Heat Transfer

The material which has lower thermal condutivity should be insulated first or the insulation should increase order of k to get effective insulation.

By applying higher insulation layer at lower surface & lower at upper surface,

  Q/A=K1*(dT/dX)
 Q/A=K2*(dT/dX)
  K1(DT)1+K2DT2=Q/A*X
  FOR(q/A) MAX.
 d(Q/A)/dX=0

           q/a is directly proportional to k

            to make less q/a less value of k requird 

            therefore K2 comes first

I do have a question here, If the material of lower insulation be bounded to the first system, doesn't that result in heat loss?

I dont think you can generalise this problem - at least not for flat plane and cylindrical co-ordinates. It really depends on how much bigger k2 is relative to k1 and how big the pipe thickness is relative to the diameter.