r'''Calculates the two-phase boiling heat transfer coefficient of a 
    liquid and gas flowing inside a plate and frame heat exchanger, as
    developed in [1]_ and again in the thesis [2]_. Depends on the properties
    of the fluid and not the heat exchanger's geometry.
    
    .. math::
        h = 1.87\times10^{-3}\left(\frac{k_l}{d_o}\right)\left(\frac{q d_o}
        {k_l T_{sat}}\right)^{0.56}
        \left(\frac{H_{vap} d_o^2}{\alpha_l^2}\right)^{0.31} Pr_l^{0.33}

        d_o = 0.0146\theta\left[\frac{2\sigma}{g(\rho_l-\rho_g)}\right]^{0.5}\\
        \theta =  35^\circ

    Note that this model depends on the specific heat flux involved and
    the saturation temperature of the fluid.
            
    Parameters
    ----------
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    mul : float
        Viscosity of the liquid [Pa*s]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    Hvap : float
        Heat of vaporization of the fluid at the system pressure, [J/kg]
    sigma : float
        Surface tension of liquid [N/m]
    Cpl : float
        Heat capacity of liquid [J/kg/K]
    q : float
        Heat flux, [W/m^2]
    Tsat : float
        Actual saturation temperature of the fluid at the system pressure, [K]
    angle : float, optional
        Contact angle of the bubbles with the wall, assumed 35 for refrigerants 
        in the development of the correlation [degrees]

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

    Notes
    -----
    Developed with 222 data points for R134a and R507A with only two of them
    for ammonia and R12. Chevron angles ranged from 28 to 60 degrees, heat 
    fluxes from 1.85 kW/m^2 to 10.75 kW/m^2, mass fluxes 5.6 to 52.25 kg/m^2/s,
    qualities from 0.21 to 0.95, and saturation temperatures in degrees Celcius
    of 1.9 to 13.04.
    
    The inclusion of the saturation temperature makes this correlation have
    limited predictive power for other fluids whose saturation tempratures
    might be much higher or lower than those used in the development of the
    correlation. For this reason it should be regarded with caution.
    
    As first published in [1]_ a power of two was missing in the correlation
    for bubble diameter in the dimensionless group with a power of 0.31. That
    made the correlation non-dimensional. 
    
    A second variant of this correlation was also published in [2]_ but with
    less accuracy because it was designed to mimick the standard pool boiling 
    curve.
    
    The correlation is reviewed in [3]_, but without the corrected power. It
    was also changed there to use hydraulic diameter, not bubble diameter.
    It still ranked as one of the more accurate correlations reviewed. 
    [4]_ also reviewed it without the corrected power but found it predicted
    the lowest results of those surveyed.

    Examples
    --------
    >>> h_boiling_Huang_Sheer(rhol=567., rhog=18.09, kl=0.086, mul=156E-6, 
    ... Hvap=9E5, sigma=0.02, Cpl=2200, q=1E4, Tsat=279.15)
    4401.055635078054

    References
    ----------
    .. [1] Huang, Jianchang, Thomas J. Sheer, and Michael Bailey-McEwan. "Heat 
       Transfer and Pressure Drop in Plate Heat Exchanger Refrigerant 
       Evaporators." International Journal of Refrigeration 35, no. 2 (March 
       2012): 325-35. doi:10.1016/j.ijrefrig.2011.11.002.
    .. [2] Huang, Jianchang. "Performance Analysis of Plate Heat Exchangers 
       Used as Refrigerant Evaporators," 2011. Thesis.
       http://wiredspace.wits.ac.za/handle/10539/9779
    .. [3] Amalfi, Raffaele L., Farzad Vakili-Farahani, and John R. Thome. 
       "Flow Boiling and Frictional Pressure Gradients in Plate Heat Exchangers.
       Part 1: Review and Experimental Database." International Journal of 
       Refrigeration 61 (January 2016): 166-84.
       doi:10.1016/j.ijrefrig.2015.07.010.
    .. [4] Eldeeb, Radia, Vikrant Aute, and Reinhard Radermacher. "A Survey of
       Correlations for Heat Transfer and Pressure Drop for Evaporation and 
       Condensation in Plate Heat Exchangers." International Journal of 
       Refrigeration 65 (May 2016): 12-26. doi:10.1016/j.ijrefrig.2015.11.013.

def h_boiling_Huang_Sheer(rhol, rhog, mul, kl, Hvap, sigma, Cpl, q, Tsat, 
                          angle=35.):
    r'''Calculates the two-phase boiling heat transfer coefficient of a 
    liquid and gas flowing inside a plate and frame heat exchanger, as
    developed in [1]_ and again in the thesis [2]_. Depends on the properties
    of the fluid and not the heat exchanger's geometry.
    
