Thermal performance, transmittance of composite wall

Thermal performance of building sections

Thermal performance is the ability of a wall, roof, floor or window to resist heat flow and keep indoor conditions comfortable. It depends on the conductivity ($k$) and thickness ($t$) of its layers, surface films, air gaps, thermal mass (time lag and decrement) and the colour of the surface. Good performance means low heat gain in summer and low heat loss in winter, giving comfort with less energy.

Transmittance

Thermal transmittance (U-value) is the rate of heat flow through one square metre of a building element for a temperature difference of 1 °C between the air on its two sides, in W/m²°C. It is the reciprocal of the total resistance.

$$U = \frac{1}{R_{total}} = \frac{1}{\frac{1}{f_i} + \sum \frac{t}{k} + \frac{1}{f_o}}$$

with $f_i$ and $f_o$ the internal and external surface conductances.

Calculation

Layers from inside to outside: inner surface film, 12 mm plaster, 110 mm brick, 25 mm thermocole, 25 mm cavity, 110 mm brick, 12 mm plaster, outer surface film.

$$\begin{aligned} R_{total} &= 0.1232 + 0.0167 + 0.0957 + 0.7353 + 0.9615 + 0.0957 + 0.0167 + 0.1000 = 2.1446\ \text{m}^2\text{°C/W} \\ U &= \frac{1}{2.1446} = 0.466\ \text{W/m}^2\text{°C} \end{aligned}$$

Answer: $U = 0.466$ W/m²°C.

Thermal gradient

The temperature drop across each layer is proportional to its resistance. For example, take 25 °C inside and 5 °C outside ($\Delta T = 20$ °C). The heat flux is $q = U\Delta T = 0.466 \times 20 = 9.33$ W/m². The drop in each layer is $\Delta T_i = qR_i$:

 25C ‾\
       \___ brick  (gentle)
           \
            \  thermocole (steep)
             \
              \  cavity (steep)
               \___ brick, plaster
                   \ 5C
 in |P|B|Ins|Cav|B|P| out

The steepest falls are in the cavity and the thermocole, because they have the largest resistances.