U-value: a not so well-known concept

Most of us have a general idea of the concepts of U- value and g- value when dealing with thermal properties of facades. This post presents some issues not so well known about U-value. A future one will deal with g-value and finally a third one will unify both of them under a building physics perspective.

Low U-values of two walls of Jukka Talo, a Finnish supplier of prefabricated timber houses. 
Left, 318mm + 48mm mineral wool insulation; U-value: 0,11W/m2ºK. 
Right, 318mm mineral wool + 50mm polyurethane insulation; U-value: 0,10W/m2ºK.

Let's start with the basics we know already.

• U-value, or thermal transmittance, is the heat flow density going through one m2 of a specific wall element when both sides of the wall are subject to a temperature difference of one ºK. Heat is a form of energy and thus heat flow is measured in Joules/second, that is, in Watt. According to this definition, U-value is measured in W/m2ºK. 
• Another definition (by Limb in 'Air infiltration and ventilation glossary', 1992) describes U-value as the heat flow transmitted through a unit area of a given structure, divided by the difference between the effective ambient temperature on either side of the structure, under steady state conditions.
• That is, the interaction between the wall and the outer / inner air layers, the thickness of the wall or the fact that the wall has one or several layers are all combined within the U-value: what it tells us is the amount of heat that gets through a certain wall per m2 per ºK, as simple as that. Or not that simple?

The U-value of a glass pane is determined in Europe by calculation according to EN 673 or by measurement according to EN 674. Under the same boundary conditions, calcs and measurements result in very similar U-values. Funnily, the American code for glass, ASHRAE/NFRC, yield a slightly worse (that is, higher) U-value than the European standards. The difference can be around 0.1 - 0.2W/m2ºK. Furthermore, the ASHRAE U-value is separated into winter and summer conditions.

Does U-value measure convection, conduction or radiation?
It is clear that g-value refers to solar radiation through transparent materials such as window glass surfaces. It does not measure heat exchanges due to conduction or convection. What about U-value? Does it only measure heat flows due to convection and conduction, or does it also measure radiation? Interestingly, the primary mode of heat transfer impeded by thermal insulation in a facade is convection, but in fact U-value measures heat loss by all three heat transfer modes: conduction, convection, and radiation:

• Convection occurs because of changes in air density with temperature, creating a movement of the air that transfers heat. Insulation materials greatly retard natural convection in air filled cavities, so that convective heat loss is significantly reduced.
• Conduction implies heat being transferred between substances in physical contact. The mineral wool or foam required to prevent convection slightly increases the heat conduction in a cavity compared to still air, because the insulation density is higher than air. But, roughly speaking, the conduction effect of heat transmission increases with density. Insulation materials are in general low conductive materials because of their low density.
• Radiation is the transmission of heat through space by the propagation of infrared energy, without necessarily warming the space between. Radiative heat transfer is minimised by having many surfaces interrupting a "clear view" between the inner and outer surfaces of the wall. Remember: radiation is best transmitted in total absence of matter such as in interplanetary space, as the sun demonstrates every clear day. Finally, radiation is also reduced by low emissivity (highly reflective) surfaces. Thermal insulation, with its foamy or capillary structure, behaves as a multiple filter to radiative heat.

Thermal conductivity of common materials
Thermal conductivity (expressed by the Greek letter lambda) is a thermal property of a material, of its ability to conduct heat. It is measured as the rate of heat flow (W) over unit lenght (m) through that material over unit area (m2), caused by unit temperature difference (K): W.m/m2.K, by cancellation: W/mK. The lower the conductivity of a material, the better it acts as a thermal insulator.

Glass has a thermal conductivity of 1.05W/mK. Is this high or low? It is rather high, although very small if we compare it with metalic materials as steel (54), aluminium (250) or copper (401). Glass is a rock, so its thermal conductivity is not too far away from a typical stone (1.7 to 3) or standar concrete (1.7). Dry earth has a value of 1.5W/mK. A solid brick (1.3) is more conductive than a brick wall (0.69) because the latter has air in the hollow ceramic bricks.

What about insulation materials? Air conductivity is 0.024W/mK, a very low one, even less than that of EPS or XPS (0.03 - 0.033) or mineral wool (0.04). Cork (0.07) and cotton (0.03) are also more conductive than air. Only polyurethane foam (0.02) has a lower conductivity than air, but not that different. By the way, snow is a good thermal insulation in winter. When the outer temperature is below 0ºC, snow lambda is around 0.05 to 0.25W/mK, depending on its density. Water is much worse as a thermal insulator (0.58). High density wood does insulate: 0.12 to 0.17, not bad.

Why do we use insulation materials instead of just air cavities? Clearly because it is difficult to have the air still and quiet in a chamber, and avoid the convective currents. Is there a material with a thermal conductivity lower than air, but not suffering from air convective currents? Yes, and these are the noble gases: argon (0.016), krypton (0.0095) and xenon (0.00565). More about them right now.

