def Nu_vertical_helical_coil_Prabhanjan_Rennie_Raghavan(Pr, Gr):
    """Calculates Nusselt number for natural convection around a vertical
    helical coil inside a tank or other vessel according to the Prabhanjan,
    Rennie, and Raghavan [1]_ correlation.

    .. math::
        Nu_H = 0.0749\\text{Ra}_H^{0.3421}
        
    The range of Rayleigh numbers is as follows:
        
    .. math::
        9 \\times 10^{9} < \\text{Ra} < 4 \\times 10^{11}
    
    Parameters
    ----------
    Pr : float
        Prandtl number calculated with the film temperature -
        wall and temperature very far from the coil average, [-]
    Gr : float
        Grashof number calculated with the film temperature -
        wall and temperature very far from the coil average,
        and using the total height of the coil [-]

    Returns
    -------
    Nu : float
        Nusselt number using the total height of the coil
        and the film temperature, [-]

    Notes
    -----    
    [1]_ also has several other equations using different characteristic
    lengths.
    
    Examples
    --------
    >>> Nu_vertical_helical_coil_Prabhanjan_Rennie_Raghavan(4.4, 1E11)
    720.6211067718227

    References
    ----------
    .. [1] Prabhanjan, Devanahalli G., Timothy J. Rennie, and G. S. Vijaya
       Raghavan. "Natural Convection Heat Transfer from Helical Coiled Tubes." 
       International Journal of Thermal Sciences 43, no. 4 (April 1, 2004): 
       359-65.
    """
    Ra = Pr * Gr
    return 0.0749 * Ra ** 0.3421
