Physics of Heat Transfer of Radiant Tubing

This is a new topic dedicated to the physics of heat transfer in radiant tubing. I'm going to cover some physics heat transfer concepts and discuss various materials and their heat transfer properties. I would like to keep this topic to physics concepts only - if you want to discuss material properties outside of their thermal properties - please link to another topic where these concerns are discussed.

Difference between Thermal Resistance (commonly denoted as R-value) and Thermal Mass:

Thermal Resistance is a measurement of a material's resistance to heat flow.

Wikipedia on Thermal Resistance: http://en.wikipedia.org/wiki/Thermal_resistance

Table of Thermal Conductivity of Materials: http://wiki.gekgasifier.com/w/page/6123766/Insulation%20Data - please note units are System International (SI) - Thermal conductivity is the inverse of thermal resistance.

The table linked above has some surprising numbers. Dry sand has a thermal resistance of 4-6.6667 (mK/W). Converted to IP units: 0.576 - 0.96 R-value/inch. For comparison, different types of wood have a thermal resistance varying from 18.18 mK/W for balsa wood to 8.33 mK/W for softwoods and 5.88 mK/W for oak. IP Units: Balsa: 2.6 R-value/inch; Softwoods: 1.2 R-value per inch; Oak: 0.8476 R-value per inch. So dry sand can me MORE thermally resistive than wood!

SATURATED sand is quite conductive 0.25 - 0.5 mK/W. IP Units: 0.036 - 0.072 R-value Per Inch.

In another topic, a poster said something like "there's no way that sand and wood have the same thermal properties!" But, we've just seen above that they can have similar insulating properties. They have very different thermal Mass:

Thermal Mass is a measurement of a material's ability to store heat

Wikipedia on Thermal Mass: http://en.wikipedia.org/wiki/Thermal_mass

Water has the highest heat capacity of common materials. Here's a table I put together of common materials and their thermal mass:

SO, sand can have a higher thermal mass than wood, but it really helps if it is wet.

I think I'm limited to the number of images I can post at one time, so read on for how this effects radiant tubing and heating effectiveness.

Radiant tubing heat transfer effectiveness:

I won't write it all out here, because there is a really well written argument that goes over how radiant heat works, and some of it's benefits:

http://www.taco-hvac.com/uploads/FileLibrary/Radiant_Floor_Heating_-_ASHRAE_Journal_2002-7.pdf

Specifically, look at page 5 of the PDF (labeled as page 23) - there is a table that shows how the floor surface temperature effects the heat output of the floor. How does this relate to the discussion of materials above? I'll show you:

When radiant tubing is installed below an insulating material, it requires hotter temperature water to get the surface temperatures required to heat the space.

The two images below show the difference in floor surface temperature when tubing is embedded in dry sand versus wet sand. In both cases, the heat source is 1/2" tubing 1.5" below the floor surface. The tubing temperature is 105 F and the room is assumed to be 72 F. The lower boundary is assumed to be adiabatic - no heat transfer or perfect insulation below. This is not achievable in reality, but for now I want to focus on the effects floor material has on floor surface temperature. The floor surface is the green line at the top of the image.

The surface temperature for the dry sand varies from about 75 F to 78 F. For wet sand, surface temperatures vary from 87 to 92F. According to the paper linked above, the difference between using these two materials means that just by changing the material, the heat capacity of the floor doubles.

Hi Karen,

I just can't find the suggested quote as written about wood and sand similarities, either by me or someone else. I do believe what I wrote was:

Jay C. White Cloud wrote:Wood and sand simply are two vastly different materials and have completely different thermal storage capacities, and physical dynamics. Repeating "advertised" information as "good science," rather than the "comparative advertising" that it is does conversation like this a disservice in my opinion and the information from such companies is "subjective" at its best.

It is just my thoughts and conclusions that wood and sand don't share that much in common when it comes to overall physical characteristics. I would like to suggest perhaps that there is a lot of murky statistics on the internet and we have to be really careful with them...

Regards,

j

Hi Jay,

First of all, I'm sorry if I offended you for not quoting you directly. I did not mention your name, and I summarized a concern that came up in another thread. I don't want to get into a long argument about this, so I hope you can accept this apology and we can concentrate on discussing physics in this thread.

The wiki page that I linked that has the thermal tables used units of thermal conductance (W/mK). Because and most people think of insulating material in terms of thermal resistance, the numbers I quoted are inverted, ie mk/W instead of W/mK. If you want to get my numbers, just divide the number 1 by the numbers listed in the table.

