the slab.
The analysis performed was also based on steady state conditions. It doesn't predict the consequences of the longer response times associated with deeper tubing. These could be significant in situations where a building is recovering from a setback condition, or when heat flow from the slab needs to be reduced quickly to accommodate internal heat gains.
Considering the tradeoffs, perhaps it is time we pay more attention to quality control procedures to ensure that performance is not compromised as concrete is poured over radiant tubing circuits.
When future archeologists dig up the ruins of our buildings several centuries from now, will they ponder why we put the heating tubing at the bottom of the slab? Might they wonder if we didn't know any better? Would they conclude that some builders of the time were just too lazy to bother lifting the tubing? Thinking back to how ancient Romans used lead piping for water supplies, perhaps those archeologists will conclude that even after centuries of experience, we still had a hard time doing this pipe thing right.
[FIGURE 4 OMITTED], [FIGURE 5 OMITTED]
|Table of Insulation Material Properties|
|Average water temperatures needed for heat output of 15 and 30 Btuh/sq ft.|
|Upward Heat Flux Requirement (Btuh/[ft.sup.2])||Tubing Depth 2" Below Slab Surface, Average Water Temp. Required °F.||Tubing Depth at Bottom of 4" Slab, Average Water Temp. Required °F.|
|15 Btuh||95 °F||102 °F|
|30 Btuh||120 °F||134 °F (1)|
NOTE: (1) regarding the "134 °F" in the bottom right of the above table: This is moving down just 2" deeper. We estimate maybe 168 degrees water temperature would be needed at 4" down and well over 200 deg heating water would be needed in tubing 6" down. In the slab in our construction project, the critical tubing, leaving the heating boiler, was placed more than 12" deep in poured concrete. Heating energy costs will increase consistent with the increase in heating water operating temperature requirements.
John Siegenthaler, is a professional engineer specializing in radiant heat designs and heat transfer theory in buildings. Mr. Siegenthaler principal of Appropriate Design, a consulting engineering firm specializing in hydronic heating design. He is the author of Modern Hydronic Heating and Radiant Precision (available from the Radiant Panel Association (www.radiantpanelassociation.org, 800-660-7187).
Siegenthaler explains in various articles that the rate at which a hydronic heating system can actually move "sensible heat" from the heating source (perhaps hot water in tubing in a radiant floor slab) into the occupied space (perhaps a room in a building over such a floor) can be calculated as q=(8.01 x D x c) x f x (deltaT). This formula is not as intimidating as it may seem.
Reader Question from Wenell: I would like to know what the persons that wrote and researched this article thinks about what Montana has on research. On their web page MONTANA SLAB EDGE INSULATION ANALYSIS FOR 2006 IECC ADOPTION. There seem to be so many theories on this.
One thing we have found that if the soil conditions are quite damp, there definitely needs to have some type of insulation under the slab.
Another theory I have read is that the heat as it goes down, which it will, some is that it radiates horizontally, which makes insulating the edge quite well. - Wendell Schubloom
Wendell, there is not actually any contradiction between the Montana (DOE) research you cite above and radiant heat floor slab insulation requirements. The study you cite does not focus on radiant slab heating designs but or a more narrow question about the benefits of foundation/floor slab perimeter insulation. The DOE photo (below left) shows a typical Montana construction practice that gives a thermal break between a concrete floor slab (not yet poured) and the exterior foundation wall.
I've read quite a lot of supporting research on slab and slab perimeter insulation for radiant heat flooring, and I have some direct experience with installing radiant heat and more with inspecting radiant heat flooring problems.
Quoting from the conclusions of the Montana DOE-sponsored study you cite,  [photo at left showing interior foundation insulation before the slab is poured, U.S. DOE, op cit.]
This study shows that insulating slab edges with R-10 insulation to 4-ft depth along the slab edge saves about 3% annual energy and reduces annual fuel cost by between 1 and 2%. The energy savings vary slightly depending on the insulation configuration and building type.
Although the current installation practice in Montana does not extend the interior footing insulation to the top of the slab, based on empirical data, this study concludes that irrespective of the insulation installation configuration, Montana buildings will save energy by insulating the slab edge with R-10 insulation to a depth of 4 ft.
The payback period could vary from 4 years for small retail commercial buildings to 12 years in small office buildings.
This study, using eQUEST, Version 3.0 simulation modeling, compared full versus partial slab perimeter insulation schemes and found that there was useful energy cost savings even with partial insulation. The study data includes comparison with fully-insulated slabs too, but most important for our discussion, it does not address radiant-in-floor-slab heating designs that, without full insulation, can find an easier heat flow into the ground than into the building - not what we want to see nor pay for in heating bills. Quoting:
The local practice of insulating the slab footing on the interior allows heat loss along the slab perimeter and thus does not achieve the full savings that could be achieved with full edge insulation configurations, but the savings are still significant.
The risk in misinterpreting the Montana study conclusions above would be to apply them generally to radiant heat floor designs and that to improperly infer that complete under-radiant-heat-floor-slab insulation is not needed in cold climates. That study makes a general conclusion for all Montana buildings and by no means does the conclusion adequately address radiant in-slab heating system designs.
