def Nu_Bringer_Smith(Re, Pr):
    """Calculates internal convection Nusselt number for turbulent vertical
    upward flow in a pipe under near-supercritical conditions according to 
    [1]_ and as shown in [2]_ and [3]_.
        
    .. math::
        Nu_x = 0.0266Re_x^{0.77}Pr_w^{0.55}

    Parameters
    ----------
    Re : float
        Reynolds number with fluid properties at T_ref, [-]
    Pr : float
        Prandtl number with wall fluid properties, [-]

    Returns
    -------
    Nu : float
        Nusselt number with fluid properties at T_ref, [-]

    Notes
    -----
    Fit to data somewhat distant from the critical and pseudo-critical regions.
    Found to fit the data in [3]_ fourth best; in [2]_ however, it was ranked
    so low that no ranking was given.
    
    Tref and the properties therein should be evaluated as follows:
    
    .. math::
        T_{ref} = T_b \\text{ if } \\frac{T_{pc}-T_b}{T_w-T_b} < 0

    .. math::
        T_{ref} = T_{pc} \\text{ if } 0 < \\frac{T_{pc}-T_b}{T_w-T_b}  < 1
        
    .. math::
        T_{ref} = T_w \\text{ if } \\frac{T_{pc}-T_b}{T_w-T_b} > 1
    
    Examples
    --------
    >>> Nu_Bringer_Smith(1E5, 1.2)
    208.17631753279107

    References
    ----------
    .. [1] Bringer, R. P., and J. M. Smith. "Heat Transfer in the Critical 
       Region." AIChE Journal 3, no. 1 (March 1, 1957): 49-55. 
       doi:10.1002/aic.690030110. 
    .. [2] Chen, Weiwei, Xiande Fang, Yu Xu, and Xianghui Su. "An Assessment of
       Correlations of Forced Convection Heat Transfer to Water at 
       Supercritical Pressure." Annals of Nuclear Energy 76 (February 2015): 
       451-60. doi:10.1016/j.anucene.2014.10.027.
    .. [3] Yu, Jiyang, Baoshan Jia, Dan Wu, and Daling Wang. "Optimization of 
       Heat Transfer Coefficient Correlation at Supercritical Pressure Using 
       Genetic Algorithms." Heat and Mass Transfer 45, no. 6 (January 8, 2009): 
       757-66. doi:10.1007/s00231-008-0475-4.
    """
    return 0.0266 * Re ** 0.77 * Pr ** 0.55
