polykin.hmt.correlations

Nu_combined

Nu_combined(
    Nu_forced: float, Nu_free: float, assisted: bool
) -> float

Calculate the combined Nusselt number for forced and free convection.

The combined Nusselt number is given by the following expression:

\[ Nu = \sqrt[3]{Nu_{forced}^3 \pm Nu_{free}^3} \]

where the sign depends on the relative motion of the forced and free flows. The plus sign is for assisted or transverse flow and the minus sign is for opposing flows.

Tip

Combined free and forced convection is important when \(Gr/Re^2 \approx 1\).

References

• Incropera, Frank P., and David P. De Witt. "Fundamentals of heat and mass transfer", 4th edition, 1996, p. 515.

PARAMETER	DESCRIPTION
Nu_forced	Nusselt number for forced convection. TYPE: float
Nu_free	Nusselt number for free convection. TYPE: float
assisted	Flag to indicate the relative motion of the forced and free flows. Set True for assisted or transverse flow and False for opposing flows. TYPE: bool

RETURNS	DESCRIPTION
float	Combined Nusselt number.

Examples:

Calculate the combined Nusselt number for a transverse flow where the free and forced Nusselt numbers are 10.0 and 20.0, respectively.

>>> from polykin.hmt import Nu_combined
>>> Nu = Nu_combined(Nu_forced=20.0, Nu_free=10.0, assisted=True)
>>> print(f"Nu={Nu:.1f}")
Nu=20.8

Source code in src/polykin/hmt/correlations.py

def Nu_combined(Nu_forced: float,
                Nu_free: float,
                assisted: bool) -> float:
    r"""Calculate the combined Nusselt number for forced and free convection.

    The combined Nusselt number is given by the following expression:

    $$ Nu = \sqrt[3]{Nu_{forced}^3 \pm Nu_{free}^3} $$

    where the sign depends on the relative motion of the forced and free flows.
    The plus sign is for assisted or transverse flow and the minus sign is for
    opposing flows.

    !!! tip

        Combined free and forced convection is important when
        $Gr/Re^2 \approx 1$.

    **References**

    * Incropera, Frank P., and David P. De Witt. "Fundamentals of heat and
      mass transfer", 4th edition, 1996, p. 515.

    Parameters
    ----------
    Nu_forced : float
        Nusselt number for forced convection.
    Nu_free : float
        Nusselt number for free convection.
    assisted : bool
        Flag to indicate the relative motion of the forced and free flows. Set
        `True` for assisted or transverse flow and `False` for opposing flows.  

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

    Examples
    --------
    Calculate the combined Nusselt number for a transverse flow where the free
    and forced Nusselt numbers are 10.0 and 20.0, respectively.
    >>> from polykin.hmt import Nu_combined
    >>> Nu = Nu_combined(Nu_forced=20.0, Nu_free=10.0, assisted=True)
    >>> print(f"Nu={Nu:.1f}")
    Nu=20.8
    """
    if assisted:
        return cbrt(Nu_forced**3 + Nu_free**3)
    else:
        return cbrt(Nu_forced**3 - Nu_free**3)