Thermal Mass Effect
Theory: what the U-value doesn't tell
Overview
Wall insulation is compared by U-value. Is thermal mass something separate?
It's separate. U-value describes heat flow at a steady temperature difference and can't capture behaviour when temperatures vary in time. How a wall responds to the daily cycle depends on how much it delays outdoor changes (time lag), how much it shrinks them (decrement factor) and how much heat it can exchange on the room side (admittance). These depend strongly on heat capacity and layer order. Let's compare concrete and lightweight walls, and internal versus external insulation, with transfer matrices.
Transfer matrix
Layer matrices are multiplied in order from the inside surface resistance (0.13 m²K/W) to the outside one (0.04 m²K/W). δ is the penetration depth for period P (24 h).
Time lag and decrement factor
$Y_{12}$ is the periodic thermal transmittance — the room-side heat-flux amplitude per kelvin of outdoor swing; the decrement factor f divides it by the steady U-value.
The wisdom of thick walls
Traditional houses in deserts and around the Mediterranean used thick stone or earth walls to delay daytime heat into the night and carry night coolness into the day. The admittance method, developed in Britain and elsewhere in the 1960s and 70s, put this empirical wisdom into equations and leads to today's transfer-matrix method in ISO 13786. Even in well-insulated modern buildings, the placement of thermal mass is being revisited to curb temperature rise from summer sun and internal gains.
Worked example: daily cycle
Concrete (1.8 W/mK, 2,400 kg/m³, 1,000 J/kgK), 100 mm EPS insulation (0.035 W/mK); lightweight wall of 12.5 mm gypsum + 100 mm mineral wool + 12.5 mm gypsum.
Comparison of walls
| Wall | U-value | Decrement | Time lag | Room-side admittance |
|---|---|---|---|---|
| Concrete 200 mm | 3.56 | 0.51 | 5.7 h | 5.70 |
| Concrete + external insulation | 0.32 | 0.17 | 7.9 h | 5.94 |
| Internal insulation + concrete | 0.32 | 0.33 | 7.0 h | 0.34 |
| Lightweight (gypsum + mineral wool) | 0.36 | 0.99 | 1.0 h | 0.90 |
U-value and admittance in W/m²K.
Concrete thickness
| Thickness | Decrement | Time lag |
|---|---|---|
| 100 mm | 0.83 | 2.8 h |
| 200 mm | 0.51 | 5.7 h |
| 300 mm | 0.30 | 8.3 h |
| 400 mm | 0.18 | 11.0 h |
Inside and outside insulation share a U-value, yet room-side admittance differs seventeenfold.
U-value ignores layer order, but the time-varying response depends on which layer faces the room. With external insulation the concrete faces the room, absorbing heat when the room warms and releasing it when it cools — captured by a room-side admittance of 5.9 W/m²K. With internal insulation the insulation separates the concrete from the room, leaving only 0.34 W/m²K; from the room it behaves like a lightweight wall, so sun and occupants raise temperature quickly. For outdoor heat, external insulation also damps better, with a decrement factor of 0.17, half that of internal insulation.
Design tips
- Compare decrement, time lag and room-side admittance as well as U-value.
- To use thermal mass, put heavy layers on the room side and insulation outside.
- Combine with night ventilation to purge stored heat.
- Coverings (carpet, ceiling panels) over thermal mass reduce its effect.
- Evaluate annual loads with hourly dynamic simulation.
“More insulation, hotter summers”
An office renovation added insulation inside its concrete walls plus a suspended ceiling. Winters grew warmer, but summer afternoon temperature rises became larger than before: the concrete mass was cut off from the room by insulation and ceiling panels and could no longer absorb sun and internal gains. Adding night ventilation and opening parts of the ceiling to expose the concrete brought summer rises back under control.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Comparing U only | Summer overheating missed | Check dynamic metrics |
| Ignoring layer order | Mass effect wrong | Use transfer matrices |
| Omitting finishes | Mass overrated | Actual build-up |
| Steady-state load calculation | Wrong peak loads | Dynamic simulation |
| No night ventilation | Heat accumulates | Provide a heat purge |
I'd like to learn related topics.
Related pages include building energy analysis, passive cooling, PCM in buildings, periodic heating and radiant heating and cooling.
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