    .. math::
        h = 1.87\times10^{-3}\left(\frac{k_l}{d_o}\right)\left(\frac{q d_o}
        {k_l T_{sat}}\right)^{0.56}
        \left(\frac{H_{vap} d_o^2}{\alpha_l^2}\right)^{0.31} Pr_l^{0.33}

        d_o = 0.0146\theta\left[\frac{2\sigma}{g(\rho_l-\rho_g)}\right]^{0.5}\\
        \theta =  35^\circ

    Note that this model depends on the specific heat flux involved and
    the saturation temperature of the fluid.
            
    Parameters
    ----------
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    mul : float
        Viscosity of the liquid [Pa*s]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    Hvap : float
        Heat of vaporization of the fluid at the system pressure, [J/kg]
    sigma : float
        Surface tension of liquid [N/m]
    Cpl : float
        Heat capacity of liquid [J/kg/K]
    q : float
        Heat flux, [W/m^2]
    Tsat : float
        Actual saturation temperature of the fluid at the system pressure, [K]
    angle : float, optional
        Contact angle of the bubbles with the wall, assumed 35 for refrigerants 
        in the development of the correlation [degrees]

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

    Notes
    -----
    Developed with 222 data points for R134a and R507A with only two of them
    for ammonia and R12. Chevron angles ranged from 28 to 60 degrees, heat 
    fluxes from 1.85 kW/m^2 to 10.75 kW/m^2, mass fluxes 5.6 to 52.25 kg/m^2/s,
    qualities from 0.21 to 0.95, and saturation temperatures in degrees Celcius
    of 1.9 to 13.04.
    
    The inclusion of the saturation temperature makes this correlation have
    limited predictive power for other fluids whose saturation tempratures
    might be much higher or lower than those used in the development of the
    correlation. For this reason it should be regarded with caution.
    
    As first published in [1]_ a power of two was missing in the correlation
    for bubble diameter in the dimensionless group with a power of 0.31. That
    made the correlation non-dimensional. 
    
    A second variant of this correlation was also published in [2]_ but with
    less accuracy because it was designed to mimick the standard pool boiling 
    curve.
    
    The correlation is reviewed in [3]_, but without the corrected power. It
    was also changed there to use hydraulic diameter, not bubble diameter.
    It still ranked as one of the more accurate correlations reviewed. 
    [4]_ also reviewed it without the corrected power but found it predicted
    the lowest results of those surveyed.

    Examples
    --------
    >>> h_boiling_Huang_Sheer(rhol=567., rhog=18.09, kl=0.086, mul=156E-6, 
    ... Hvap=9E5, sigma=0.02, Cpl=2200, q=1E4, Tsat=279.15)
    4401.055635078054

    References
    ----------
    .. [1] Huang, Jianchang, Thomas J. Sheer, and Michael Bailey-McEwan. "Heat 
       Transfer and Pressure Drop in Plate Heat Exchanger Refrigerant 
       Evaporators." International Journal of Refrigeration 35, no. 2 (March 
       2012): 325-35. doi:10.1016/j.ijrefrig.2011.11.002.
    .. [2] Huang, Jianchang. "Performance Analysis of Plate Heat Exchangers 
       Used as Refrigerant Evaporators," 2011. Thesis.
       http://wiredspace.wits.ac.za/handle/10539/9779
    .. [3] Amalfi, Raffaele L., Farzad Vakili-Farahani, and John R. Thome. 
       "Flow Boiling and Frictional Pressure Gradients in Plate Heat Exchangers.
       Part 1: Review and Experimental Database." International Journal of 
       Refrigeration 61 (January 2016): 166-84.
       doi:10.1016/j.ijrefrig.2015.07.010.
    .. [4] Eldeeb, Radia, Vikrant Aute, and Reinhard Radermacher. "A Survey of
       Correlations for Heat Transfer and Pressure Drop for Evaporation and 
       Condensation in Plate Heat Exchangers." International Journal of 
       Refrigeration 65 (May 2016): 12-26. doi:10.1016/j.ijrefrig.2015.11.013.
    '''
    do = 0.0146*angle*(2.*sigma/(g*(rhol - rhog)))**0.5
    Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
    alpha_l = thermal_diffusivity(k=kl, rho=rhol, Cp=Cpl)
    h = 1.87E-3*(kl/do)*(q*do/(kl*Tsat))**0.56*(Hvap*do**2/alpha_l**2)**0.31*Prl**0.33
    return h