docs: def Nu_Gupta(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_w = 0.004 Re_w^{0.923} \bar{Pr}_w^{0.773}
          \left(\frac{\rho_w}{\rho_b}\right)^{0.186}
          \left(\frac{\mu_w}{\mu_b}\right)^{0.366}
          
          \bar{Cp} = \frac{H_w-H_b}{T_w-T_b}
          
      Parameters
      ----------
      Re : float
          Reynolds number with wall fluid properties, [-]
      Pr : float
          Prandtl number with wall 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 wall fluid properties, [-]
  
      Notes
      -----
      For the data used to develop the correlation, P was set at 24 MPa, and D 
      was 10 mm. G varied from 200-1500 kg/m^2/s and q varied from 0 to 1250 
      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 most accurate correlation in 
      [2]_ with a MAD of 18.1%.
      
      If the extra density and viscosity information is not provided, it will 
      not be used.
  
      Examples
      --------
      >>> Nu_Gupta(1E5, 1.2, 330, 290., 8e-4, 9e-4)
      186.20135477175126
  
      References
      ----------
      .. [1] Gupta, Sahil, Amjad Farah, Krysten King, Sarah Mokry, and Igor 
         Pioro. "Developing New Heat-Transfer Correlation for SuperCritical-Water
         Flow in Vertical Bare Tubes," January 1, 2010, 809-17. 
         doi:10.1115/ICONE18-30024.
      .. [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 = 0.004*Re**0.923*Pr**0.773
      if rho_w and rho_b:
          Nu *= (rho_w/rho_b)**0.186
      if mu_w and mu_b:
          Nu *= (mu_w/mu_b)**0.366
      return Nu