The fallacious concept held by the contractor in our horror story was that "once you heat up the earth below your building it will start "giving back" heat to the building and you'll be just fine. His theory was nonsense, as both expert advice and actual field experience proved.
The earth in a cold climate like Montana or Minnesota, is for practical and design purposes, an infinite heat sink. A radiant floor slab heating system will, if improperly designed, keep pumping heat into the ground as long as the heat is turned on. Forever. We saw this in astronomical heating bills and a cold building interior in the Minnesota home discussed above. Heat always flows, and continues to flow from a warmer material into a cooler material.
Heated the soil beneath a building where insulation was incomplete, inadequate, or omitted, will never reach some magic perimeter after which it stops sending heat into the surrounding soil any more than an ice cube placed into the sea will stop melting because it's "cooled down" the water around itself.
As the principal author of this material I relied largely on the concrete industry and the radiant flooring industry's radiant floor slab design specifications and advice  as they, above all, have a huge vested interest in their installations being successful.
There is no doubt that in virtually every radiant-heat-floor-slab design we need continuous insulation under the slab and at slab perimeter, though the appropriate insulation amount might vary depending on the local climate. The folks who seem to disagree have been people like the bully contractor who himself admitted he had never read instructions, attended a class, nor asked for expert advice.
As is often the case with small contractors in remote areas and without expertise, he was "winging it". Don't try mentioning "thermodynamics" or "heat flow theory" to a bully.
Just how bad an uninsulated, under-insulated, or incompletely insulated floor slab will perform with radiant in-slab floor heating depends on some additional variables: climate, soil moisture (read thermal conductivity as you suggest), and critically, the depth of tubing in the slab. In ALL cases we want the insulation in place.
But in the horrible installation we describe in these articles, the contractor not only provided incomplete and no perimeter slab insulation, he also buried the tubing so deep in the concrete that heat moved much more down into the cold earth than upwards into the occupied space. There was so much heat loss that we could not get the room temperature up even in cold but not bitter cold weather, and even though the same contractor had done a great job insulating the upper portions of the structure's roof and walls. (He was a framer/carpenter, and should not have attempted radiant slab installation nor tile work.) That's why we had to abandon the whole radiant floor installation.
If the floor slab had been very well insulated, the installation still would not have performed well because of the excessive tubing depth in the slab ( over 12" down in some sections ).
I appreciate the Montana reference and have added it to this article below at references .
We are in the steel building business so we have a lot of in floor heat done. with the experienced heating people we use, have had no problems.
But the question I have is- in North and South Dakota there is a Cat dealer by the name of ButlerCat.
They have built huge shops and I found out this spring what they do for floor hear.
They place the foam down and put the PEX directly to this and then place 4 to 6" of sand on top before pouring the floor. I ask why and was told if the have any floor problems they can remove any thing need to. They done this on I think four bldg's
What are your thought's
Wendell it's a fair question, and I welcome the disccussion. But I suspect this may be a case of intelligent people who think things up on their own, make up an explanation that sounds reasonable, but may not know the whole story.
The deeper you put radiant heating tubing in the slab the worse the heating system will perform in delivering heat to the interior. Furthermore, the thermal conductivity of sand is much below that of tubing directly in contact with the concrete slab itself.
The expert sources I found on this want tubing in the concrete and very close to the slab top surface, an inch or two at most down is best.
I agree that if there is enough insulation under the slab and it's well done and complete, in the design (foam, tubing, sand, concrete) you describe you will eventually probably warm the slab upper surface, but consider that there are heat flow rates through insulation too, it's not "heat proof".
With 6" of sand and say nominally 6" of concrete, your tubing is 12" down - way too deep, and furthermore, the first 6" of material (sand) between the tubing and the occupied space, does not quite the same level of thermal conductivity as tubing in contact with solid concrete.
The sources I cite at references below point out that there is heat flow resistance through concrete and sand as well. So while it may not be intuitively obvious, and while it's true that the thermal conductivity of concrete and even sand (which is not as good as concrete) is greater than insulation, if we have enough sand or concrete above the tubing, and little-enough insulation below the tubing, heat flow down through the insulation can still be significant.
Think of it as "heat flow resistance" through various materials. You can have a more conductive material above the tubing, but if you have a lot of it, the total heat flow resistance can still be significant.
Finally, the supposition that "if they have floor problems they can remove anything they need to" sounds highly suspect to me - it's not thought out. In any case you'd have to chop entirely through the floor slab to get to the tubing below, and meanwhile you are paying in higher heating bills than necessary over the life of the building.
The following un-edited discussions, a continuation of RADIANT HEAT MISTAKES, illustrates efforts to track down the reason that a radiant-heat slab system is not heating adequately.
Also see RADIANT HEAT DESIGN FAQs - questions & answers about installing & troubleshooting radiant heating systems
(Oct 16, 2015) Sue said:
The floor heats unevenly. Some spots are cold even though other spots are toasty warm. This just started last winter. Can the pipes plug up?