Here are a couple other links for thermal properties of materials. Please be aware of units on all sites, and not all sites cover all materials:

http://www.coloradoenergy.org/procorner/stuff/r-values.htm

ASHRAE 90.1 has thermal properties of common conventional construction. Unfortunately, this document must be purchased.

This paper also discusses thermal properties of different materials, and has lots of valuable information including an extensive list of documents for further reading: http://www.bre.co.uk/filelibrary/pdf/rpts/BR_443_(2006_Edition).pdf

This is an incredibly detailed paper about the thermal properties of soil: http://www.eng.usf.edu/~gmullins/downloads/Thermal/Thermal%20Properties%20of%20Soils.pdf

http://www.new-learn.info/packages/clear/thermal/buildings/building_fabric/properties/conductivity.html

two academic papers about determining the thermal conductivity of soil mixtures:

http://www.hou.usra.edu/meetings/8thmars2014/pdf/1107.pdf

I hope you can forgive that this paper is hosted by a geothermal company website. If not, I think I've provided enough information above to back up my original calculations:

http://www.geothermal-energy.org/pdf/IGAstandard/WGC/2010/2952.pdf

I will cover the thermal mass effects of radiant heating as it relates to tubing buried in a particular material. It does take some time to find the resources and do the calculations.

Hi Karen, et al,

I am not, nor actually have ever been "offended" by anyone...

I do get confused sometimes with the logic that is applied to situations, or by the way information is taken or disseminated. I own (apologies for this) that my tone too often is "show me" or "prove it" within my personal nature, yet as a native southern Missourian, as well as being an academic myself...its kind of the culture (no excuse just a reason for what seem to be a "tone" in my writing sometimes.)

Karen Walk wrote:...Dry sand has a thermal resistance of 4-6.6667 (mK/W). Converted to IP units: 0.576 - 0.96 R-value/inch....

I appreciate the many links and will go through them slowly as I try and digest the data. In the interim (presuming of course that this has been done?) can you help with a basic run down of how you verified-vetted the math behind these figures in the above quote? Was it by doing the math yourself or by demonstrated data results of the same outcome in many sources? As stated before, they are not reflected in the data I can find, nor are they reflected elsewhere in the many sources I have cross referenced with. I am still really lost about these stat's as they don't seem to reflect the usual averages and I am either missing something or seeing this data out of context. That is why I reached out to Terry Ruth to see if he can shed some additional light on these numbers?

So to begin with the basics of this, can you please demonstrate how "dry sand" has an R Factor of almost 1 (you referenced arriving at a number of 0.96.) Everything I can get my eyes over reflects sand never having an R Factor higher than 0.09 which is 10.67 times less than stated in your quote (0.96/0.09=10.66666667) This makes it a "very poor insulator" but a wonderful thermal capacitor.

I think it is reasonable and fair that I am skeptical of much of what is reflected in these numbers (though willing to discuss them) as in many of the documents there is probably more reference to "theory" and "averages" than empirical hard data wilt long term and undeviating results or what is called DVR (data validation and reconciliation.) As has been reflected in much of my writing, I stand by being very pragmatic, which can be both a gift and a curse.

I am a very open minded "free thinker" as I love art and creativity, however, being a long time student of the building sciences I can share with other readers that "extrapolating"...good data...for much of what comes out of these statistics is difficult at best and can only be used as "averages." When we find a 10.67 deviation from "know reported averages" for a materials then something is "afoot, or afoul."

So before we get to deep into a great deal of information (and theory) lets just examine this reflected inconsistency...above...... That would be great!

Regards,

j

Hi Jay,

I want to respond to your question. I don't know exactly where your numbers are coming from, but I think it'll help if I take you all the way through an example.

Let's do Oak Wood.

On this site: http://wiki.gekgasifier.com/w/page/6123766/Insulation%20Data

Oak is given a thermal conductivity of 0.17 W/mK

W (watts) is a rate of energy use.
m (meters) is a unit of length
K (Kelvin) is a unit of temperature

In my original post, I converted to units of thermal resistance, because that is how most people think. So we have:

1/(0.17 W/mK) = 5.88 mK/W

This still doesn't make much sense to people in the US because we are still stuck on IP units.

If you look at the website, there is a conversation table, and we can use it to help us convert to IP units. The IP units I choose are:

Btu in / (h ft2 oF)

Btu (British Thermal Unit) this is a measurement of energy, and is the amount of energy needed to raise one pound of water one degree Fahrenheit

in (inch) unit of length

h (hour) unit of time.

ft2 (square feet) unit of area

oF (degrees Fahrenheit) unit of Temperature

According to the conversation table, to convert from W/mK to Btu in / (h ft2 oF) multiply by 6.94

So, for IP units of thermal conductivity,
6.94*(0.17 W/mK) = 1.1798 (Btu in / (h ft2 oF))

For IP units of thermal resistance:

1/(1.1798 (Btu in / (h ft2 oF))) = 0.8476 (h ft2 oF) / (Btu in)

These units are very confusing but they are the actual units behind the R-value per inch I quoted above.

