For the following cases how much energy is lost every day

Question

A steam pipe, made of carbon steel (k = 50 W/m.C) is covered with three colored insulators of 1.5 cm thick each. The thermal conductivity (k) for insulators is:

Blue = 0.01 W/m.C, Red = 0.03 W/m.C, and Green = 0.05 W/m.C.

The pipe has an in-diameter of D1 Cm, a thickness of 1 cm, and a length of 50m.

For the following cases: How much energy is lost every day when the steam temperature is maintained at 200^oC, and the surrounding average air temperature is 20.0^oC, and the surroundings average air temperature is 20.0^oC? Neglect losses though the ends of the pipe.

Case 1: the pipe is covered by Blue-Red-Green

Case 2: the pipe is covered by Red-Green-Blue

Case 3: the pipe is covered by Green-Blue-Red

Case 4: the pipe is covered by Red-Green-Blue

If the price of insulators per m3 is: $200 Blue-$250 Red- $100 Green.

Calculate the total cost of each case and which case you think is the best.

For Steam hi = 80 W/m2.C, ambient air h0 = 22 W/m2.C