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 = 1.07 Ra_H^{0.28},\; 2\times 10^{6} < Ra < 2\times 10^{8}

        Nu_H = 0.152 Ra_H^{0.38},\; 2\times 10^{8} < Ra < 2\times 10^{11}

    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 diameters 0.475 cm to 7.62 cm, L/D from 8 to 127. Isothermal
    boundary condition was assumed, but not verified. Transition between ranges
    is not smooth. If outside of range, no warning is given. The higher range
    of [1]_ is not shown in [3]_, and the formula for the first is actually for
    the second in [3]_.

    Examples
    --------
    >>> Nu_vertical_cylinder_Carne_Morgan(.7, 2E8)
    204.31470629065677

    References
    ----------
    .. [1] J. B. Carne. "LIX. Heat Loss by Natural Convection from Vertical
       Cylinders." The London, Edinburgh, and Dublin Philosophical Magazine and
       Journal of Science 24, no. 162 (October 1, 1937): 634-53.
       doi:10.1080/14786443708565140.
    .. [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_Carne_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 = 1.07 Ra_H^{0.28},\; 2\times 10^{6} < Ra < 2\times 10^{8}

        Nu_H = 0.152 Ra_H^{0.38},\; 2\times 10^{8} < Ra < 2\times 10^{11}

    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 diameters 0.475 cm to 7.62 cm, L/D from 8 to 127. Isothermal
    boundary condition was assumed, but not verified. Transition between ranges
    is not smooth. If outside of range, no warning is given. The higher range
    of [1]_ is not shown in [3]_, and the formula for the first is actually for
    the second in [3]_.

    Examples
    --------
    >>> Nu_vertical_cylinder_Carne_Morgan(.7, 2E8)
    204.31470629065677

    References
    ----------
    .. [1] J. B. Carne. "LIX. Heat Loss by Natural Convection from Vertical
       Cylinders." The London, Edinburgh, and Dublin Philosophical Magazine and
       Journal of Science 24, no. 162 (October 1, 1937): 634-53.
       doi:10.1080/14786443708565140.
    .. [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 > 2E8 and turbulent is None):
        return 0.152*Ra**0.38
    else:
        return 1.07*Ra**0.28