What is the role of air thickness and infill in a double glass unit?
The insulating efficiency of a standard double glass unit depends on the thickness of the air space between glass sheets. Too little space results in conductive heat loss: the inside surface of one pane cools the surface of the other pane. Too wide a gap results in convection current losses: air begins to circulate because of temperature differences and transfers heat between the panes. Glass sealed units achieve their maximum insulating values using an intermediate space between 16 and 19 mm.
This is fine, but not enough. Reducing the U-value from 2.9 down to 2.6W/m2ºK is fine, but it represents a 10% reduction only. Why do we get an even lower thermal transmittance (and thus a lower U-value) by replacing air with argon in a double glass unit or in a high quality foam insulation? Which one of the three heat transfer modes is retarded here?

Replacing the air in the intermediate space with a heavy gas, slightly denser but much more viscous than oxygen and nitrogen, is helpful because its higher viscosity reduces convective heat transfer. Argon (whose thermal conductivity is 67% that of air), krypton (with a conductivity 2.5 times smaller than air) or xenon (4.2 times smaller) do increase the insulating performance of the whole glass unit because of their reduced convective transmission besides their lower thermal conductivity. Argon, krypton and xenon are used because they are non-toxic, clear, odorless, chemically inert, and commercially available, but their cost grows exponentially with their alphabetic order. That is why argon is the one most commonly used, always in combination with low-e coatings. By the way, the more effective a fill gas, the thinner its optimum thickness becomes. For example, the optimum thickness for argon is lower than for air, and lower for krypton than for argon. This is good to know because these infills are expensive. All considered, an air space of 15mm with argon at 95% or more is a very good selection if you have to reduce your U-value in glass. But remember to add a low-e coating as well!

Is U-value really constant?
More tricky things: the U-value is calculated under standardized conditions, usually under an air temperature of 20ºC inside and 10ºC outside, a surface emissivity of 0.9, a 50% humidity and an external wind speed of 4m/s. Air in movement should have a certain influence on the thermal resistance of an outer surface: wind increases the interaction between the wall and the outer air layer, and conductivity is higher. But the air temperature? Does this mean that U-values vary with temperature? Yep. Now, does U-value increase under cold or hot temperatures? Does U-value increase or decrease with a strong wind? Which of those two variables is more important?

Air movement and temperature inside and outside the wall do affect the surface resistance values of the wall. Let's forget the inside face of the wall: its temperature and air movement variations are too small to affect the U-value. The surface resistance is the combination of a convective coefficient and a radiative coefficient. The convective coefficient depends directly on wind speed, and its range of variation is huge: convection is 'pushed' by a 10m/s wind speed eleven times more than under a total still air. The radiative coefficient varies with temperature, but not that much, just +/- 20% under extreme external temperatures. If we are in Norway and the outer temperature is -10º, the external surface resistance of the wall will be 0.042 ºKm2/W instead of 0.04. If we are in Saudi, +40º outside, expect something around 0.038 ºKm2/W

To cut a long story short, what are the parameters that can really modify the mean U-value of a wall?

• External temperature has a very small influence. It does not affect at all opaque, well insulated walls. For glazed walls the variation is also very small: a curtain wall with a mean U-value of 1.75W/m2ºK at +10ºC outside will have the same value at -10ºC outside, and will raise to 1,76W/m2ºK when the outer temperature is +30ºC.
• Emissivity of materials can have an influence, and it varies depending on the material. We know it is critical in glass (lowering its U-value from 2.5 to 1.7W/m2ºK, for instance). When a material has an intrinsic low emissivity it is difficult to make a difference on the U-value if we reduce it even further. That is the case with aluminium: reducing its emissivity with special coatings has a very small influence on the mean U-value of the wall (especially if it's a glazed curtain wall).
• Wind speed has an important influence if our wall is a glazed facade, and it doesn't affect the mean U-value if it's a well insulated opaque wall. Let's suppose we have a curtain wall with a mean U-value of 1.75W/m2ºK (that's a high-performant curtain wall by all standards). Now comes the surprise: if wind speed moves up from 4m/s to 10m/s (nothing extraordinary for curtain walls, especially in high rise buildings) the mean U-value due to wind speed raises from 1.75 up to 1.82W/m2ºK. An increase of 4%: that's not the same thing! 

U-value matters, but so does air permeability
Please remember this: the insulation quality of a wall is affected by other factors not addressed by U-value classification. Although the U-value laboratory test captures the effects of convective loops within the insulation, it cannot measure the amount of air leakage through a real wall assembly once the insulation is installed. The rate of air permability in a wall is affected by:

• the density and continuity of the insulation,
• the presence or absence of an air barrier in the wall assembly,
• the wind speed, and
• the pressure difference between outside and inside the wall.

