docs: def Nu_vertical_cylinder_Kreith_Eckert(Pr, Gr, turbulent=None):
      r'''Calculates Nusselt number for natural convection around a vertical
      isothermal cylinder according to the results of [1]_  correlated by
      [2]_, also as presented in [3]_, [4]_, and [5]_.
  
      .. math::
          Nu_H = 0.555 Ra_H^{0.25},\; 10^{5} < Ra < 10^{9}
  
          Nu_H = 0.021 Ra_H^{0.4},\; 10^{9} < Ra < 10^{12}
  
      Parameters
      ----------
      Pr : float
          Prandtl number [-]
      Gr : float
          Grashof number [-]
      turbulent : bool or None, optional
          Whether or not to force the correlation to return the turbulent
  		 result; will return the laminar regime if False; leave as None for
          automatic selection
  
      Returns
      -------
      Nu : float
          Nusselt number, [-]
  
      Notes
      -----
      Transition between ranges is not smooth. If outside of range, no warning is
      given.
  
      Examples
      --------
      >>> Nu_vertical_cylinder_Kreith_Eckert(.7, 2E10)
      240.25393473033196
  
      References
      ----------
      .. [1] Eckert, E. R. G., Thomas W. Jackson, and United States. Analysis of
         Turbulent Free-Convection Boundary Layer on Flat Plate. National
         Advisory Committee for Aeronautics, no. 2207. Washington, D.C.: National
         Advisoty Committee for Aeronautics, 1950.
      .. [2] Kreith, Frank, Raj Manglik, and Mark Bohn. Principles of Heat
         Transfer. Cengage, 2010.
      .. [3] Morgan, V.T., The Overall Convective Heat Transfer from Smooth
         Circular Cylinders, in Advances in Heat Transfer, eds. T.F. Irvin and
         J.P. Hartnett, V 11, 199-264, 1975.
      .. [4] Popiel, Czeslaw O. "Free Convection Heat Transfer from Vertical
         Slender Cylinders: A Review." Heat Transfer Engineering 29, no. 6
         (June 1, 2008): 521-36. doi:10.1080/01457630801891557.
      .. [5] Boetcher, Sandra K. S. "Natural Convection Heat Transfer From
         Vertical Cylinders." In Natural Convection from Circular Cylinders,
         23-42. Springer, 2014.
      '''
      Ra = Pr*Gr
      if turbulent or (Ra > 1E9 and turbulent is None):
          return 0.021*Ra**0.4
      else:
          return 0.555*Ra**0.25