# 2.2.2 *U*-Values

Conduction, convection and radiation all contribute to the complex process of heat loss through a wall, window, roof, etc. In practice, the actual thermal performance of any particular building element is usually specified by a *U*-value, defined so that:

- heat flow through one square metre =
*U*-value × temperature difference.

The *U*-value is thus the heat flow per square metre divided by the temperature difference. The heat flow has units of watts (W) and the temperature difference has units of kelvins (K). The *U*-value thus has the units of watts per square metre kelvin - W / m^{2} K. In this course we have used the convention that units in a divisor are given a negative power, so this becomes W m^{-2} K^{-1}. The lower the *U*-value, the better the insulation performance.

## Box 2 Degrees Celsius or kelvins?

Temperatures can be measured in degrees Celsius (°C) or kelvins (K). Kelvins are more likely to be used in official documents and scientific papers. The ‘size’ of a degree is the same on both scales, so temperature differences are identical in °C and K. The Kelvin scale is used to measure the **absolute temperature**, that is the temperature above **absolute zero**. Absolute zero has been measured as about –273°C, so 0°C is 273 K, and the temperature in kelvins can be obtained simply by adding 273 to the Celsius temperature.

Note that a temperature expressed in kelvins doesn't need a degree sign.

Current UK building regulations use the kelvin in specifying *U*-values and other thermal quantities, and it is used in this section. In practice, *U*-values are widely quoted as W m^{-2} °C ^{–1} in architectural literature and the trade press, simply because the degree Celsius is more familiar. Technical literature can use a range of different presentations of the units of *U*-values: W m^{-2} K^{−1}, W/m^{2} K, W m^{-2} °C^{−1} and W/m^{2} °C. These are all identical.

## Window *U*-values

Table 2 gives some indicative *U*-values for different glazing options. Note that these are only ‘indicative’ and better *U*-values for double and triple glazing are commercially available. By way of comparison, a solid brick wall has a *U*-value of 1.5 - 2 W m^{2} K^{-1}, and 10 cm of opaque fibreglass insulation one of about 0.4 W m^{–2} K^{–1}.

Glazing type | U-value/W m |
---|---|

Single-glazing | 4.8 |

Double-glazing (normal glass, air-filled) | 2.7 |

Double-glazing (hard coat low-e, emissivity = 0.15, air-filled) | 2.0 |

Double-glazing (hard coat low-e, emissivity = 0.2, argon-filled) | 2.0 |

Double-glazing (soft coat low-e, emissivity = 0.05, argon-filled) | 1.7 |

Triple glazing (soft coat low-e, emissivity = 0.05, argon-filled) | 1.3 |

UK buildings have traditionally used single-glazing. It has been estimated that in 1974 less than 10% of British housing had any form of double-glazing (BEIS, 2013). It was only made mandatory for new houses in England and Wales in 2002 and this was extended to replacement windows for all existing houses in 2005.

There has been continuing improvement in *U-*values for double-glazing through the use of soft-coat low-e glass, insulated spacers at the edge of the panes and better insulated frames. Currently commercially available double glazed windows may have *U*-values of 1.5 W m^{-2} K^{-1} or better, far lower than the *U*-value of 4.8 W m^{-2} K^{-1} shown for single glazing above.

It is also important that windows have a good transparency to let in light and solar gains and are airtight when closed. Currently windows in the UK are sold with a Window Energy Rating on a scale A – G which takes into account the *U*-value, airtightness and transparency. A reasonably airtight double glazed window with a *U*-value of 1.6 W m^{-2} K^{-1} and a solar transparency of 50% would get a ‘C’ rating. Under the 2013 UK building regulations this rating is now the minimum acceptable for new and replacement windows and even this standard may be tightened in the next few years. Essentially to get a good rating a double-glazed window must have a good low-e coating *and* use insulating spacers around the edges of the glass *and* have a good transparency.

Argon-filled double-glazed units require a relatively thick gap of 12–16 mm between the panes. This makes their use difficult in retrofitting older timber sash windows, for example in historic listed buildings. For these, slimmer double-glazing units can be used to meet the required UK window regulation *U*-values, using a krypton/xenon filling in an 8 mm gap or alternatively vacuum glazing with only a 0.2 mm gap.

By 2015 it was estimated that 80% of the UK housing stock had full whole-house double-glazing (BEIS, 2018c).

## Activity 2

Table 2 gives typical *U*-values of various types of window glazing system.

What is the rate of heat loss in watts through a large single-glazed window with an area of 2 m^{2}, on a day when the outdoor and indoor temperatures are 5°C and 20°C respectively?

### Answer

Table 2 shows that the *U*-value for this window is 4.8 W m^{–2} K^{–1} − The heat loss heat flow through one square metre = *U*-value × temperature difference.

The total loss rate is thus 2 × 4.8 × (20 − 5) = 144 watts

## Activity 3

If the temperature difference remained the same throughout 24 hours, what would be the total heat loss in kilowatt-hours over the day? What would it have been using the best of the glazing types shown in Table 2?

### Answer

For a single glazed window the heat loss over 24 hours will be 144 watts × 24 hours = 3456 watt-hours or just over 3.4 kilowatt-hours.

For a triple-glazed window with a *U*-value of 1.3 W m^{–2} K^{–1} the heat loss rate would be 2 × 1.3 × (20 − 5) = 39 W and the total heat loss over 24 hours would be 39 × 24 = 936 Wh, or under 1 kWh.