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Eucken Thermal Conductivity Model

Eucken Thermal Conductivity Model#

The Eucken pure component gas thermal conductivity model can be imported from idaes.models.properties.modular_properties.pure. In order to use it, methods to compute visc_d_phase_comp and cp_mol_ig_comp are also required.

Formulation#

The version of the Eucken model used here is derived from that in The Properties of Gases and Liquids, Section 10-3-1. Pure component gas thermal conductivity is given by the equation

\[k = \frac{\mu}{M}\left(f_\text{int}C_p \left(15/4 - 5/2 f_\text{int}\right) \right)\]

in which \(k\) is the thermal conductivity, \(\mu\) is the dynamic viscosity, \(M\) is the molar mass, \(C_p\) is the pure gas constant pressure heat capacity, \(R\) is the universal gas constant, and \(f_\text{int}\) is a dimensionless constant that accounts for thermal conductivity due to a molecule’s internal degrees of freedom. Eucken originally chose \(f_\text{int}=1\), but subsequent authors have variously chosen \(f_\text{int}=1.32\) or \(f_\text{int}=1.15\). No value of \(f_\text{int}\) is clearly superior at predicting thermal conductivity.

This equation does not appear in The Properties of Gases and Liquids, but was derived from Equation 10-3.2 by the approximation, exact for ideal gases, that \(C_p = C_v + R\), in which \(C_v\) is the constant volume heat capacity.

List of Parameters#

Parameter Name

Description

Units

mw

Molecular weight \(M\)

Mass/Amount

f_int_eucken

Eucken internal DOF factor \(f_\text{int}\)

Dimensionless

visc_d_phase_comp

Method to compute pure gas viscosity \(\mu\)

Pressure*Time

cp_mol_ig_comp

Method to compute pure ideal gas constant pressure heat capacity

Energy/(Amount*Temperature)

Example#

The code snippet below demonstrates how to specify use of the Eucken model for pure component gas thermal conductivity as part of the modular property framework. Note that if you specify therm_cond_phase_comp for one phase, you must specify it for all phases, even if only to pass None as the method.

from idaes.models.properties.modular_properties.pure import Eucken, ChapmanEnskogLennardJones, NIST

configuration = {
  "components":{
    "H2O": {
      "type": Component,
      "valid_phase_types": [PhaseType.vaporPhase, PhaseType.liquidPhase],
        ...
      "cp_mol_ig_comp": NIST,
      "visc_d_phase_comp": {"Vap": ChapmanEnskogLennardJones, "Liq": None},
      "therm_cond_phase_comp": {"Vap": Eucken, "Liq": None}
      "parameter_data": {
        "mw": (0.01801528, pyunits.kg / pyunits.mol),
        ...
        "f_int_eucken": 1,
      }
      ...
    }
    ...
  }
  ...
}

References#

Poling, Bruce, E. et al. The Properties of Gases and Liquids. 5th ed. New York: NcGraw-Hill, 2001.

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