Heat Conduction
Heat flow, thermal resistance, and U-value through a material layer.
Through 10 m² with a 20.0 K difference. Heat always flows from hot to cold — the sign only tells you which way.
L ÷ (k × A). Resistances in series simply add, which is how multi-layer walls are analysed — and why one thin layer of insulation can dominate a thick masonry wall.
The U-value is heat flow per square metre per kelvin — the figure building regulations specify. Lower is better insulated.
This is steady-state conduction through one layer only. A real wall also has surface films on both faces, and often several layers — add their resistances in series. Note the thousand-fold spread in conductivity: 200 mm of brick resists heat about as well as 13 mm of mineral wool.
Fourier's law gives Q = kA·ΔT ÷ L. A 200 mm brick wall of 10 m² with 20 K across it conducts 0.6 × 10 × 20 ÷ 0.2 = 600 W. Thermal resistance is L ÷ kA, here 0.033 K/W.
Heat flow behaves like current
Conduction through a wall follows the same shape of equation as current through a resistor. Temperature difference plays the role of voltage, heat flow the role of current, and thermal resistance the role of electrical resistance: Q = ΔT ÷ R, exactly parallel to I = V ÷ R.
That analogy is not a teaching gimmick — it is how multi-layer construction is actually analysed. Resistances in series simply add, so a wall of brick, insulation, and plasterboard is handled by summing three resistances and dividing the temperature difference by the total.
Conductivity spans a thousandfold
The material property k ranges from about 0.03 W/(m·K) for foam insulation to 385 for copper — more than four orders of magnitude. This is why insulation works at all: 200 mm of brick has roughly the same thermal resistance as 13 mm of mineral wool.
It is also why a metal component bridging an insulated wall is such a problem. A steel fixing with k around 50 conducts more than a thousand times as readily as the foam around it, creating a thermal bridge that can dominate the heat loss of an otherwise well-insulated assembly.
k is thermal conductivity in W/(m·K), L the thickness in metres, and A the area in m². The U-value is heat flow per m² per kelvin, which is the figure building regulations specify.
Worked example: a 200 mm brick wall
Resistance and heat flow are two views of the same calculation:
- 1 Convert the thickness to metres. 200 mm = 0.2 m. Mixing millimetres into the formula is the most common error here.
- 2 Take the temperature difference. 20 °C inside and 0 °C outside gives ΔT = 20 K. A difference in °C equals the same difference in K.
- 3 Apply Fourier’s law. 0.6 × 10 m² × 20 K ÷ 0.2 m = 600 W.
- 4 Or work through resistance. R = 0.2 ÷ (0.6 × 10) = 0.0333 K/W, and 20 ÷ 0.0333 = 600 W. Same answer.
- 5 Get the U-value. k ÷ L = 0.6 ÷ 0.2 = 3.0 W/(m²·K) — very poor by modern standards, where walls target below 0.3.
Thermal conductivity of common materials
Approximate values at room temperature, in W/(m·K). Lower conducts less and insulates better.
| Material | k | Thickness matching 200 mm brick |
|---|---|---|
| Polyurethane foam | 0.03 | 10 mm |
| Mineral wool | 0.04 | 13 mm |
| Timber | 0.13 | 43 mm |
| Brick | 0.6 | 200 mm |
| Glass | 1.0 | 333 mm |
| Concrete | 1.4 | 467 mm |
| Steel | 50 | 16.7 m |
| Copper | 385 | 128 m |
What this model leaves out
Three simplifications are worth naming. First, this is steady state: it assumes temperatures have settled and nothing is still warming up. Transient problems — how long a component takes to reach temperature — need the material's heat capacity as well, and a different equation.
Second, conduction is only one of three mechanisms. A real wall also loses heat by convection at each surface and by radiation, both of which are captured as additional surface resistances in building calculations. Ignoring them overstates the heat flow somewhat.
Third, this covers a single uniform layer. Real assemblies are layered, and the useful move there is to compute each layer's resistance and add them — which also immediately shows which layer is doing the work. In a typical insulated wall the insulation contributes the overwhelming majority of the total resistance, and the masonry contributes surprisingly little.