% Natural convection between walls of concentric spheres
function [hcirc, NuS, RaS] = ConcSphEnclNatNuT(T1,T2,R1,R2,mat)
  S = 2^-(1/3)*(1./R1-1./R2).^(4/3)./(R1.^(-7/5)+R2.^(-7/5)).^(5/3); 
  [RaS,Pr,kf] = Ra(T1,T2,S,mat);                                     
  if max(RaS) > 1e4 warning = 'ConcSphEnclNatNu: RaS > 1e4' 
  end
  keff=kf*max(0.74*(Pr.*RaS./(0.861+Pr)).^0.25,1);                   
  hcirc=(R1.^2+R2.^2).*keff./R1./R2./(R2-R1);
  NuS=hcirc*S/kf;
end
