docs: def Nu_Bishop(Re, Pr, rho_w=None, rho_b=None, D=None, x=None):
      r'''Calculates internal convection Nusselt number for turbulent vertical
      upward flow in a pipe under supercritical conditions according to [1]_.
      Correlation includes an adjustment for the thermal entry length.
      One of the most common correlations for supercritical convection.
          
      .. math::
          Nu_b = 0.0069 Re_b^{0.9} \bar Pr_b^{0.66}
          \left(\frac{\rho_w}{\rho_b}\right)^{0.43}(1+2.4D/x)
  
          \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]
      D : float, optional
          Diameter of tube, [m]
      x : float, optional
          Axial distance along the tube, [m]
  
      Returns
      -------
      Nu : float
          Nusselt number with wall fluid properties, [-]
  
      Notes
      -----
      For the data used to develop the correlation, P varied from 22.8 to 27.6 
      MPa, and D was x/D varied from 30-365. G varied from 651-3662 kg/m^2/s and 
      q varied from 310 to 3460 kW/m^2. T_b varied from 282 to 527 degrees 
      Celsius.
      
      Cp used in the calculation of Prandtl number should be the average value
      of those at the wall and the bulk temperatures.
  
      For enhanced heat transfer, this was the 11th most accurate correlation in 
      [2]_ with a MAD of 19.0%. On the overall database in [3]_, it was the 
      most accurate correlation however.
      
      If the extra density information is not provided, it will not be used.
      If both diameter and axial distance are not provided, the entrance 
      correction is not used.
  
      Examples
      --------
      >>> Nu_Bishop(1E5, 1.2, 330, 290., .01, 1.2)
      265.3620050072533
  
      References
      ----------
      .. [1] Bishop A.A., Sandberg R.O., Tong L.S. (1965) Forced convection heat 
         transfer to water at near-critical temperature and supercritical 
         pressures. In: AIChE J. Chemical engineering symposium series, no. 2.
         Institute of Chemical Engineers, London
      .. [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.
      .. [4] Jäger, Wadim, Victor Hugo Sánchez Espinoza, and Antonio Hurtado. 
         "Review and Proposal for Heat Transfer Predictions at Supercritical 
         Water Conditions Using Existing Correlations and Experiments." Nuclear 
         Engineering and Design, (W3MDM) University of Leeds International 
         Symposium: What Where When? Multi-dimensional Advances for Industrial 
         Process Monitoring, 241, no. 6 (June 2011): 2184-2203. 
         doi:10.1016/j.nucengdes.2011.03.022. 
      '''
      Nu = 0.0069*Re**0.9*Pr**0.66
      if rho_w and rho_b:
          Nu *= (rho_w/rho_b)**0.43
      if D and x:
          Nu *= (1 + 2.4*D/x)
      return Nu