I tried the lumped system analysis, but my understanding is that for this method to be valid, Biot Number (Bi) has to be less than 0.1 (Bi<0.1).
Now consider a fluid with thermal conductivity k=0.14 W/m K, and heat capacity Cp= 2500 J/kg K, and density of 780 kg/m3.
Now for long pipes, Nu=3.68...