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

    .. math::
        Nu_H = 0.555 Ra_H^{0.25},\; 10^{4} < Ra < 10^{8}

        Nu_H = 0.129 Ra_H^{1/3},\; 10^{8} < 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
    -----
    Cylinder of diameter 3.5 cm, length from L/D = 4.3. Air as fluid.
    Transition between ranges is not smooth.
    If outside of range, no warning is given. Results are presented rounded in
    [4]_, and the second range is not shown in [3]_.

    Examples
    --------
    >>> Nu_vertical_cylinder_Jakob_Linke_Morgan(.7, 2E10)
    310.90835207860454

    References
    ----------
    .. [1] Jakob, M., and Linke, W., Warmeubergang beim Verdampfen von
       Flussigkeiten an senkrechten und waagerechten Flaschen, Phys. Z.,
       vol. 36, pp. 267-280, 1935.
    .. [2] 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.
    .. [3] 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.
    .. [4] 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_Jakob_Linke_Morgan(Pr, Gr, turbulent=None):
    r'''Calculates Nusselt number for natural convection around a vertical
    isothermal cylinder according to the results of [1]_ correlated by [2]_, as
    presented in [3]_ and [4]_.

    .. math::
        Nu_H = 0.555 Ra_H^{0.25},\; 10^{4} < Ra < 10^{8}

        Nu_H = 0.129 Ra_H^{1/3},\; 10^{8} < 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
    -----
    Cylinder of diameter 3.5 cm, length from L/D = 4.3. Air as fluid.
    Transition between ranges is not smooth.
    If outside of range, no warning is given. Results are presented rounded in
    [4]_, and the second range is not shown in [3]_.

    Examples
    --------
    >>> Nu_vertical_cylinder_Jakob_Linke_Morgan(.7, 2E10)
    310.90835207860454

    References
    ----------
    .. [1] Jakob, M., and Linke, W., Warmeubergang beim Verdampfen von
       Flussigkeiten an senkrechten und waagerechten Flaschen, Phys. Z.,
       vol. 36, pp. 267-280, 1935.
    .. [2] 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.
    .. [3] 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.
    .. [4] 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 > 1E8 and turbulent is None):
        Nu = 0.129*Ra**(1/3.)
    else:
        Nu = 0.555*Ra**0.25
    return Nu