Thermal Conductivity Formula
The thermal conductivity formula calculates heat transfer through materials based on temperature difference and thickness.
The Formula
This is Fourier's Law of heat conduction, published by Joseph Fourier in France in 1822. It describes the rate at which heat flows through a material. Higher thermal conductivity means the material transfers heat faster. This formula is fundamental to building insulation, electronics cooling, and industrial heat exchanger design.
Variables
| Symbol | Meaning |
|---|---|
| Q/t | Rate of heat transfer (measured in watts, W, or BTU/hour) |
| k | Thermal conductivity of the material (W/m·K or BTU/hr·ft·°F) |
| A | Cross-sectional area through which heat flows (m² or ft²) |
| ΔT | Temperature difference between the two sides (K, °C, or °F) |
| d | Thickness of the material (m or ft) |
Thermal Conductivity Values
| Material | k (W/m·K) | Category |
|---|---|---|
| Copper | 385 | Excellent conductor |
| Aluminum | 205 | Good conductor |
| Steel | 50 | Moderate conductor |
| Glass | 0.8 | Poor conductor |
| Brick | 0.6 | Insulator |
| Wood | 0.12 | Good insulator |
| Fiberglass insulation | 0.04 | Excellent insulator |
| Styrofoam | 0.03 | Excellent insulator |
| Air (still) | 0.025 | Excellent insulator |
Example 1 (Metric)
A glass window is 0.005 m thick and 1.5 m² in area. The inside temperature is 22°C and outside is -5°C. How much heat is lost per second? (k for glass = 0.8 W/m·K)
Identify values: k = 0.8, A = 1.5, ΔT = 22 - (-5) = 27°C, d = 0.005
Q/t = 0.8 × 1.5 × 27 / 0.005
Q/t = 32.4 / 0.005
Q/t = 6,480 W (6.48 kW)
Example 2 (Imperial)
A brick wall is 8 inches (0.667 ft) thick and 100 ft². Inside is 70°F, outside is 30°F. k for brick = 0.4 BTU/hr·ft·°F. What is the heat loss rate?
Q/t = 0.4 × 100 × (70-30) / 0.667
Q/t = 0.4 × 100 × 40 / 0.667
Q/t = 2,399 BTU/hour
When to Use It
Use this formula for any situation involving heat flow through solid materials.
- Designing building insulation and calculating heat loss through walls, roofs, and windows
- Sizing heat sinks for electronics and computer processors
- Engineering industrial heat exchangers and cooling systems
- Comparing insulation materials (lower k = better insulator)
- Estimating heating and cooling costs based on wall construction
- Selecting materials for cookware (high k heats food evenly)
R-Value Connection
The R-value used in building insulation is the inverse of thermal conductance.
R = d / k (thickness divided by thermal conductivity).
Higher R-value means better insulation. Double the thickness = double the R-value.