Thermal Diffusivity Calculator

Thermal diffusivity is α = k / (ρ × c_p), where k is thermal conductivity in W/(m·K), ρ is density in kg/m³, and c_p is specific heat capacity in J/(kg·K). The result is in m²/s. The same relation can be rearranged to solve for any variable: k = α·ρ·c_p, ρ = k/(α·c_p), c_p = k/(α·ρ).

For air at 20 °C: k = 0.026 W/(m·K), ρ = 1.2 kg/m³, c_p = 1007 J/(kg·K). Then α = 0.026 / (1.2 × 1007) = 0.026 / 1208.4 = 2.1516 × 10⁻⁵ m²/s, i.e. 21.516 × 10⁻⁶ m²/s or 21.516 mm²/s.

Copper: k = 401 W/(m·K), ρ = 8960 kg/m³, c_p = 385 J/(kg·K) → α = 1.1625 × 10⁻⁴ m²/s (116.245 × 10⁻⁶ m²/s, or 4.5045 ft²/h). Water at 20 °C: k = 0.598, ρ = 997, c_p = 4182 → α = 1.4342 × 10⁻⁷ m²/s (0.143424 mm²/s). Copper responds about 28.7 times faster than stainless steel 304 (α = 4.05 × 10⁻⁶ m²/s).

The SI unit is m²/s. Common alternatives: mm²/s (1 m²/s = 10⁶ mm²/s), cm²/s (1 m²/s = 10⁴ cm²/s), ft²/s (1 m²/s = 10.7639 ft²/s) and ft²/h (1 m²/s = 38750.08 ft²/h). Metals are usually quoted in ×10⁻⁶ m²/s, e.g. aluminum 97.86 × 10⁻⁶ m²/s.

Thermal penetration depth δ = √(α × t) estimates how far a temperature change has propagated into a solid after time t. Example: for air (α = 2.1516 × 10⁻⁵ m²/s) after 1 hour, δ = √(2.1516 × 10⁻⁵ × 3600) = √(0.077458) = 0.27831 m, about 278.31 mm.

Rearrange α = k/(ρ·c_p). Density: ρ = k/(α·c_p). Specific heat: c_p = k/(α·ρ). Conductivity: k = α·ρ·c_p. Example: α = 21.516 × 10⁻⁶ m²/s, k = 0.026 W/(m·K), c_p = 1007 J/(kg·K) → ρ = 0.026 / (21.516 × 10⁻⁶ × 1007) = 1.2 kg/m³ (0.0749 lb/ft³).