The document discusses optimizing the thickness of insulation on a horizontal 1" steel pipe carrying steam at 180°C. It provides conditions such as a thermal conductivity of 0.06 W/mK for the insulation material and a cost of $200x per meter of pipe length, where x is the thickness in meters. The optimal thickness is needed to minimize total annual cost over a 10 year period with a 15% time value of money.

1. Problem No.6 Coruna, Michael A Flores, Juan Paolo T. Madridejo, Jerome B. Punzalan, Mark Emile H.

2. Determine the optimum economic thickness of insulation that should be used under the following conditions: saturated steam is being passed continuously in a horizontal 1” Sch 40 steel pipe. The temperature of the steam is 180 o C, and the steam is valued at $0.0035/kg. The pipe is to be insulated with a material that has a thermal conductivity of 0.06 W/mK. The cost of the installed insulation per m of pipe length is $ 200x, where x is the thickness of the insulation in meters. Life of the installation is 10 years with time value of money equal to 15%. The total length of the pipe is 250 m, and the average temperature of the surroundings is 27 o C. Heat transfer resistances due to steam film, scale, pipe wall are negligible. The air film coefficient at the outside of the insulation may be assumed constant for all insulation thicknesses and given by the equation:

3. Solution Emissivity is assumed to be 0.9 because the type of material used for insulation is not given

4. Solution cm Assume Tw:

5. Solution Check:

7. Solution