polykin.properties.thermal_conductivity

KVMX2_Wassilijewa

KVMX2_Wassilijewa(
    y: FloatVectorLike,
    k: FloatVectorLike,
    M: FloatVectorLike,
) -> float

Calculate the thermal conductivity of a gas mixture from the thermal conductivities of the pure components using the mixing rule of Wassilijewa, with the simplification of Herning and Zipperer.

\[ k_m = \frac{\displaystyle \sum_{i=1}^N y_i M_i^{1/2} k_i} {\displaystyle \sum_{i=1}^N y_i M_i^{1/2}} \]

Note

In this equation, the units of mole fraction \(y_i\) and molar mass \(M_i\) are arbitrary, as they cancel out when considering the ratio of the numerator to the denominator.

References

• RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids 4th edition, 1986, pp. 410, 531.

PARAMETER	DESCRIPTION
y	Mole fractions of all components. Unit = Any. TYPE: FloatVectorLike
k	Thermal conductivities of all components. Unit = Any. TYPE: FloatVectorLike
M	Molar masses of all components. Unit = Any. TYPE: FloatVectorLike

RETURNS	DESCRIPTION
float	Mixture thermal conductivity, \(k_m\). Unit = [k].

Examples:

Estimate the thermal conductivity of a 50 mol% styrene/ethyl-benzene gas mixture at 25°C and 0.1 bar.

>>> from polykin.properties.thermal_conductivity import KVMX2_Wassilijewa
>>> y = [0.5, 0.5]
>>> k = [1.00e-2, 1.55e-2] # W/(m·K), from literature
>>> M = [104.15, 106.17]   # g/mol
>>> k_mix = KVMX2_Wassilijewa(y, k, M)
>>> print(f"{k_mix:.2e} W/(m·K)")
1.28e-02 W/(m·K)

Source code in src/polykin/properties/thermal_conductivity/vapor.py

def KVMX2_Wassilijewa(y: FloatVectorLike,
                      k: FloatVectorLike,
                      M: FloatVectorLike
                      ) -> float:
    r"""Calculate the thermal conductivity of a gas mixture from the thermal
    conductivities of the pure components using the mixing rule of Wassilijewa,
    with the simplification of Herning and Zipperer.

    $$ k_m = \frac{\displaystyle \sum_{i=1}^N y_i M_i^{1/2} k_i}
                  {\displaystyle \sum_{i=1}^N y_i M_i^{1/2}} $$

    !!! note

        In this equation, the units of mole fraction $y_i$ and molar mass
        $M_i$ are arbitrary, as they cancel out when considering the ratio of
        the numerator to the denominator.

    **References**

    *   RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids
        4th edition, 1986, pp. 410, 531.

    Parameters
    ----------
    y : FloatVectorLike
        Mole fractions of all components. Unit = Any.
    k : FloatVectorLike
        Thermal conductivities of all components. Unit = Any.
    M : FloatVectorLike
        Molar masses of all components. Unit = Any.

    Returns
    -------
    float
        Mixture thermal conductivity, $k_m$. Unit = [k].

    Examples
    --------
    Estimate the thermal conductivity of a 50 mol% styrene/ethyl-benzene gas
    mixture at 25°C and 0.1 bar.
    >>> from polykin.properties.thermal_conductivity import KVMX2_Wassilijewa
    >>> y = [0.5, 0.5]
    >>> k = [1.00e-2, 1.55e-2] # W/(m·K), from literature
    >>> M = [104.15, 106.17]   # g/mol
    >>> k_mix = KVMX2_Wassilijewa(y, k, M)
    >>> print(f"{k_mix:.2e} W/(m·K)")
    1.28e-02 W/(m·K)
    """
    y = np.asarray(y)
    k = np.asarray(k)
    M = np.asarray(M)

    a = y*sqrt(M)
    a /= a.sum()

    return dot(a, k)