My $0.02 worth:

You're both right!

Individual quartz grains have low heat resistance... not a good insulator, but how the grains are arranged matters a lot.

Think about solid granite or concrete... very low heat resistance, made of quartz grains (and other stuff) all packed together. The key point is that there are no air spaces. Air makes insulation work. So if you make a layer of sand than maximizes the airspaces, and minimizes the contact between grains, then you have a good insulator (far better than the same mass of granite).

The best sand insulator, then, is made of grains that are all the same size (to maximize pore space), are round (so the contact between grains is a single point), and dry.

Adding anything between the grains changes the sand from a good insulator to a poor one - it replaces the insulating air spaces, and increases the number of contact points between grains that conduct heat. If you fill in all the pore spaces with smaller grains, you have rammed earth - poor insulator, but excellent thermal flywheel.

So you can find, or make, sand with a wide range of insulative properties, by choosing the moisture, particle shape and size distribution. Dry, well sorted, round-grained sand = good insulation... wet, unsorted, sharp sand = poor insulation.

...

For the purpose of making a floor with high heat capacity and low heat resistance (high conductivity), sand needs some help - sharp sand is a little better than round, a mixed range of sizes is better than well-sorted, and adding a little silt and clay helps a lot to fill in the interstitial air spaces to increase conductivity.

...

BB

Hi Karen,

I do want to thank you for putting forth this kind of effort for trying to make everything clearer...

I also just want to share with others readings of this post thread, that while important to understand these different material dynamics, and how "we think" all this may work, much of this is extremely academic and theoretical...

As I have described myself already...I am slow when doing this stuff (mainly because I don't do it enough anymore..) and because much of it is so generic and or broad in comparison between what happens in the "lab" to get these number and what happens in the real world with how these materials behave I lost interest years ago, as the actual "real world" performance in a dynamic living environment seldom follows these numbers and they must be worked up for every single temperature, humidity, and atmospheric pressure variant not just a specific factor like a material at the temperature of, "25 degrees Centigrade."

Its been my experience and others that I correspond with even here like Terry Ruth, et al, that we get way more "why did that happen??" than we get "that worked as expected" when dealing with material dynamics in modern applications and trying to understand there possible reasoning of use in history. So I actually have done these equations many times and they must rely on projected charts unless we literally go all the way down to "scratch" which is where I would love to go, but have found that even this has so many variables it soon reveals that much of this is a really "new ground," in the world of building and material science and highly capricious when we try to narrow it down to specifics.

So even with oak at 25 degrees Centigrade, we are challenged with a very narrow range compared to real world applications. Oak's given thermal conductivity (as with many hardwoods) is actually shown as 0.16 W/mk in the referenced chart, not 0.17 W/mK. I don't mean this observation as finding fault with Karen's math per se, yet more as evidence that when employing these figures things can get off really quickly when attention to detail is lost or all the math isn't really well understood as it needs to be if we are to even going to extrapolate "theoretical" behaviors in the materials we try to examine..

1/(0.17 W/mK) = 5.88 mK/W

Compared to:

1/(0.16 @/mK) = 6.25 mK/W

So, cumulatively through other temperature gradients the 0.37 difference between employing a mistaken number like 0.17 and 0.16 could lead to some significant bias in other statistics we may think we have a handle on...

Now the next "plug in" number was 6.94.

I think here also there may have been an error in which numbers are select from the referenced chart if the goal was to convert to Btu in / (h ft2 o F) ??

First it isn't 6.94 that would have gotten plug into the equation but rather .0000693 because the chart clearing indicates the plug in number to be "6.93 10-5" unless I am mistaken. 6.93 to the 10th negative power of 5 is 0.0000693. I would also note at this time that "6.93 10-5" is for the conversion to "Erg / (cm s oC)" not "Btu ft / (h ft2 oF)" which would be the number "12" from said referenced chart.

At this time, if our readers and our OP would give me the kind indulgence, I would like to start over, as I am in my own "murky water" now and down't want to confuse things even more perhaps than they are.

What I really had these questions about was..."dry sand," and it being a better insulator than wood as reflected in the comment below...

