Thermal Conductivity of Duocel® Foam Materials

Overview: Duocel® open-cell foam is a high-performance, engineered material used in thermal management applications across aerospace, electronics, and energy systems. Its thermal conductivity is a function of multiple parallel and interacting mechanisms. The total effective thermal conductivity k_eff includes contributions from conduction through the solid ligaments, conduction through the contained gas, gas convection, and radiative transfer.

1.  General Thermal Conductivity Equation for Open-Cell Foam

k_eff = k_solid + k_gas + k_convection + k_radiation

• k_eff : Total effective thermal conductivity (W/m·K)
• k_solid: Solid-phase conduction
• k_gas: Gas-phase conduction
• k_convection: Convection through gas motion
• k_radiation: Radiative heat transfer

2. Solid Ligament Conduction

k_solid = k_bulk ⋅ ρ_rel ⋅ τ

• k_bulk: Bulk thermal conductivity (W/m·K)
• ρ_rel: Relative density (e.g., 10% = 0.10)
• τ: Tortuosity factor (∼0.33)

Material Values (10% Relative Density):

• Aluminum: 200 ⋅ 0.1 ⋅ 0.33 = 6.6
• Copper: 400 ⋅ 0.1 ⋅ 0.33 = 13.2
• SiC: 150 ⋅ 0.1 ⋅ 0.33 = 4.95
• Carbon: 2 ⋅ 0.1 ⋅ 0.33 = 0.066

3. Gas Conduction

k_gas = k_gas, bulk ⋅ (1 − ρ_rel)

• k_gas, bulk: Thermal conductivity of the fill gas (e.g., air ≈ 0.026 W/m·K)

Example

(Air, 10% RD): k_gas = 0.026 ⋅ 0.9 = 0.0234

Relative Impact:

• Aluminum, Copper: Negligible
• SiC: Minor
• Carbon: Significant

4. Convection

k_convection ≈ 0 (for small pore sizes or vacuum)

Rayleigh number:

Ra = (g ⋅ β ⋅ ΔT ⋅ d³) / (ν ⋅ α)

• g: Gravitational acceleration
• β: Thermal expansion coefficient
• ΔT: Temperature difference
• d: Characteristic pore size
• ν, α: Kinematic viscosity and thermal diffusivity

Suppression Strategy: Use fine-pore foam (80–100 PPI)

Relative Impact:

• Aluminum, Copper: Negligible
• SiC: Minor
• Carbon: Potentially significant

5. Radiative Transfer
k_radiative = (16 ⋅ σ ⋅ T³ ⋅ ε_eff) / (3 ⋅ β)

• σ: Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²·K⁴)
• T: Absolute temperature (K)
• ε_eff: Effective emissivity
• β: Extinction coefficient (related to pore size)

Typical Emissivity:

• Aluminum: ∼0.1–0.2
• Copper: ∼0.05–0.1
• SiC: ∼0.8–0.9
• Carbon: ∼0.9

Relative Impact:

• Aluminum, Copper: Minor
• SiC, Carbon: Significant at T > 500 K

Summary Table (10% RD, Air, 27°C(300K))

* Estimated for T ∼ 500–600 K with typical pore sizes.

Use these equations and values to estimate total thermal conductivity or for input into thermal simulation models. For high-fidelity modeling and design optimization, please contact us.