docs: def Nu_Xu(Re, Pr, rho_w=None, rho_b=None, mu_w=None, mu_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 = 0.02269 Re_b^{0.8079} \bar{Pr}_b^{0.9213}
          \left(\frac{\rho_w}{\rho_b}\right)^{0.6638}
          \left(\frac{\mu_w}{\mu_b}\right)^{0.8687}
          
          \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]
      mu_w : float, optional
          Viscosity at the wall temperature, [Pa*s]
      mu_b : float, optional
          Viscosity at the bulk temperature, [Pa*s]
  
      Returns
      -------
      Nu : float
          Nusselt number with bulk fluid properties, [-]
  
      Notes
      -----
      For the data used to develop the correlation, P varied from 23 to 30 MPa,
      and D was 12 mm. G varied from 600-1200 kg/m^2/s and q varied from 100 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.
  
      For deteriorated heat transfer, this was the third most accurate  
      correlation in [2]_ with a MAD of 20.5%.
      
      If the extra density and viscosity information is not provided, it will 
      not be used.
  
      Examples
      --------
      >>> Nu_Xu(1E5, 1.2, 330, 290., 8e-4, 9e-4)
      289.133054256742
  
      References
      ----------
      .. [1] Xu, F., Guo, L.J., Mao, Y.F., Jiang, X.E., 2005. "Experimental 
         investigation to the heat transfer characteristics of water in vertical 
         pipes under supercritical pressure". J. Xi'an Jiaotong University 39, 
         468-471.
      .. [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 = 0.02269*Re**0.8079*Pr**0.9213
      if rho_w and rho_b:
          Nu *= (rho_w/rho_b)**0.6638
      if mu_w and mu_b:
          Nu *= (mu_w/mu_b)**0.8687
      return Nu