Karen Walk wrote:... Dry sand has a thermal resistance of 4-6.6667 (mK/W). Converted to IP units: 0.576 - 0.96 R-value/inch. For comparison, different types of wood have a thermal resistance varying from 18.18 mK/W for balsa wood to 8.33 mK/W for softwoods and 5.88 mK/W for oak. IP Units: Balsa: 2.6 R-value/inch; Softwoods: 1.2 R-value per inch; Oak: 0.8476 R-value per inch. So dry sand can me MORE thermally resistive than wood!

I still (respectfully ) contend that these number are also in error either because of mistakes of improper "plug ins" or perhaps misunderstanding the equation applications for ascertaining thermal resistance of a material like sand.

I am not sure if I have the "chops" for doing this, and perhaps I can find it or someone like Terry Ruth can do it for us and then break it down. I would love to see this done for sand, and if I am in error and "sand" actually does indeed have the same or similar thermal resistance as a "soft wood" (or a "hard wood") while still displaying the known thermal storage capacity it is know for, I would be very happy to study these theories further.

Thanks everyone for there patients and time...

Regards,

j

Hi BB,

I love your "consensus building" way of thinking...

I am not sure, and from my experience the variability of a sands grain size, or "....how the grains are arranged..." plus other elements like "angle of repose" and such is not going to actually render this material to being as "thermally resistant as a soft wood. I am not really sure, in everything I have read, studied, and observed that it does matters a lot if a dry sand is grad screened to a certain grain size. I am sure it would make some difference yet haven't ever found such factors to be dynamically that much of a variable in material performance.

I do agree completely that granite and similar materials do have a very low heat resistance and its normal state of density (aka "all packed together," ) I can also follow the logic of thinking that "dead air space" between the grains of highly graded sands would have a mitigating effect on thermal storage capacity and thermal resistance. However, I don't believe, nor have I found consistent evidence of, or research - documentation to suggest this mitigation is more than marginal at its very best. With the difference being similar to comparing a non-vitrified brick and a peace of dense stone like soapstone or basalt. Basalt (more than granite or concrete) is very dense yet its thermal storage capacity only marginally better than the brick and neither could be referred to as a "loft insulation" or come near the thermal resistance capacity of a pine board, timber or log.

So, whether we add clay, water, or or just air to super graded sand the margins are narrow at best and not till you get to a mineral like heated perlite, vermiculite, expanded clay or mineral wood do we see a mineral based "thermal resistance" insulation.

That is just what I have discovered, and read over the years, but would love to see math or well vetted research to indicate otherwise.

Regards,

j

Another $0.02 (or less).

I also did the math manually and using online calculators.
I have the same numbers as Karen.
Please see these links for more data and a confirmation that dry sand has an u value around 0.25 w/mk.
Determination of the thermal conductivity of sands under varying conditions
Determination of Thermal Conductivity of Coarse and Fine Sand Soils

My actual $0.02 or less is something else.
In real life (not in a lab) you cannot decouple a material's u/r value from it's c (specific heat) value.
In laymen terms it means you cannot treat the insulative/conductive traits separate from it's thermal mass.
You could do this for materials that are on one end or the other of the spectrum.
One example is foam (EPS, polyiso, mineral wool, etc.) that has very good r values (very low u values) and extremely low thermal mass.
The other end of the spectrum is not so clear cut.
There we have water and metals in varying degrees.

So, in the labs, they create special conditions to actually measure one or the other.
But the real world is the real world.
That's why we treat the material as a whole, not just by having the r/u or c glasses on.

Imagine you have an enclosed volume (let's say a room) with different temperatures on the inside and outside, Ti and To.
To is fixed since it's the outside environment and let's say it has infinite energy.
Now, think like this:
- how much energy passes thru the wall area that's due to the wall's material's u/r value ?
- how much energy enters/exits the wall area that's due to the wall material's c value (thermal mass) ?

And now, the real $0.0...
What is the wall's actual, actually measured, PERFORMANCE ?
You cannot calculate Performance, not to a very precise value.
Why ?
Because inside a wall, especially one built with natural materials like earth or earth/fibre mixtures, you don't know all physical phenomena going on.
We are in the 21'st century and don't know precisely why cob gives better performance than according to calculus.
We can think why but we don't truly know.
This may be so because we are so enamored with concrete to actually look at dirt ... pardon, earth.

I think that Jay C. is talking about PERFORMANCE and not just u/r and c values.
I have experienced dry sand's performance capacities.
They are real.
How good performing are they ?
I don't know, i haven't measured but it has some "insulative" capacity.
On a hot July day i walked on the beach and got feetburns because sand was 80 something centigrade - 176 F.
After digging down 10cm - 4in it got to about 30 centigrade - 86 F.
Of course, deeeper, the sand was moister and temperature dropped fast.

