Hong Life CalculatorsUnderstanding the thermal diffusivity calculator — concept and principle
Thermal diffusivity tells you how quickly a temperature change spreads through a material. This calculator combines thermal conductivity, density and specific heat into the diffusivity in three units, and also gives the volumetric heat capacity, the thermal effusivity and a rough time for heat to soak through a given thickness. Engineers, students and cooks comparing pan materials use it.
How it is calculated
α = k ÷ (ρ × cp)
Volumetric heat capacity = ρ × cp
Effusivity e = √(k × ρ × cp)
Characteristic time t ≈ L² ÷ α
- k is thermal conductivity in W/(m·K), ρ density in kg/m³, cp specific heat in J/(kg·K).
- α is shown in m²/s, mm²/s (×10⁶) and cm²/s (×10⁴).
- L is the thickness in mm, converted to metres for the time estimate.
The principle
Conductivity k says how easily heat flows; ρcp says how much heat each cubic metre must absorb to warm by one kelvin. A material that conducts well but stores little heat lets a temperature change race through it, so α is their ratio. It appears as the only material constant in the heat equation ∂T/∂t = α∇²T. Because heat spreads by diffusion, distance grows with the square root of time, so the time to reach a depth L grows with L². Doubling the thickness makes it take about four times as long. Effusivity describes something different: how much heat a surface exchanges on contact, which is why metal feels colder than wood at the same temperature.
Worked example
Default inputs: k = 237 W/(m·K), ρ = 2,700 kg/m³, cp = 900 J/(kg·K) (aluminium), thickness 10 mm.
- ρcp = 2,700 × 900 = 2,430,000 J/(m³·K) = 2.43 MJ/(m³·K).
- α = 237 ÷ 2,430,000 = 0.00009753 m²/s = 97.53 mm²/s = 0.9753 cm²/s.
- Effusivity = √(237 × 2,430,000) = 23,998 W·s½/(m²·K).
- Characteristic time = (0.010 m)² ÷ 0.00009753 = 1.025 s.
| Density ρ (kg/m³) | Thermal diffusivity α (m²/s) |
|---|---|
| 675 | 0.0003901 |
| 1,350 | 0.0001951 |
| 2,025 | 0.00013 |
| 2,700 | 0.00009753 |
| 3,375 | 0.00007802 |
| 4,050 | 0.00006502 |
| 5,400 | 0.00004877 |
How to read the result
Metals such as aluminium and copper have high diffusivity, so they heat evenly and quickly. Stone, glass and water are much lower, and insulating materials and wood are lower still. A large L²/α means a part's inside lags far behind its surface during heating or cooling. The time scale is an order-of-magnitude guide: actual times also depend on shape, surface heat transfer and how close to the final temperature you need to be.
Common mistakes
- Mixing specific heat in J/(g·K) with density in kg/m³; enter cp in J/(kg·K).
- Treating L²/α as the exact heating time instead of a scale.
- Using room-temperature properties for very hot or cold conditions.
Frequently asked questions
What is the difference between conductivity and diffusivity?
Conductivity measures how much heat flows for a given temperature gradient; diffusivity measures how fast the temperature itself changes.
Why does metal feel colder than wood at the same temperature?
Metal's much higher effusivity draws heat from your skin faster.
What is the Fourier number?
Fo = α t ÷ L², a dimensionless time; Fo ≈ 1 corresponds to the characteristic time shown here.
Sources: J. Wilson, "Thermal Diffusivity", Electronics Cooling, August 2007 · OpenStax, College Physics, specific heat table