r'''Calculates the two-phase non-boiling heat transfer coefficient of a 
    liquid and gas flowing inside a tube of any inclination, as in [1]_ and 
    reviewed in [2]_.

    .. math::
        \frac{h_{TP} D}{k_l} = 0.060\left(\frac{\rho_L}{\rho_G}\right)^{0.28}
        \left(\frac{DG_{TP} x}{\mu_L}\right)^{0.87}
        \left(\frac{C_{p,L} \mu_L}{k_L}\right)^{0.4}
        
    Parameters
    ----------
    m : float
        Mass flow rate [kg/s]
    x : float
        Quality at the specific tube interval [-]
    D : float
        Diameter of the tube [m]
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    Cpl : float
        Constant-pressure heat capacity of liquid [J/kg/K]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    mul : float
        Viscosity of liquid [Pa*s]

    Returns
    -------
    h : float
        Heat transfer coefficient [W/m^2/K]

    Notes
    -----
    Developed for both vertical and horizontal flow, and flow patters of 
    annular or mist annular flow. Steam-water and air-water were the only 
    considered fluid combinations. Quality ranged from 0.1 to 1 in their data.
    [1]_ claimed an AAE of 17%.

    Examples
    --------
    >>> Davis_David(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6, 
    ... mul=1E-3)
    1437.3282869955121

    References
    ----------
    .. [1] Davis, E. J., and M. M. David. "Two-Phase Gas-Liquid Convection Heat
       Transfer. A Correlation." Industrial & Engineering Chemistry 
       Fundamentals 3, no. 2 (May 1, 1964): 111-18. doi:10.1021/i160010a005.
    .. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. 
       Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with 
       Seven Sets of Experimental Data, Including Flow Pattern and Tube 
       Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1, 
       1999): 15-40. doi:10.1080/014576399271691.

def Davis_David(m, x, D, rhol, rhog, Cpl, kl, mul):
    r'''Calculates the two-phase non-boiling heat transfer coefficient of a 
    liquid and gas flowing inside a tube of any inclination, as in [1]_ and 
    reviewed in [2]_.

    .. math::
        \frac{h_{TP} D}{k_l} = 0.060\left(\frac{\rho_L}{\rho_G}\right)^{0.28}
        \left(\frac{DG_{TP} x}{\mu_L}\right)^{0.87}
        \left(\frac{C_{p,L} \mu_L}{k_L}\right)^{0.4}
        
    Parameters
    ----------
    m : float
        Mass flow rate [kg/s]
    x : float
        Quality at the specific tube interval [-]
    D : float
        Diameter of the tube [m]
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    Cpl : float
        Constant-pressure heat capacity of liquid [J/kg/K]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    mul : float
        Viscosity of liquid [Pa*s]

    Returns
    -------
    h : float
        Heat transfer coefficient [W/m^2/K]

    Notes
    -----
    Developed for both vertical and horizontal flow, and flow patters of 
    annular or mist annular flow. Steam-water and air-water were the only 
    considered fluid combinations. Quality ranged from 0.1 to 1 in their data.
    [1]_ claimed an AAE of 17%.

    Examples
    --------
    >>> Davis_David(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6, 
    ... mul=1E-3)
    1437.3282869955121

    References
    ----------
    .. [1] Davis, E. J., and M. M. David. "Two-Phase Gas-Liquid Convection Heat
       Transfer. A Correlation." Industrial & Engineering Chemistry 
       Fundamentals 3, no. 2 (May 1, 1964): 111-18. doi:10.1021/i160010a005.
    .. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L. 
       Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with 
       Seven Sets of Experimental Data, Including Flow Pattern and Tube 
       Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1, 
       1999): 15-40. doi:10.1080/014576399271691.
    '''
    G = m/(pi/4*D**2)
    Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
    Nu_TP = 0.060*(rhol/rhog)**0.28*(D*G*x/mul)**0.87*Prl**0.4
    return Nu_TP*kl/D