Because of these factors, a wall assembly insulated with fiberglass or mineral wool blankets will usually perform worse than a wall assembly insulated with a continuous sprayed foam, even when the foam has the same U-value as the blankets. The difference is due to the spray foam’s ability to reduce air leakage, not to any difference in U-value between the two materials.
To obtain the best performance from fiberglass or mineral wool insulation, the US Energy Star Homes program requires most fiberglass-insulated framing cavities to be enclosed by air barriers on all six sides. It makes sense, but it’s hard to achieve on site.

Cold bridges or thermal bridges are clearly an interruption to the continuity of insulation and thus an increase of the general U-value of the wall. But there is a less obvious type of cold bridge, shown above, known as thermal looping: an air gap of more than 1mm between the insulation and the inner wall leaf allows air circulation, creating convective currents and leading to a significant reduction of the overall U-value. This was first presented by Jan Lecompte in a paper of 1990, named 'Influence of natural convection in an insulated cavity on the thermal performance of a wall'. How many of us know about it, and take care of it in our details?

Well, somebody knows it, but not too well. The standard EN ISO 6946:2007 has an annex D called 'Correction to thermal transmittance'. One of the corrections covers thermal looping. I don't like the way it's done though, because it does not include the gap thickness as a variable, and the so-called correction is too small: you just have to add less than 0.04W/m2K. In this case, sorry to say chaps, calculations don't match measurements!

Some suppliers of radiant barriers or spray foam insulation, well aware of these issues, tend to imply that U-value measurements are meaningless. U-value is of course a very useful measurement, but just because you know a product’s U-value doesn’t mean you know everything necessary to predict the real heat flow through a wall or a roof. No one has yet invented a magic number that replaces the requirement for designers to study and understand building physics principles.

Does radiant heat pass through insulation?
We have just mentioned radiant barriers. Another tactic employed by some suppliers of these products is the idea that conventional insulation materials - sometimes called mass insulation - allow radiant heat to pass right through them. Some radiant barrier brochures happily state that 'mass insulation is transparent to radiant heat'. The implication is that a layer of aluminium foil is always necessary to prevent radiant heat from traveling like radio waves right through a deep layer of cellulose, foam or XPS.
In fact, most mass insulation products do stop most of the radiant heat flow. Radiant heat easily travels through air (for example, from a wood stove to your nearby skin) or a vacuum (for example, from the sun to the earth). But radiant energy can’t travel that easy through a denser material. When radiant heat hits one side of a deep layer of insulation, only a tiny percentage of that radiant heat manages to miss all of the fibers in the insulation blanket and emerge unscathed on the other side.

The fact that heat flows through a layer of insulation doesn’t mean that the insulation isn’t working. By definition, insulation slows down heat flow; it doesn’t stop it. Heat will always flow from hot to cold. The more insulation and the lower the air permeability, as we have seen, the slower the heat flow.

Transmittance (U-value) and air-to-air resistance (Ra-a)
The reciprocal of the U-value is the air-to-air resistance (Ra-a, measured in m2K/W) which is the sum of each of the wall resistances: resistances of the external and internal surfaces of the wall plus resistances of each of its layers. E.g., for a wall of two layers:

Ra-a = Rso + R1 +R2 + Rsi.

The R-value of any homogenous layer is its thickness (in m) divided by the conductivity of its material. Thus, a good insulation material which has a very low conductivity will have a high resistance. Conductivity is a constant for any given material under certain conditions, while R-value depends on the material thickness. That is why most of the insulation materials in the market come with their R-value: each value defines every product (given a certain conductivity and a commercial thickness). Good insulation materials have an R-value of 5, 6 or even 10. These values are not in the SI, but in the typical US unit system: ft2·ºF·h/BTU·in (notice that ·in at the denominator: R-values are usually expressed per inch, to allow for comparison)

American marketed products come with their R-value/in expressed in US units. It takes time to translate them to SI values, now measured per cm. Here is a list of insulation materials with their R-value expressed in US units (per inch) and also in SI units (per cm):

Where can I learn more?
European (EN) and worldwide (ISO) standards have a bad reputation: they are definitely not easy to read. How could they be easy, having been written by a committee? But that doesn't mean they are not interesting, if what you are looking for is guidance or precision.
These are my five favourites in relation to thermal transmission:

a) EN ISO 6946:2007 for opaque elements: walls, roofs and floors.

And its referenced documents:

• ISO 7345, Thermal insulation - physical quantities and definitions.
• ISO 10456, Building materials and products - Hygrothermal properties - Tabulated design values.
• ISO 13789, Thermal performance of buildings - Transmission and ventilation heat transfer coefficients.

b) EN ISO 13370, for heat transfer via the ground.

c) EN ISO 10077-1 for doors, windows and other glazed elements.

d) EN 13947, for curtain walls.

e) ISO 10221, for thermal bridges