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Maxwell–Garnett Conductivity Model

Mathematical Modelling — Fluid Dynamics & Heat TransferContinuum mechanics; boundary-layer similarity theory

The effective thermal and electrical conductivity of the dilute, spherical-particle suspension.

Dimension I

Definition

What it is — and what it is not

What it is
  • S1The Maxwell–Garnett correlation for the effective conductivity of a dilute suspension. [1.1]
Boundary of meaning
  • S2Assumes dilute, non-interacting, spherical particles. [1.1]
Attributes
  • S3It gives both the thermal conductivity k_hnf and the electrical conductivity σ_hnf from the particle and fluid values. [1.1]

Dimension II

In practice

How to deal with it

No practical guidance recorded yet.

Sub-topics 4

Related

References

  1. Aziz et al. (2021), DOI 10.1007/s10973-020-10210-2.

    • 1.1

      Article property model — Evidence that the steady comparison article applies an effective-conductivity closure; Maxwell/Maxwell Garnett primary sources are seeded separately.

      AmbiguityCorroborated

      The two-species pseudo-particle extension remains a declared dilute-mixture assumption, not a result established by Aziz.

  2. Maxwell (1881), Treatise, 2nd ed.

    • 2.1

      Treatise, Vol. 1, Ch. IX — Effective conductivity of dilute spherical inclusions. This model extends it with p_s=(φ₁p_s₁+φ₂p_s₂)/(φ₁+φ₂) for p∈{k,σ}, then p_hnf/p_f=[p_s+2p_f+2φ(p_s−p_f)]/[p_s+2p_f−φ(p_s−p_f)].

      AmbiguityEstablished

      The two-species pseudo-particle extension is a declared modelling assumption, valid only for dilute non-interacting inclusions; φ=0 must use the continuous base-fluid limit rather than evaluate 0/0.

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