r'''Calculates Nusselt number for natural convection around a vertical
    isothermal cylinder according to the results of [1]_ and [2]_ correlated by
    [3]_, as presented in [4]_, [5]_, and [6]_.

    .. math::
        Nu_H = 0.59 Ra_H^{0.25},\; 10^{4} < Ra < 10^{9}

        Nu_H = 0.13 Ra_H^{1/3.},\; 10^{9} < Ra < 10^{12}

    Parameters
    ----------
    Pr : float
        Prandtl number [-]
    Gr : float
        Grashof number [-]
    turbulent : bool or None, optional
        Whether or not to force the correlation to return the turbulent
		 result; will return the laminar regime if False; leave as None for
        automatic selection
    Returns
    -------
    Nu : float
        Nusselt number, [-]

    Notes
    -----
    Transition between ranges is not smooth. If outside of range, no warning is
    given. For ranges under 10^4, a graph is provided, not included here.

    Examples
    --------
    >>> Nu_vertical_cylinder_McAdams_Weiss_Saunders(.7, 2E10)
    313.31849434277973

    References
    ----------
    .. [1] Weise, Rudolf. "Warmeubergang durch freie Konvektion an
       quadratischen Platten." Forschung auf dem Gebiet des Ingenieurwesens
       A 6, no. 6 (November 1935): 281-92. doi:10.1007/BF02592565.
    .. [2] Saunders, O. A. "The Effect of Pressure Upon Natural Convection in
       Air." Proceedings of the Royal Society of London A: Mathematical,
       Physical and Engineering Sciences 157, no. 891 (November 2, 1936):
       278-91. doi:10.1098/rspa.1936.0194.
    .. [3] McAdams, William Henry. Heat Transmission. 3E. Malabar, Fla:
       Krieger Pub Co, 1985.
    .. [4] Morgan, V.T., The Overall Convective Heat Transfer from Smooth
       Circular Cylinders, in Advances in Heat Transfer, eds. T.F. Irvin and
       J.P. Hartnett, V 11, 199-264, 1975.
    .. [5] Popiel, Czeslaw O. "Free Convection Heat Transfer from Vertical
       Slender Cylinders: A Review." Heat Transfer Engineering 29, no. 6
       (June 1, 2008): 521-36. doi:10.1080/01457630801891557.
    .. [6] Boetcher, Sandra K. S. "Natural Convection Heat Transfer From
       Vertical Cylinders." In Natural Convection from Circular Cylinders,
       23-42. Springer, 2014.

def Nu_vertical_cylinder_McAdams_Weiss_Saunders(Pr, Gr, turbulent=None):
    r'''Calculates Nusselt number for natural convection around a vertical
    isothermal cylinder according to the results of [1]_ and [2]_ correlated by
    [3]_, as presented in [4]_, [5]_, and [6]_.

    .. math::
        Nu_H = 0.59 Ra_H^{0.25},\; 10^{4} < Ra < 10^{9}

        Nu_H = 0.13 Ra_H^{1/3.},\; 10^{9} < Ra < 10^{12}

    Parameters
    ----------
    Pr : float
        Prandtl number [-]
    Gr : float
        Grashof number [-]
    turbulent : bool or None, optional
        Whether or not to force the correlation to return the turbulent
		 result; will return the laminar regime if False; leave as None for
        automatic selection
    Returns
    -------
    Nu : float
        Nusselt number, [-]

    Notes
    -----
    Transition between ranges is not smooth. If outside of range, no warning is
    given. For ranges under 10^4, a graph is provided, not included here.

    Examples
    --------
    >>> Nu_vertical_cylinder_McAdams_Weiss_Saunders(.7, 2E10)
    313.31849434277973

    References
    ----------
    .. [1] Weise, Rudolf. "Warmeubergang durch freie Konvektion an
       quadratischen Platten." Forschung auf dem Gebiet des Ingenieurwesens
       A 6, no. 6 (November 1935): 281-92. doi:10.1007/BF02592565.
    .. [2] Saunders, O. A. "The Effect of Pressure Upon Natural Convection in
       Air." Proceedings of the Royal Society of London A: Mathematical,
       Physical and Engineering Sciences 157, no. 891 (November 2, 1936):
       278-91. doi:10.1098/rspa.1936.0194.
    .. [3] McAdams, William Henry. Heat Transmission. 3E. Malabar, Fla:
       Krieger Pub Co, 1985.
    .. [4] Morgan, V.T., The Overall Convective Heat Transfer from Smooth
       Circular Cylinders, in Advances in Heat Transfer, eds. T.F. Irvin and
       J.P. Hartnett, V 11, 199-264, 1975.
    .. [5] Popiel, Czeslaw O. "Free Convection Heat Transfer from Vertical
       Slender Cylinders: A Review." Heat Transfer Engineering 29, no. 6
       (June 1, 2008): 521-36. doi:10.1080/01457630801891557.
    .. [6] Boetcher, Sandra K. S. "Natural Convection Heat Transfer From
       Vertical Cylinders." In Natural Convection from Circular Cylinders,
       23-42. Springer, 2014.
    '''
    Ra = Pr*Gr
    if turbulent or (Ra > 1E9 and turbulent is None):
        return 0.13*Ra**(1/3.)
    else:
        return 0.59*Ra**0.25