## Auau R

In this wall, the fixing of the mineral wool insulation in its timber sub-frame is such that there is no air movement on the warm side, but there are some air gaps penetrating the insulation layer. As the air gaps are in the mineral wool and timber sub-frame, Rl = Rit = 1.815. Referring to Table 5.1, the correction for air gaps is level 1, and so AU11 = 0.01. With RT = 3.170, the correction is thus:

1.815 2

As this is less than 3% of U, it may be ignored. The final U-value is rounded to two decimal places:

Example 5.2 Timber framed wall

Figure 5.5 shows a timber framed wall consisting of an outer layer of brickwork, a clear ventilated cavity, 10 mm plywood, 38 x 140 mm timber stud framing with 140 mm mineral wool quilt insulation placed between the studs, and two sheets of 12.5 mm plasterboard with an integral vapour check. The timber studs account for 15% of the area, corresponding to 38 mm studs at 600 mm centres, with allowances for horizontal noggins and additional framing at junctions and around openings. The thermal data for this wall is given in Table 5.8.

The upper resistance limit, Rupper

Each possible heat flow path through the wall is considered separately, and in this case it can be seen that there are two such paths. This is illustrated in

Fig. 5.5 Timber frame wall.
 Thermal Thermal Material Thickness conductivity resistance mm W/mK m2K/W External surface — — 0.040 Outer brickwork 102 0.77 0.132 Cavity, vented — — 0.090 Plywood 10 0.13 0.077 Mineral wool quilt insulation 140 0.038 3.684 Timber framing 140 0.13 1.077 Plasterboard 25 0.25 0.100 Internal surface — — 0.130

Fig. 5.6. The resistance of each path is calculated on the basis that the materials are in series, and then the two paths are combined on the basis that they are in parallel. The first part of the calculation is illustrated in Table 5.9. The two paths are now combined in parallel to find Rupper:

-upper R2 4.253 1.646

Rupper = 3.437 m2K/W

Fig. 5.6 Upper resistance limit - timber frame wall.

Table 5.9 Calculation of the upper resistance limit, timber frame wall.

Thermal resistance, m2K/W

Table 5.9 Calculation of the upper resistance limit, timber frame wall.

Thermal resistance, m2K/W

 Path 1 Path 2 External surface resistance 0.040 0.040 Resistance of brickwork 0.132 0.132 Resistance of cavity 0.090 0.090 Resistance of plywood 0.077 0.077 Resistance of mineral wool quilt 3.684 — Resistance of timber — 1.077 Resistance of plasterboard 0.100 0.100 Internal surface resistance 0.130 0.130 Total thermal resistance of path 4.253 2.988 Fractional area of path 85% 15% = 0.85 = 0.15

The lower resistance limit, Riower

Each thermal bridge in the construction element is first converted to a single combined resistance. There is only one bridge in this case, formed by the mineral wool in its timber frame, as shown in Fig. 5.7. The combined resistance of the thermal bridge, Rit is found from:

Rit Rinsulation Rtimber 3.684 L°77 Rit = 2.703 m2K/W

This combined resistance may now be used to find the lower resistance limit, as shown in Table 5.10. Note again that Rupper is an overestimate of the true resistance, whereas Rlower is an underestimate. The average of these is very close to the true value. Hence, the total resistance of the wall is found from

Rt = 2 (Rupper + Rlower) = 2 (3.437 + 3.272) = 3.354 m2K/W

Fig. 5.7 Lower resistance limit - timber frame wall.
 Thermal resistances, m2 Thermal bridges K/W Components Combined External surface resistance Resistance of brickwork Resistance of cavity Resistance of plywood Resistance of mineral wool (85%) Resistance of timber (15%) Resistance of plasterboard Internal surface resistance 3.684J 1.077 J 2.703 0.100 0.130 Total thermal resistance, Rlower 3.272

and the U-value is:

Corrections to the U-value for air gaps and mechanical fixings As in the previous example, there is the possibility of a correction for small air gaps. Again it can be assumed that the fixing of the mineral wool insulation in its timber sub-frame is such that there is no air movement on the warm side, but there are some air gaps penetrating the insulation layer. As the air gaps are in the mineral wool and timber sub-frame, Rl = Rit = 2.703. Referring to Table 5.1, the correction for air gaps is level 1, and so AU11 = 0.01. With RT = 3.354, the correction is thus:

As this is less than 3% of U, it may be ignored. The final U-value is rounded to two decimal places, and so the result is