% Natural convection between walls of concentric horizontal cylinders
function [hcirc, NuS, RaS] = HorzAnnNatNuT(T1,T2,R1,R2,mat)
  S = 2*log(R2./R1).^(4/3)./(R1.^(-3/5)+R2.^(-3/5)).^(5/3); 
  [RaS,Pr,kf] = Ra(T1,T2,S,mat);                            
  if max(RaS) > 1e7 warning = 'HorzAnnNatNuT: RaS > 1e7' 
  end
  keff=kf*max(0.386*(Pr.*RaS./(0.861+Pr)).^0.25,1);         
  hcirc=keff.*(R1+R2)./R1./R2./log(R2./R1);                 
  NuS=hcirc*S/kf;
end
