Fourier's Law of Heat Conduction formula
| Symbol | Quantity | SI unit | Meaning |
|---|---|---|---|
| Q̇ | Heat transfer rate | W | Rate of heat flow through the slab |
| k | Thermal conductivity | W/(m·K) | Thermal conductivity of the material |
| A | Area | m² | Cross-sectional area |
| ΔT | Temperature difference | K | Temperature difference across the slab |
| L | Thickness | m | Thickness of the slab |
What is Fourier's Law of Heat Conduction?
Fourier's Law of Heat Conduction: The rate of heat flow through a material is proportional to the negative temperature gradient and to the area through which heat flows. — Joseph Fourier, 1822
Fourier's law is the heat-transfer twin of Fick's first law. Heat flows down a temperature gradient, just as mass diffuses down a concentration gradient. For a flat wall at steady state, the gradient is ΔT/L.
The quantity L/(kA) is the wall's thermal resistance. Layers in series add, like electrical resistors, which is how insulation performance (R-values and U-values) is calculated.
How to use this calculator
- Choose the quantity you want to find in the Calculate menu. It is highlighted as the result field.
- Enter the known values. Scientific notation such as
1.6e-11is accepted. - Select a unit for each value. Units are converted to SI automatically.
- The answer updates as you type. Open Show calculation steps to see the working, or use Copy result to share a link with your inputs.
Worked example
A 20 cm brick wall (k = 0.8 W/(m·K)) of area 10 m² has a 20 K temperature difference across it.
- Q̇ = 0.8 × 10 × 20 / 0.20 = 800 W.
- Heat flux = 80 W/m².
Frequently asked questions
Typical thermal conductivities?
In W/(m·K): copper ≈ 400, aluminium ≈ 237, steel ≈ 50, glass ≈ 1, brick ≈ 0.6–1, water 0.6, wood ≈ 0.12, mineral wool ≈ 0.04, air 0.026.
How does this relate to U-value?
For a single layer, U = k/L in W/(m²·K), and Q̇ = U·A·ΔT. For several layers, add their resistances L/k and invert the total.