docs: def Nu_Ornatsky(Re, Pr_b, Pr_w, rho_w=None, rho_b=None):
      r'''Calculates internal convection Nusselt number for turbulent vertical
      upward flow in a pipe under supercritical conditions according to [1]_ as
      shown in both [2]_ and [3]_.
          
      .. math::
          Nu_b = 0.023Re_b^{0.8}(\min(Pr_b, Pr_w))^{0.8}
          \left(\frac{\rho_w}{\rho_b}\right)^{0.3}
  
      Parameters
      ----------
      Re : float
          Reynolds number with bulk fluid properties, [-]
      Pr_b : float
          Prandtl number with bulk fluid properties, [-]
      Pr_w : float
          Prandtl number with wall fluid properties, [-]
      rho_w : float, optional
          Density at the wall temperature, [kg/m^3]
      rho_b : float, optional
          Density at the bulk temperature, [kg/m^3]
  
      Returns
      -------
      Nu : float
          Nusselt number with bulk fluid properties, [-]
  
      Notes
      -----
      [2]_ ranked it thirteenth in the enhanced heat transfer
      category, with a MAD of 19.8% and 11th in the normal heat transfer with a
      MAD of 17.6%. [3]_ ranked it seventh on a combined database.
      
      If the extra density information is not provided, it will not be used.
  
      Examples
      --------
      >>> Nu_Ornatsky(1E5, 1.2, 1.5, 330, 290.)
      276.63531150832307
  
      References
      ----------
      .. [1] Ornatsky A.P., Glushchenko, L.P., Siomin, E.T. (1970). The research
         of temperature conditions of small diameter parallel tubes cooled by 
         water under supercritical pressures. In: Proceedings of the 4th 
         international heat transfer conference, Paris-Versailles, France. 
         Elsevier, Amsterdam, vol VI, Paper no. B, 8 November 1970
      .. [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.
      .. [3] Yu, Jiyang, Baoshan Jia, Dan Wu, and Daling Wang. "Optimization of 
         Heat Transfer Coefficient Correlation at Supercritical Pressure Using 
         Genetic Algorithms." Heat and Mass Transfer 45, no. 6 (January 8, 2009): 
         757-66. doi:10.1007/s00231-008-0475-4.
      '''
      Nu = 0.023*Re**0.8*min(Pr_b, Pr_w)**0.8
      if rho_w and rho_b:
          Nu *= (rho_w/rho_b)**0.3
      return Nu