Yes individual circuits or loops can clog, particularly if they were run as separate loops off of a main. If there is a leak in radiant heat floor tubing the boiler may automatically take on make-up water through a water feeder valve so you may not recognize the leak, particularly if the leaking heating tubing leaks down into soils rather than up into the occupied space.
But a thermal scan of the floor can often find where leaks are occurring by noticing the spread of heat pattern.
2015/11/06 Melissa said:
I have a in floor heating system that we have been battling with for 2 years. The only time that it will heat up the floor is when the outside temp is warmer outside. The system cannot keep up heating when it is cold outside. Is it possible that insulation was missed. The plumber cannot figure out the problem and is close to washing his hands of it.
Yes, Melissa, certainly there could be missing or inadequate insulation. Have you done a thermal scan of the floor?
2015/11/07 Melissa said:
We have not done thermal imaging, but what exactly would that show, or should we be looking for if we are able to do it?
Additional information. Let's say we set the thermostat at 24 deg celcius. The thermostat will activate the pump and will send hot water into the floor. The pipe at the tank is almost too hot to touch. The tubes coming out of the floor are noticeably cooler. The temperature does not climb in the basement and therefore the thermostat never stops asking for heat. I have a few theories;
1) Improper insulation. The energy is lost before it has a chance to heat the slab and when the system loses too much energy the time it takes the tank to reheat the coil all is lost and the system starts from square one again, and this constantly repeats itself, and the system essentially continuously chases it's tail.
2) Pump is unable to circulate the hot water quick enough through the system, and is actually the reason why the system isn't able to stay ahead.
Our plumber wants to more the thermostat because he feels that the fish tank that is about 4 feet away may be pushing heat into the thermostat, confusing it. As well 4 feet below the thermostat is out fresh air vent, so the plumber feels that it may also be confusing the thermostat.
If you turn on and run up the heat the image will show hot and cold spots that might tell us that the layout was insufficient, the loops mis-run, that there's been a leak, or that there are sections that look uninsulated; a thermography scan of the building exterior can give similar information around the floor perimeter.
In the article above I document what happens in a cold climate if the insulation is incomplete or the tubing too deep in the slab.
Certainly you can test the plumber's idea by simply insulating the thermostat from the fish and from any warm air drafts but I doubt that's needed. It'd be appropriate IF the thermostat was turning OFF the heat - thus thinking that you're warm enough.
We are hoping that the problem isn't the lack of insulation. Is there any other problems that we could try to troubleshoot? We have switched out the thermostat already. The new one behaves the same way as the first one. The pump is definitely pumping, and we have a pressure gauge on the system showing rougly 18 psi at return.
I've suggested tubing too deep in slab and also tubing that runs through a too-cold section without proper insulation; you need to check the output and return temps at the boiler.
Thank you so much for your replies. Unfortunately I think in the end we may discover that this system will never work. It has been a long drawn out battle to try and get the plumber to come, and the plumbers next solution was to shut the system off and pretend it was never there with no refund of our money. We will bring in a different plumber and also look into the thermal imaging that you suggested. Thanks again!
I would not abandon the radiant heat system before we have a clear list of everything that has been investigated - so that we can compare that with other ideas that need to be checked. It would be a shame to give up on an installed radiant heat system as "unrepairable" only to discover years later that a tiny switch on a circuit board was not set to the proper temperature range.
2015/11/07 Melissa said:
I completely agree. I am hoping that the new plumber will be able to troubleshoot and try and figure out possible causes of why the system won't heat the slab. It seems like people who take a look at our system are completely baffled as to why it won't work. When we first got the system it only worked for a few short months in the winter, but it did work at one time.
I am just worried that the the plumber that I am bringing in won't be able to figure anything out for us, in which we will be left with a very expensive system that just won't work. Anyway the plumber is coming in a few days so we shall see.
As I often discover in longer discussions with clients or readers, more clues emerge. The fact that your radiant floor heat worked properly at one time suggests that (barring something odd like a rising water table) the concerns of a innate design or installation errors such as tubing too deep or insulation left out are pretty much squashed.
So it sounds more like a control problem or even a tubing damage or leak or obstruction.
Before bringing in a plumber let's do some detective work: get a detailed thermographic scan of the floor and of the perimeter of the bottom of the building in cold weather with the heat on.
Send me the results.
See THERMAL IMAGING, THERMOGRAPHY for an introduction to thermography and what to expect.
Continue reading at RADIANT HEAT TEMPERATURES or select a topic from closely-related articles below, or see our complete INDEX to RELATED ARTICLES below.
Or see RADIANT HEAT MISTAKES FAQs - questions, comments, arguments posted originally at this page.
Or see RADIANT HEAT DESIGN FAQs - questions & answers about installing & troubleshooting radiant heating systems
Or see FLOOR TILE INSTALL on CONCRETE where we discuss cracks that appeared in the ceramic tile installed over the failed radiant heat floor discussed in this article
Or see SOIL R-VALUES
Or see THERMAL MASS in BUILDINGS
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