# Thermal Calculations & Theory

As you start looking at insulating materials like facade insulation you may quickly become bogged down by some quite complicated technical terms. In this article we look to simplify them, so you can hold your own when talking insulation

**LambdaThermal Conductivity of insulating materials**

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.

If you were to use sheep’s wool to insulate you property this comes in about 0.034 W/mK, about the same as most of the other wool and fibre insulating materials.

**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 m2 K/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 Facade Slab Ultimate (with thermal conductivity λ=0.032W/mK and R-value of 0.08 / 0.032 = 2.5 m2K/W), you would have a total R-value for the insulated wall of 0.18 + 2.5 = 2.68 m2K/W. Therefore it would improve the thermal resistance by more than 15 times!

The R-value is therefore a relatively simple way to compare two insulating materials if you have the thermal conductivity for each material.It also allows you to see the impact of adding thicker layers of the same insulating material.

In real buildings, a wall is made up of many different material layers. The total thermal resistance of the entire wall is calculated by adding the thermal resistance of each separate layer.

Unfortunately heat moves in and out of your home in several different ways and R-values only take into account conduction. It does not include either convection or radiation.

Therefore you may choose to use the U-value which takes into account all the different mechanisms of heat loss – read on to find out how this is calculated!

**U-Values **

The U-value signifies the heat lost through a given thickness of a particular element (wall, roof, window). A U-value calculation includes includes the three major ways in which heat loss occurs – conduction, convection and radiation. Often, you don’t really need to understand the mechanics of how it is calculated – instead it is useful to be able to compare different builds by their U-values.

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 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

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 tree major ways in which heat loss occurs - conduction, convection and radiation.

The environmental temperatures insude and outside a building play an important role when calculating the U-value of an element. If we imagine the insude surface of a 1m2 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 insude the building and by convestion 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.