docs: def Nu_vertical_cylinder_Al_Arabi_Khamis(Pr, Gr, L, D, turbulent=None):
      r'''Calculates Nusselt number for natural convection around a vertical
      isothermal cylinder according to [1]_, also as presented in [2]_ and [3]_.
  
      .. math::
          Nu_H = 2.9Ra_H^{0.25}/Gr_D^{1/12},\; 9.88 \times 10^7 \le Ra_H \le 2.7\times10^{9}
  
          Nu_H = 0.47 Ra_H^{0.333}/Gr_D^{1/12},\; 2.7 \times 10^9 \le Ra_H \le 2.95\times10^{10}
  
      Parameters
      ----------
      Pr : float
          Prandtl number [-]
      Gr : float
          Grashof number with respect to cylinder height [-]
      L : float
          Length of vertical cylinder, [m]
      D : float
          Diameter of cylinder, [m]
      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
      -----
      For air. Local Nusselt number results also given in [1]_. D from 12.75 to
      51 mm; H from 300 to 2000 mm. Temperature kept constant by steam condensing.
  
      If outside of range, no warning is given. Applies for range of:
  
      .. math::
          1.08 \times 10^4 \le Gr_D \le 6.9 \times 10^5
  
      Examples
      --------
      >>> Nu_vertical_cylinder_Al_Arabi_Khamis(.71, 2E10, 10, 1)
      280.39793209114765
  
      References
      ----------
      .. [1] Al-Arabi, M., and M. Khamis. "Natural Convection Heat Transfer from
         Inclined Cylinders." International Journal of Heat and Mass Transfer 25,
         no. 1 (January 1982): 3-15. doi:10.1016/0017-9310(82)90229-0.
      .. [2] 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.
      .. [3] Boetcher, Sandra K. S. "Natural Convection Heat Transfer From
         Vertical Cylinders." In Natural Convection from Circular Cylinders,
         23-42. Springer, 2014.
      '''
      Gr_D = Gr/L**3*D**3
      Ra = Pr*Gr
      if turbulent or (Ra > 2.6E9 and turbulent is None):
          return 0.47*Ra**(1/3.)*Gr_D**(-1/12.)
      else:
          return 2.9*Ra**0.25*Gr_D**(-1/12.)