docs: def Nu_Zhu(Re, Pr, rho_w=None, rho_b=None, k_w=None, k_b=None):
      r'''Calculates internal convection Nusselt number for turbulent vertical
      upward flow in a pipe under supercritical conditions according to [1]_.
          
      .. math::
          Nu_b = 0.0068 Re_b^{0.9} \bar{Pr}_b^{0.63}
          \left(\frac{\rho_w}{\rho_b}\right)^{0.17}
          \left(\frac{k_w}{k_b}\right)^{0.29}
  
          \bar{Cp} = \frac{H_w-H_b}{T_w-T_b}
          
      Parameters
      ----------
      Re : float
          Reynolds number with bulk fluid properties, [-]
      Pr : float
          Prandtl number with bulk fluid properties and an average heat capacity
          between the wall and bulk temperatures [-]
      rho_w : float, optional
          Density at the wall temperature, [kg/m^3]
      rho_b : float, optional
          Density at the bulk temperature, [kg/m^3]
      k_w : float, optional
          Thermal conductivity at the wall temperature, [W/m/K]
      k_b : float, optional
          Thermal conductivity at the bulk temperature, [W/m/K]
  
      Returns
      -------
      Nu : float
          Nusselt number with bulk fluid properties, [-]
  
      Notes
      -----
      For the data used to develop the correlation, P varied from 22 to 30 MPa,
      and D was 26 mm. G varied from 600-1200 kg/m^2/s and q varied from 200 to 
      600 kW/m^2.    
      
      Cp used in the calculation of Prandtl number should be the average value
      of those at the wall and the bulk temperatures.
  
      On the overall database in [2]_, this was the 8th most accurate 
      correlation,and ninth most accurate against normal heat transfer.
      
      If the extra density and thermal conductivity information is not provided, 
      it will not be used.
  
      Examples
      --------
      >>> Nu_Zhu(1E5, 1.2, 330, 290., 0.63, 0.69)
      240.1459854494706
  
      References
      ----------
      .. [1] Zhu, Xiaojing, Qincheng Bi, Dong Yang, and Tingkuan Chen. "An 
         Investigation on Heat Transfer Characteristics of Different Pressure 
         Steam-Water in Vertical Upward Tube." Nuclear Engineering and Design 
         239, no. 2 (February 2009): 381-88. doi:10.1016/j.nucengdes.2008.10.026.
      .. [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.
      '''
      Nu = 0.0068*Re**0.9*Pr**0.63
      if rho_w and rho_b:
          Nu *= (rho_w/rho_b)**0.17
      if k_w and k_b:
          Nu *= (k_w/k_b)**0.29
      return Nu