polykin.transport.heat

Nu_bank_tubes

Nu_bank_tubes(
    v: float,
    rho: float,
    mu: float,
    Pr: float,
    Prs: float,
    aligned: bool,
    D: float,
    ST: float,
    SL: float,
    NL: int,
) -> float

Calculate the Nusselt number for cross flow over a bank of tubes.

For flow across a bank of aligned or staggered tubes, the average Nusselt number \(\overline{Nu}=\bar{h}D/k\) is estimated by the following expression:

\[ \overline{Nu} = C_2 C Re_{max}^m Pr^{0.36} \left(\frac{Pr}{Pr_s} \right)^{1/4} \]

where \(Re_{max}\) is the Reynolds number based on the maximum fluid velocity within the bank of tubes, and \(Pr\) is the Prandtl number. Additionally, \(C_2\), \(C\) and \(m\) are tabulated constants that depend on the tube bundle configuration.

References

• Žukauskas, Algirdas. "Heat transfer from tubes in crossflow", Advances in heat transfer. Vol. 8. Elsevier, 1972. 93-160.
• Incropera, Frank P., and David P. De Witt. "Fundamentals of heat and mass transfer", 4th edition, 1996, p. 376-381.

PARAMETER	DESCRIPTION
v	Nominal velocity outside the tube bank, \(v_{\infty}\) (m/s). TYPE: float
rho	Density (kg/m³). TYPE: float
mu	Viscosity (Pa·s). TYPE: float
Pr	Prandtl number. TYPE: float
Prs	Prandtl number at the surface of the tubes. TYPE: float
aligned	Aligned or staggered tubes. TYPE: bool
D	Diameter (m). TYPE: float
ST	Transversal pitch (m). TYPE: float
SL	Longitudinal pitch (m). TYPE: float
NL	Number of rows of tubes. TYPE: int

RETURNS	DESCRIPTION
float	Average Nusselt number of the tube bank.

See also

• Nu_tube: specific method for a single tube.

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

def Nu_bank_tubes(v: float,
                  rho: float,
                  mu: float,
                  Pr: float,
                  Prs: float,
                  aligned: bool,
                  D: float,
                  ST: float,
                  SL: float,
                  NL: int) -> float:
    r"""Calculate the Nusselt number for cross flow over a bank of tubes.

    For flow across a bank of aligned or staggered tubes, the average Nusselt
    number $\overline{Nu}=\bar{h}D/k$ is estimated by the following
    expression:

    $$ \overline{Nu} = 
        C_2 C Re_{max}^m Pr^{0.36} \left(\frac{Pr}{Pr_s} \right)^{1/4} $$

    where $Re_{max}$ is the Reynolds number based on the maximum fluid velocity
    within the bank of tubes, and $Pr$ is the Prandtl number. Additionally,
    $C_2$, $C$ and $m$ are tabulated constants that depend on the tube bundle
    configuration. 

    **References**

    * Žukauskas, Algirdas. "Heat transfer from tubes in crossflow", Advances
      in heat transfer. Vol. 8. Elsevier, 1972. 93-160.
    * Incropera, Frank P., and David P. De Witt. "Fundamentals of heat and
      mass transfer", 4th edition, 1996, p. 376-381.

    Parameters
    ----------
    v : float
        Nominal velocity outside the tube bank, $v_{\infty}$ (m/s).
    rho : float
        Density (kg/m³).
    mu : float
        Viscosity (Pa·s).
    Pr : float
        Prandtl number.
    Prs : float
        Prandtl number at the surface of the tubes.
    aligned : bool
        Aligned or staggered tubes.
    D : float
        Diameter (m).
    ST : float
        Transversal pitch (m).
    SL : float
        Longitudinal pitch (m).
    NL : int
        Number of rows of tubes.

    Returns
    -------
    float
        Average Nusselt number of the tube bank.

    See also
    --------
    * [`Nu_tube`](Nu_tube.md): specific method for a single tube.
    """

    # Maximum fluid velocity
    vmax = v * ST/(ST - D)
    if not aligned:
        SD = sqrt(SL**2 + (ST/2)**2)
        if SD < (ST + D)/2:
            vmax = v*ST/(2*(SD - D))

    Re_max = rho*vmax*D/mu

    check_range_warn(Re_max, 1e1, 2e6, 'Re_max')
    check_range_warn(Pr, 0.7, 500, 'Pr')

    # Nu for NL>=20
    if aligned:
        if Re_max < 1e2:
            C = 0.8
            m = 0.4
        elif Re_max >= 1e2 and Re_max < 1e3:
            C = 0.51
            m = 0.50
        elif Re_max >= 1e3 and Re_max < 2e5:
            C = 0.27
            m = 0.63
        else:
            C = 0.021
            m = 0.84
    else:
        if Re_max < 1e2:
            C = 0.9
            m = 0.4
        elif Re_max >= 1e2 and Re_max < 1e3:
            C = 0.51
            m = 0.50
        elif Re_max >= 1e3 and Re_max < 2e5:
            m = 0.60
            if ST/SL < 2:
                C = 0.35*(ST/SL)**0.2
            else:
                C = 0.40
        else:
            C = 0.022
            m = 0.84

    Nu = C * Re_max**m * Pr**0.36 * (Pr/Prs)**(1/4)

    # Correction for NL<20
    if NL < 20:
        if aligned:
            C2 = np.interp(
                NL,
                [1, 2, 3, 4, 5, 7, 10, 13, 16, 20],
                [0.70, 0.80, 0.86, 0.90, 0.92, 0.95, 0.97, 0.98, 0.99, 1.00])
        else:
            C2 = np.interp(
                NL,
                [1, 2, 3, 4, 5, 7, 10, 13, 16, 20],
                [0.64, 0.76, 0.84, 0.89, 0.92, 0.95, 0.97, 0.98, 0.99, 1.00])
    else:
        C2 = 1.

    return C2*Nu