r'''Calculates Nusselt number for a fluid flowing inside a curved 
    pipe such as a helical coil under turbulent conditions, using the method of 
    Mori and Nakayama [1]_, also shown in [2]_ and [3]_.
            
    For :math:`Pr < 1`:
        
    .. math::
        Nu = \frac{Pr}{26.2(Pr^{2/3}-0.074)}Re^{0.8}\left(\frac{D_i}{D_c}
        \right)^{0.1}\left[1 + \frac{0.098}{\left[Re\left(\frac{D_i}{D_c}
        \right)^2\right]^{0.2}}\right]
            
    For :math:`Pr \ge 1`:
        
    .. math::
        Nu = \frac{Pr^{0.4}}{41}Re^{5/6}\left(\frac{D_i}{D_c}\right)^{1/12}
        \left[1 + \frac{0.061}{\left[Re\left(\frac{D_i}{D_c}\right)^{2.5}
        \right]^{1/6}}\right]
        
    Parameters
    ----------
    Re : float
        Reynolds number with `D=Di`, [-]
    Pr : float
        Prandtl number with bulk properties [-]
    Di : float
        Inner diameter of the coil, [m]
    Dc : float
        Diameter of the helix/coil measured from the center of the tube on one
        side to the center of the tube on the other side, [m]

    Returns
    -------
    Nu : float
        Nusselt number with respect to `Di`, [-]

    Notes
    -----    
    At very low curvatures, the predicted heat transfer coefficient
    grows unbounded.
    
    Applicable for :math:`Re\left(\frac{D_i}{D_c}\right)^2 > 0.1`

    Examples
    --------
    >>> helical_turbulent_Nu_Mori_Nakayama(2E5, 0.7, 0.01, .2)
    496.2522480663327

    References
    ----------
    .. [1] Mori, Yasuo, and Wataru Nakayama. "Study on Forced Convective Heat 
       Transfer in Curved Pipes." International Journal of Heat and Mass 
       Transfer 10, no. 5 (May 1, 1967): 681-95. 
       doi:10.1016/0017-9310(67)90113-5. 
    .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and 
       Correlations for Convection Heat Transfer and Pressure Losses in 
       Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0
       (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693.
    .. [3] Hardik, B. K., P. K. Baburajan, and S. V. Prabhu. "Local Heat 
       Transfer Coefficient in Helical Coils with Single Phase Flow." 
       International Journal of Heat and Mass Transfer 89 (October 2015): 
       522-38. doi:10.1016/j.ijheatmasstransfer.2015.05.069.

def helical_turbulent_Nu_Mori_Nakayama(Re, Pr, Di, Dc):
    r'''Calculates Nusselt number for a fluid flowing inside a curved 
    pipe such as a helical coil under turbulent conditions, using the method of 
    Mori and Nakayama [1]_, also shown in [2]_ and [3]_.
            
    For :math:`Pr < 1`:
        
    .. math::
        Nu = \frac{Pr}{26.2(Pr^{2/3}-0.074)}Re^{0.8}\left(\frac{D_i}{D_c}
        \right)^{0.1}\left[1 + \frac{0.098}{\left[Re\left(\frac{D_i}{D_c}
        \right)^2\right]^{0.2}}\right]
            
    For :math:`Pr \ge 1`:
        
    .. math::
        Nu = \frac{Pr^{0.4}}{41}Re^{5/6}\left(\frac{D_i}{D_c}\right)^{1/12}
        \left[1 + \frac{0.061}{\left[Re\left(\frac{D_i}{D_c}\right)^{2.5}
        \right]^{1/6}}\right]
        
    Parameters
    ----------
    Re : float
        Reynolds number with `D=Di`, [-]
    Pr : float
        Prandtl number with bulk properties [-]
    Di : float
        Inner diameter of the coil, [m]
    Dc : float
        Diameter of the helix/coil measured from the center of the tube on one
        side to the center of the tube on the other side, [m]

    Returns
    -------
    Nu : float
        Nusselt number with respect to `Di`, [-]

    Notes
    -----    
    At very low curvatures, the predicted heat transfer coefficient
    grows unbounded.
    
    Applicable for :math:`Re\left(\frac{D_i}{D_c}\right)^2 > 0.1`

    Examples
    --------
    >>> helical_turbulent_Nu_Mori_Nakayama(2E5, 0.7, 0.01, .2)
    496.2522480663327

    References
    ----------
    .. [1] Mori, Yasuo, and Wataru Nakayama. "Study on Forced Convective Heat 
       Transfer in Curved Pipes." International Journal of Heat and Mass 
       Transfer 10, no. 5 (May 1, 1967): 681-95. 
       doi:10.1016/0017-9310(67)90113-5. 
    .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and 
       Correlations for Convection Heat Transfer and Pressure Losses in 
       Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0
       (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693.
    .. [3] Hardik, B. K., P. K. Baburajan, and S. V. Prabhu. "Local Heat 
       Transfer Coefficient in Helical Coils with Single Phase Flow." 
       International Journal of Heat and Mass Transfer 89 (October 2015): 
       522-38. doi:10.1016/j.ijheatmasstransfer.2015.05.069.
    '''
    D_ratio = Di/Dc
    if Pr < 1:
        term1 = Pr/(26.2*(Pr**(2/3.) - 0.074))*Re**0.8*D_ratio**0.1
        term2 = 1. + 0.098*(Re*D_ratio*D_ratio)**-0.2
    else:
        term1 = Pr**0.4/41.*Re**(5/6.)*(Di/Dc)**(1/12.)
        term2 = 1. + 0.061/(Re*(Di/Dc)**2.5)**(1/6.)
    return term1*term2