I also have experienced wood's performance ability.
I can say it's a lot better than sand but that's empirical.
And remember, wood thermal characteristics depends on grain direction.
On grain direction it has much better r value than across grain.

So take all this with a grain (not wood) of sand ...

First, a correction - THERM was created by Lawrence Berkley National Laboratory (LBNL), not National Renewable Energy Laboratory (NREL).

Hi B - You hit the nail on the head. Sand will have different thermal properties depending on the type of rock it is, how tightly it is packed, how much water is nit it, etc. Any time you take a rock and break it apart, it takes up more space - about double from my experience. Even trying to pack it back together you'll have limited success. I think that as long as you have pieces that are large enough to be categorized as "sand", you'll have significant spaces between them. Adding materials that are smaller than sand - silt and clay - will help take up that space.

I think that using sand as an insulator is pretty intriguing. On a horizontal surface, you'd have to keep it dry. I can't think of how to use it vertically, but maybe dry sand layer just under a waterproofing layer in an underground greenhouse would work well. In real life, there are thermal mass effects - I'm going to run some simulations in EnergyPlus, sticking with our existing materials and using dry vs wet sand vs wood as a radiant floor material. For the sand alternatives, I'll assume a layer of earthen tiles on top. It'll take a day or two before I can get to this, so bear with me.

In real life there are MANY factors that affect performance. Not the least of which is user preference - thermal mass works best when the temperature inside the space is allowed to fluctuate. Here's how I'm going to set up the model - if there is something you are curious about, and want me to add as an alternative, let me know. I will be a bit choosy just to keep the total number or runs reasonable.

Model setup:

1. The model will be run in a 1,500 square foot passive solar house - clear glass on the south side, with some overhang for shading. Wall, roof and glass construction will be the same in each model run.
2. Thermostat - each model run will use two options for thermostat:
a. Heating Setpoint of 70 F; Cooling Setpoint of 78 F;
b. Heating Setpoint of 62 F; Cooling Setpoint of 86 F;
(feel free to suggest different numbers...)
3. Climate - I'll choose two climate locations - one cold & sunny, one cold & cloudy.
4. The model will include other typical loads inside the house, such as lights, appliances, cooking equipment and people. The loads will be typical of an energy-conscious family.

Bear with me, I'll give anyone who's gotten this far something pithy to chew on in regards to thermal mass.

Karen:

A heat transfer concept I find useful is THERMAL DIFFUSIVITY (α). It is simply the ratio of the THERMAL CONDUCTIVITY (k) over the THERMAL MASS (density (ρ) times specific heat capacity (c)): α = k / (ρ * c)

A very low diffusivity is great for thermal storage and very high diffusivity are great for radiators. A concrete/masonry/stone has five times the diffusivity of water (or sand with very high water content), so it is much better for heating a space. Water is better as a thermal storage medium, since it dissipates less heat per unit mass.



Another point you bring up is the benefit of hydronic radiant heating vs forced air heating. Water has ~3,400 times the thermal mass compared to air (62 BTU/ft3-°F vs 0.018 BTU/ft3-°F - pardon the vulgar Imperial units). Essentially you can transport the same thermal energy with a 1/2" diameter pipe as a 24" square duct. For energy usage, it takes 1/340th the energy to transport that heat (21.0 BTU/w-min-°F vs 0.0612 BTU/w-min-°F), assuming 22 w/GPM pumping power and 0.3 w/CFM fan power per ASHRAE STD 90.1.

it's been a busy week for me, and I haven't heard much on this thread - is anyone out there waiting for the simulation results? It takes a little time to put this together - so if there's not a lot of interest, I'll go work in my garden instead! If you're interested, +1, or reply!

Thanks.

I love all the discussions. Now a basic white and question:

Thermal mass for say a RHM. One is looking for thermal storage. For an insulation one is looking to block heat transfer and not storage.
So the old school idea. Dense for storage and fluffy for insulation. I know wood in general has different resistance values dependent on the ambient temperature. Wood density changes due to its organic structure. Air gaps in sand a sand pile create dead air space so insulating effect..

All that said. Optimize the "stuff" to put in a thermal battery???
And explain the thermal mass versus thermal insulation. Perhaps I was sleeping during my heat and mass transfer classes or have been corrupted by my own desire to use engineering to a point then use old school gut instinct or practicality to yield a finish

Ugh. I believe I would rather have 10 "street smart" individuals working together than 10 "educated" people. Seems street smart is practical. The other gets bogged down in quagmire of infitesimal issues

Thanks to all.

I tend to agree with Alan... I appreciate the discussion, and use engineering to back up what I know in my gut is the right way to do it...