r'''Calculates average internal convection Nusselt number for laminar flows
    in pipe during the thermal entry region as developed in [1]_, also
    shown in [2]_.

    .. math::
        Nu_D=1.86\left(\frac{D}{L}Re_DPr\right)^{1/3}\left(\frac{\mu_b}
        {\mu_s}\right)^{0.14}

    Parameters
    ----------
    Re : float
        Reynolds number, [-]
    Pr : float
        Prandtl number, [-]
    L : float
        Length of pipe [m]
    Di : float
        Diameter of pipe [m]
    mu : float, optional
        Viscosity of fluid, [Pa*s]
    mu_w : float, optional
        Viscosity of fluid at wall temperature, [Pa*s]

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

    Notes
    -----
    Reynolds number should be less than 10000. This should be calculated
    using pipe diameter.
    Prandlt number should be no less than air and no more than liquid metals;
    0.7 < Pr <  16700
    Viscosities should be the bulk and surface properties; they are optional.
    Outside the boundaries, this equation is provides very false results.

    Examples
    --------
    >>> laminar_entry_Seider_Tate(Re=100000, Pr=1.1, L=5, Di=.5)
    41.366029684589265

    References
    ----------
    .. [1] 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.
    .. [2] Serth, R. W., Process Heat Transfer: Principles,
       Applications and Rules of Thumb. 2E. Amsterdam: Academic Press, 2014.

def laminar_entry_Seider_Tate(Re, Pr, L, Di, mu=None, mu_w=None):
    r'''Calculates average internal convection Nusselt number for laminar flows
    in pipe during the thermal entry region as developed in [1]_, also
    shown in [2]_.

    .. math::
        Nu_D=1.86\left(\frac{D}{L}Re_DPr\right)^{1/3}\left(\frac{\mu_b}
        {\mu_s}\right)^{0.14}

    Parameters
    ----------
    Re : float
        Reynolds number, [-]
    Pr : float
        Prandtl number, [-]
    L : float
        Length of pipe [m]
    Di : float
        Diameter of pipe [m]
    mu : float, optional
        Viscosity of fluid, [Pa*s]
    mu_w : float, optional
        Viscosity of fluid at wall temperature, [Pa*s]

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

    Notes
    -----
    Reynolds number should be less than 10000. This should be calculated
    using pipe diameter.
    Prandlt number should be no less than air and no more than liquid metals;
    0.7 < Pr <  16700
    Viscosities should be the bulk and surface properties; they are optional.
    Outside the boundaries, this equation is provides very false results.

    Examples
    --------
    >>> laminar_entry_Seider_Tate(Re=100000, Pr=1.1, L=5, Di=.5)
    41.366029684589265

    References
    ----------
    .. [1] 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.
    .. [2] Serth, R. W., Process Heat Transfer: Principles,
       Applications and Rules of Thumb. 2E. Amsterdam: Academic Press, 2014.
    '''
    Nu = 1.86*(Di/L*Re*Pr)**(1/3.0)
    if mu_w and mu:
        Nu *= (mu/mu_w)**0.14
    return Nu