Thermal conductivity, R-Values and U-Values simplified!
Thermal Conductivity of insulating materials
The primary feature of a thermal insulation material is its ability to reduce heat exchange between a surface and the environment, or between one surface and another surface. This is known as having a low value for thermal conductivity. Generally, the lower a material’s thermal conductivity, the greater its ability to insulate for a given material thickness and set of conditions.
Thermal conductivity, also known as Lambda (denoted by the greek symbol λ), is the measure of how easily heat flows through a specific type of material, independent of the thickness of the material in question.
The lower the thermal conductivity of a material, the better the thermal performance (i.e. the slower heat will move across a material).
It is measured in Watts per Metre Kelvin (W/mK).
To allow you to get a feel of insulating materials – their thermal conductivity varies between about 0.008 W/mK for vacuum insulated panels (so these are the best, but very expensive!) to about 0.061 W/mK for some types of wood fibre.
K-Values
K-value is simply shorthand for thermal conductivity. The ASTM Standard C168, on Terminology, defines the term as follows:
Thermal conductivity, n: the time rate of steady state heat flow through a unit area of a homogeneous material induced by a unit temperature gradient in a direction perpendicular to that unit area.
This definition is really not that complex. Let’s take a closer look, phrase by phrase.
Time rate of heat flow can be compared to water flow rate, e.g., water flowing through a shower head at so many gallons per minute. It is the amount of energy, generally measured in the United States in Btus, flowing across a surface in a certain time period, usually measured in hours. Hence, time rate of heat flow is expressed in units of Btus per hour.
Steady state simply means that the conditions are steady, as water flowing out of a shower head at a constant rate.
Homogeneous material simply refers to one material, not two or three, that has a consistent composition throughout. In other words, there is only one type of insulation, as opposed to one layer of one type and a second layer of a second type. Also, for the purposes of this discussion, there are no weld pins or screws, or any structural metal passing through the insulation; and there are no gaps.
What about through a unit area? This refers to a standard cross-sectional area. For heat flow in the United States, a square foot is generally used as the unit area. So, we have units in Btus per hour, per square feet of area (to visualize, picture water flowing at some number of gallons per minute, hitting a 1 ft x 1 ft board).
Finally, there is the phrase by a unit temperature gradient. If two items have the same temperature and are brought together so they touch, no heat will flow from one to the other because they have the same temperature. To have heat flow by conduction from one object to another, where both are touching, there must be a temperature difference or gradient. As soon as there is a temperature gradient between two touching objects, heat will start to flow. If there is thermal insulation between those two objects, heat will flow at a lesser rate.
At this point, we have rate of heat flow per unit area, per degree temperature difference with units of Btus per hour, per square foot, per degree F.
Thermal conductivity is independent of material thickness. In theory, each slice of insulation is the same as its neighboring slice. The slices should be of some standard thickness. In the United States, units of inches are typically used for thickness of thermal insulation. So we need to think in terms of Btus of heat flow, for an inch of material thickness, per hour, per square foot of area, per degree F of temperature difference.
After picking apart the ASTM C168 definition for thermal conductivity, we have units of Btu-inch/hour per square foot per degree F. This is the same as the term K-value.
C-Values
C-value is simply shorthand for thermal conductance. For a type of thermal insulation, the C-value depends on the thickness of the material; K-value generally does not depend on thickness (there are a few exceptions not in the scope of this article). How does ASTM C168 define thermal conductance?
Conductance, thermal, n: the time rate of steady state heat flow through a unit area of a material or construction induced by a unit temperature difference between the body surfaces.
ASTM C168 then gives a simple equation and units. In the inch-pound units used in the United States, those units are Btus/hour per square foot per degree F of temperature difference.
The words are fairly similar to those in the definition for thermal conductivity. What is missing is the inch units in the numerator because the C-value for a 2-inch-thick insulation board is half the value as it is for the same material 1-inch-thick insulation board. The thicker the insulation, the lower its C-value.
Equation 1: C-value = K-value / thickness
R-Values
The R-value is a measure of resistance to heat flow through a given thickness of material. So the higher the R-value, the more thermal resistance the material has and therefore the better its insulating properties.
The R-value is calculated by using the formula
Where:
l is the thickness of the material in metres and
λ is the thermal conductivity in W/mK.
The R-value is measured in metres squared Kelvin per Watt (m2K/W)
For example the thermal resistance of 220mm of solid brick wall (with thermal conductivity λ=1.2W/mK) is 0.18 m2K/W.
If you were to insulate a solid brick wall, you simply find the R-value of the insulation and then add the two together. If you insulated this with 80mm thick foil-faced polyisocyanurate (with thermal conductivity λ=0.022W/mK and R-value of 0.08 / 0.022 = 3.64 m2K/W), you would have a total R-value for the insulated wall of 0.18 + 3.64 = 3.82 m2K/W. Therefore it would improve the thermal resistance by more than 21 times!
U-Values
The U value of a building element is the inverse of the total thermal resistance of that element. The U-value is a measure of how much heat is lost through a given thickness of a particular material, but includes the three major ways in which heat loss occurs – conduction, convection and radiation.
The environmental temperatures inside and outside a building play an important role when calculating the U-value of an element. If we imagine the inside surface of a 1 m² section of an external wall of a heated building in a cold climate, heat is flowing into this section by radiation from all parts of the inside the building and by convection from the air inside the building. So, additional thermal resistances should be taken into account associated with inside and outside surfaces of each element. These resistances are referred to as Rsi and Rso respectively with common values 0.12Km²/W and 0.06Km²/W for the internal and external surfaces, respectively.
This is the measure that is always within Building Regulations. The lower the U-value is, the better the material is as a heat insulator.
This is calculated by taking the reciprocal of the R-Value and then adding convection and radiation heat losses, as follows.
U = 1/ [ Rsi + R1 + R2 +… + Rso ]
In practise this is a complicated calculation, so it is best to use U-Value calculation software.
Units are in Watts per metre squared Kelvin (W/m2K).
As a guide an uninsulated cavity wall has a U-Value of approximately 1.6 W/m2K, while a solid wall has a U-Value of approximately 2 W/m2K
Using U-Values, R-Values and Thermal conductivity
If you are confronted with thermal conductivity, R-values and U-values going forward, here are 3 simple things to remember, to make sure you get the best insulating product.
- Higher numbers are good when comparing the Thermal Resistance and R-Values of products.
- Low numbers are good when comparing U-Values.
- The U-Value is the most accurate way to judge a material’s insulating ability, taking into account all the different ways in which heat loss occurs, however it is more difficult to calculate.