### Thermal Resistance

The heat flow through a building construction depends on the temperature difference across it, the conductivity of the materials used and the thickness of the materials. Of course the temperature difference is an external factor. The thickness and the conductivity are properties of the material. A greater thickness means less heat flow and so does a lower conductivity. Together these parameters form the thermal resistance of the construction. The thermal resistance is proportional to the thickness of a layer of the construction and inversely proportional to its conductivity. A construction layer with a high thermal resistance (e.g. rock wool), is a good insulator; one with a low thermal resistance (e.g. concrete) is a bad insulator.

#### Resistance Vs Resistivity

Resistivity is a material property and refers to that material's ability to resist the flow of heat. Resistance on the other hand is an object property and depends on both the resistivity of the material and its overall thickness within that particular object.
As resistivity is the inverse of conductivity, and conductivity values are far more readily available for most building materials than resistivities, it is possible to calculate the material's resistance using conductivity as follows:

R = l/ k
Where: R = the thermal resistance per unit area of the piece of material (m²K/W),
l = represents the thickness of the material (m), and
k = represents the conductivity of the material (W/mK).

#### Total Thermal Resistance

A building structure is usually composed of a number of different materials which may be considered to act:
In Series
When materials are place in series, their thermal resistances are added so that the same area will conduct less energy for a given temperature difference. An example of this is a cavity-brick wall, with two layers of brick, an air gap and 12mm of plasterboard - all in series.
In Parallel
When materials are placed in parallel, their thermal conductances are added and the total energy flow is increased for a given temperature difference. An example of this would be a cavity-brick wall with a window inserted within it.

The total resistance of an element includes all of the resistances of the individual materials that make it up as well as both the internal and external air-film resistance. Its units are the inverse of conductivity.

i.e.: m²K/W.

#### Air Film Resistance

Air film resistance results from convection currents at the surface of a material. As the surface heats up or cools down, it affects the temperature of the air immediately adjacent. This then starts to rise or fall depending on whether it is hotter or colder. This has the same effect as increasing the resistance of the material to the flow of heat.

#### Composite Building Materials

For a composite building element made up of a number of layers of different materials, its total resistance is given as:

Rt = Rso + ∑Rn + Rsi
where the resistance of the nth layer is:

Rn = ln/kn

Rt = the total overall resistance of the element (m²K/W),

Rn = the resistance of the nth material within a composite element (m²K/W),
(m²K/W)

Rso & Rsi are the outside and inside surface resistances respectively (m²K/W)

ln = the thickness of the nth material in a composite element (m), and

kn = is the conductivity in of the nth material in a composite element (W/mK).

Fortunately, enough is known about various materials to enable the calculation of an overall thermal character for most common fixed-dimension building systems so that an overall resistance (or conductance) can be derived. Figures can be derived for single glazed and double glazed windows, concrete slab floors, suspended wooden floors, walls and so on. These characteristics are usually written as either an R-Value (for insulations) or a U-Value for other elements.

#### The R-Value

Resistance is usually given as an "R" value which is the resistance of one square metre of the material subject to a one degree temperature difference. Thus an R value of a typical fibre glass bat may be given as R = 2.4, with the implication that it has the units m²K/Watt. This means that if one takes the area of insulation in square metres multiplied by the temperature difference in degrees Kelvin and divided by 2.4, one gets the heat flow in Watts.

For example, 100 square metres of R = 2.4 insulation, exposed to a 20 degree K difference, will pass about 833 Watts.

In fact, the heat loss would be expected to be slightly from this because there is an additional resistance in getting the energy from the inside air to the wall surface, and from the outside wall surface to the outside air. Moreover, the heat transfer on the outside surface may vary with wind speed.

thermal resistance