def Nu_horizontal_cylinder_Churchill_Chu(Pr, Gr):
    """Calculates Nusselt number for natural convection around a horizontal
    cylinder according to the Churchill-Chu [1]_ correlation, also presented in
    [2]_. Cylinder must be isothermal; an alternate expression exists for
    constant heat flux.

    .. math::
        Nu_{D}=\\left[0.60+\\frac{0.387Ra_{D}^{1/6}}
        {[1+(0.559/Pr)^{9/16}]^{8/27}}\\right]^2

    Parameters
    ----------
    Pr : float
        Prandtl number [-]
    Gr : float
        Grashof number with respect to cylinder diameter, [-]

    Returns
    -------
    Nu : float
        Nusselt number with respect to cylinder diameter, [-]

    Notes
    -----
    Although transition from laminar to turbulent is discrete in reality, this
    equation provides a smooth transition in value from laminar to turbulent.
    Checked with the original source, which has its powers unsimplified but
    is equivalent.

    [1]_ recommends 1E-5 as the lower limit for Ra, but no upper limit. [2]_
    suggests an upper limit of 1E12.

    Examples
    --------
    From [2]_, Example 9.2, matches:

    >>> Nu_horizontal_cylinder_Churchill_Chu(0.69, 2.63E9)
    139.13493970073597

    References
    ----------
    .. [1] Churchill, Stuart W., and Humbert H. S. Chu. "Correlating Equations
       for Laminar and Turbulent Free Convection from a Horizontal Cylinder."
       International Journal of Heat and Mass Transfer 18, no. 9
       (September 1975): 1049-53. doi:10.1016/0017-9310(75)90222-7.
    .. [2] Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and
       David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ:
       Wiley, 2011.
    """
    Ra = Pr * Gr
    return (0.6 + 0.387 * Ra ** (1 / 6.0) / (1.0 + (0.559 / Pr) ** (9 / 
        16.0)) ** (8 / 27.0)) ** 2
