r'''Calculates internal convection Nusselt number for turbulent flows
    in pipe according to [1]_ and supposedly [2]_.

    .. math::
        Nu = 0.027Re^{4/5}Pr^{1/3}\left(\frac{\mu}{\mu_s}\right)^{0.14}

    Parameters
    ----------
    Re : float
        Reynolds number, [-]
    Pr : float
        Prandtl number, [-]
    mu : float
        Viscosity of fluid, [Pa*s]
    mu_w : float
        Viscosity of fluid at wall temperature, [Pa*s]

    Returns
    -------
    Nu : float
        Nusselt number, [-]

    Notes
    -----
    A linear coefficient of 0.023 is often listed with this equation. The
    source of the discrepancy is not known. The equation is not present in the
    original paper, but is nevertheless the source usually cited for it.

    Examples
    --------
    >>> turbulent_Sieder_Tate(Re=1E5, Pr=1.2)
    286.9178136793052
    >>> turbulent_Sieder_Tate(Re=1E5, Pr=1.2, mu=0.01, mu_w=0.067)
    219.84016455766044

    References
    ----------
    .. [1] Rohsenow, Warren and James Hartnett and Young Cho. Handbook of Heat
       Transfer, 3E. New York: McGraw-Hill, 1998.
    .. [2] Sieder, E. N., and G. E. Tate. "Heat Transfer and Pressure Drop of
       Liquids in Tubes." Industrial & Engineering Chemistry 28, no. 12
       (December 1, 1936): 1429-35. doi:10.1021/ie50324a027.

def turbulent_Sieder_Tate(Re, Pr, mu=None, mu_w=None):
    r'''Calculates internal convection Nusselt number for turbulent flows
    in pipe according to [1]_ and supposedly [2]_.

    .. math::
        Nu = 0.027Re^{4/5}Pr^{1/3}\left(\frac{\mu}{\mu_s}\right)^{0.14}

    Parameters
    ----------
    Re : float
        Reynolds number, [-]
    Pr : float
        Prandtl number, [-]
    mu : float
        Viscosity of fluid, [Pa*s]
    mu_w : float
        Viscosity of fluid at wall temperature, [Pa*s]

    Returns
    -------
    Nu : float
        Nusselt number, [-]

    Notes
    -----
    A linear coefficient of 0.023 is often listed with this equation. The
    source of the discrepancy is not known. The equation is not present in the
    original paper, but is nevertheless the source usually cited for it.

    Examples
    --------
    >>> turbulent_Sieder_Tate(Re=1E5, Pr=1.2)
    286.9178136793052
    >>> turbulent_Sieder_Tate(Re=1E5, Pr=1.2, mu=0.01, mu_w=0.067)
    219.84016455766044

    References
    ----------
    .. [1] Rohsenow, Warren and James Hartnett and Young Cho. Handbook of Heat
       Transfer, 3E. New York: McGraw-Hill, 1998.
    .. [2] Sieder, E. N., and G. E. Tate. "Heat Transfer and Pressure Drop of
       Liquids in Tubes." Industrial & Engineering Chemistry 28, no. 12
       (December 1, 1936): 1429-35. doi:10.1021/ie50324a027.
    '''
    Nu = 0.027*Re**0.8*Pr**(1/3.)
    if mu_w and mu:
        Nu *= (mu/mu_w)**0.14
    return Nu