r'''Calculates Nusselt number of a fluid passing over a bed of particles
    using a correlation shown in [1]_ and also cited in the review of [2]_.
    
    .. math::
        Nu = 1.27\frac{Pr^{1/3}}{\epsilon^{1.18}}Re^{0.36}
        + 0.033\frac{Pr^{0.5}}{\epsilon^{1.07}}Re^{0.86}

    Parameters
    ----------
    Re : float
        Reynolds number with pebble diameter as characteristic dimension, [-]
    Pr : float
        Prandtl number of the fluid [-]
    voidage : float
        Void fraction of bed packing [-]

    Returns
    -------
    Nu : float
        Nusselt number for heat transfer to the packed bed [-]

    Notes
    -----
    100 < Re < 1E5;
    0.36 < ε < 0.42;
    D/d > 20 with D as bed diameter, d as particle diameter;
    H > 4d with H as bed height.
    
    Examples
    --------
    >>> Nu_KTA(2000, 0.7, 0.4)
    102.08516480718129

    References
    ----------
    .. [1] Reactor Core Design of High-Temperature Gas-Cooled Reactors Part 2: 
       Heat Transfer in Spherical Fuel Elements (June 1983).
       http://www.kta-gs.de/e/standards/3100/3102_2_engl_1983_06.pdf
    .. [2] Abdulmohsin, Rahman S., and Muthanna H. Al-Dahhan. "Characteristics 
       of Convective Heat Transport in a Packed Pebble-Bed Reactor." Nuclear
       Engineering and Design 284 (April 1, 2015): 143-52. 
       doi:10.1016/j.nucengdes.2014.11.041.

def Nu_KTA(Re, Pr, voidage):
    r'''Calculates Nusselt number of a fluid passing over a bed of particles
    using a correlation shown in [1]_ and also cited in the review of [2]_.
    
    .. math::
        Nu = 1.27\frac{Pr^{1/3}}{\epsilon^{1.18}}Re^{0.36}
        + 0.033\frac{Pr^{0.5}}{\epsilon^{1.07}}Re^{0.86}

    Parameters
    ----------
    Re : float
        Reynolds number with pebble diameter as characteristic dimension, [-]
    Pr : float
        Prandtl number of the fluid [-]
    voidage : float
        Void fraction of bed packing [-]

    Returns
    -------
    Nu : float
        Nusselt number for heat transfer to the packed bed [-]

    Notes
    -----
    100 < Re < 1E5;
    0.36 < ε < 0.42;
    D/d > 20 with D as bed diameter, d as particle diameter;
    H > 4d with H as bed height.
    
    Examples
    --------
    >>> Nu_KTA(2000, 0.7, 0.4)
    102.08516480718129

    References
    ----------
    .. [1] Reactor Core Design of High-Temperature Gas-Cooled Reactors Part 2: 
       Heat Transfer in Spherical Fuel Elements (June 1983).
       http://www.kta-gs.de/e/standards/3100/3102_2_engl_1983_06.pdf
    .. [2] Abdulmohsin, Rahman S., and Muthanna H. Al-Dahhan. "Characteristics 
       of Convective Heat Transport in a Packed Pebble-Bed Reactor." Nuclear
       Engineering and Design 284 (April 1, 2015): 143-52. 
       doi:10.1016/j.nucengdes.2014.11.041.
    '''
    return (1.27*Pr**(1/3.)*Re**0.36/voidage**1.18 
            + 0.033*Pr**0.5/voidage**1.07*Re**0.86)