polykin.transport.heat

Nu_drop

Nu_drop(Re: float, Pr: float) -> float

Calculate the Nusselt number for a single freely falling drop.

The average Nusselt number \(\overline{Nu}=\bar{h}D/k\) is estimated by the following expression:

\[ \overline{Nu} = 2 + 0.6 Re^{1/2} Pr^{1/3} \]

\[\begin{bmatrix} 0 < Re < 1000 \\ 0.7 < Pr < 100? \\ \end{bmatrix}\]

where \(Re\) is the drop Reynolds number and \(Pr\) is the Prandtl number. The exact range for \(Pr\) in this context is unspecified. All properties are to be evaluated at the bulk temperature. This correlation was developed for use in spray drying applications.

References

• Ranz, W. and Marshall, W. (1952) "Evaporation from Drops", Chemical Engineering Progress, 48, 141-146.
• Incropera, Frank P., and David P. De Witt. "Fundamentals of heat and mass transfer", 4th edition, 1996, p. 374.

PARAMETER	DESCRIPTION
Re	Drop Reynolds number. TYPE: float
Pr	Prandtl number. TYPE: float

RETURNS	DESCRIPTION
float	Nusselt number.

See also

• Nu_sphere: generic method for spheres.

Examples:

Estimate the Nusselt number for a 1 mm styrene droplet falling in air.

>>> from polykin.transport.heat import Nu_drop
>>> D = 1e-3    # m
>>> vt = 3.8    # m/s (from vt_sphere)
>>> rho = 1.2   # kg/m³
>>> mu = 1.6e-5 # Pa.s
>>> Pr = 0.7    # from table of air properties
>>> Re = rho*vt*D/mu
>>> Nu = Nu_drop(Re, Pr)
>>> print(f"Nu={Nu:.1f}")
Nu=11.0

Source code in src/polykin/transport/heat.py

def Nu_drop(Re: float, Pr: float) -> float:
    r"""Calculate the Nusselt number for a single freely falling drop.

    The average Nusselt number $\overline{Nu}=\bar{h}D/k$ is estimated by the
    following expression:

    $$ \overline{Nu} = 2 + 0.6 Re^{1/2} Pr^{1/3} $$

    \begin{bmatrix}
    0 < Re < 1000 \\
    0.7 < Pr < 100? \\
    \end{bmatrix}

    where $Re$ is the drop Reynolds number and $Pr$ is the Prandtl number. The
    exact range for $Pr$ in this context is unspecified. All properties are to
    be evaluated at the bulk temperature. This correlation was developed for use
    in spray drying applications.

    **References**

    * Ranz, W. and Marshall, W. (1952) "Evaporation from Drops", Chemical
      Engineering Progress, 48, 141-146.
    * Incropera, Frank P., and David P. De Witt. "Fundamentals of heat and
      mass transfer", 4th edition, 1996, p. 374.

    Parameters
    ----------
    Re : float
        Drop Reynolds number.
    Pr : float
        Prandtl number.

    Returns
    -------
    float
        Nusselt number.

    See also
    --------
    * [`Nu_sphere`](Nu_sphere.md): generic method for spheres.

    Examples
    --------
    Estimate the Nusselt number for a 1 mm styrene droplet falling in air.
    >>> from polykin.transport.heat import Nu_drop
    >>> D = 1e-3    # m
    >>> vt = 3.8    # m/s (from vt_sphere)
    >>> rho = 1.2   # kg/m³
    >>> mu = 1.6e-5 # Pa.s
    >>> Pr = 0.7    # from table of air properties
    >>> Re = rho*vt*D/mu
    >>> Nu = Nu_drop(Re, Pr)
    >>> print(f"Nu={Nu:.1f}")
    Nu=11.0
    """
    check_range_warn(Re, 0, 1000, 'Re')
    check_range_warn(Pr, 0.7, 100, 'Pr')

    return 2 + 0.6*Re**(1/2)*Pr**(1/3)