A One-Parameter Transport Law for Nanofluids Capturing Nonlinear Thermal-Conductivity Enhancements

Classical effective-medium models (e.g., Maxwell, Hamilton–Crosser) systematically underpredict thermal-conductivity enhancements in nanofluids and cannot reproduce the characteristic sublinear growth and early saturation seen across metal-oxide, graphene, and carbon-nanotube (CNT) dispersions. I present a compact mesoscale correction that augments a baseline effective-medium estimate with a single compound parameter representing interfacial layering and collective micro-scale coupling. In its simplest closed form:

κₑff / κₘ = 1 + α √φ

where κₑff is the effective thermal conductivity, κₘ the base-fluid conductivity, φ the particle volume fraction, and α one system-level parameter that can be estimated once from lightweight characterization proxies (e.g., viscosity ratio, ζ-potential, dynamic light scattering size) and then held fixed for prediction across concentrations. The √φ shape encodes two bundled effects: (i) a density-linked screening length in the interfacial layer that weakens with concentration, and (ii) a narrow resonance-like coupling window that briefly boosts transport before saturation.

Using small, public datasets (Al₂O₃/water, graphene/water, CNT/water, 20–40 °C, φ ≤ 6%), the one-parameter law reproduces curvature and saturation that classical models miss, while remaining falsifiable: once α is fixed from a single calibration point, all remaining concentrations are blind predictions. I provide a predict-then-make workflow—measure 2–3 proxies → estimate α → forecast κₑff before formulation—and a design chart linking target gain to particle size, volume fraction, and surfactant level.

The talk covers (i) derivation and physical interpretation; (ii) validation on held-out concentrations and particle types; (iii) a falsifier specifying data patterns that would refute the model; and (iv) guidance for synthesis/processing to hit required conductivity gains without extensive trial-and-error.