Composite Conductivity Calculator
The thermal conductivity of a composite material depends on the conductivities of its constituent phases and how those phases are arranged. The rule of mixtures provides two fundamental bounds: the parallel bound (heat flow along phase boundaries, upper bound) and the series bound (heat flow across phase boundaries, lower bound). For a carbon fiber/epoxy composite with V_fiber = 0.60, k_fiber = 10 W/(m*K) and k_epoxy = 0.3 W/(m*K): parallel bound = 0.6*10 + 0.4*0.3 = 6.12 W/(m*K); series bound = 1/(0.6/10 + 0.4/0.3) = 0.72 W/(m*K). Enter phase conductivities and volume fraction of phase 1 to compute both bounds.
Rule of mixtures formulas
Parallel: k_eff = V1 * k1 + V2 * k2
Series: k_eff = 1 / (V1/k1 + V2/k2)
Geometric mean: k_eff = sqrt(k_parallel * k_series)
V1 and V2 are volume fractions (V1 + V2 = 1). k1 and k2 are the thermal conductivities of the two phases in W/(m*K).
Choosing the right bound
For unidirectional fiber composites: use the parallel bound when measuring conductivity along the fiber axis, and the series bound when measuring perpendicular to fibers. For random short-fiber or particulate composites, experimental values typically fall near the geometric mean. For porous materials, phase 2 would be air (k = 0.026 W/(m*K)), giving a series bound that is often close to measured values.
Composite conductivity: frequently asked questions
What is the rule of mixtures for thermal conductivity?
The rule of mixtures provides upper and lower bounds for effective composite conductivity. The parallel (upper) bound is k_parallel = V1*k1 + V2*k2, assuming heat flows parallel to phase boundaries. The series (lower) bound is k_series = 1 / (V1/k1 + V2/k2), assuming heat flows perpendicular to boundaries.
Which bound is more accurate for real composites?
Real composite conductivity typically lies between the series and parallel bounds. For fiber composites measured along the fiber direction, the parallel bound is accurate. Perpendicular to fibers, the series bound applies. Particulate composites often fall near the geometric mean: sqrt(k_parallel * k_series).
What are typical thermal conductivities of composite constituents?
Carbon fiber: 5 to 700 W/(m*K) depending on type. Epoxy resin: 0.2 to 0.4 W/(m*K). Aluminum: 205 W/(m*K). Silicon carbide: 120 W/(m*K). Glass fiber: 1.0 W/(m*K). The large difference between fiber and matrix conductivities means composite conductivity is highly direction-dependent.
Does the rule of mixtures apply to electrical conductivity too?
Yes. The same parallel and series rule of mixtures applies to electrical conductivity and resistivity. The parallel model gives the upper bound for composite electrical conductivity, and the series model gives the lower bound.
What is a volume fraction and how is it measured?
Volume fraction (V1 and V2, which must sum to 1) is the fraction of the composite's total volume occupied by each phase. It is determined by acid digestion, burn-off, image analysis of cross-sections, or from manufacturing data (fiber areal weight and resin density).
Official sources
- ASTM E1225, "Standard Test Method for Thermal Conductivity of Solids": astm.org.
- ASM International, "ASM Handbook Vol. 21: Composites": asminternational.org.
- NIST, Thermal Conductivity Reference Data: nist.gov.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.