The document is a problem statement asking to determine the optimum economic thickness of insulation for a 1" steel pipe carrying steam at 180°C. The pipe is 250m long and surrounded by air at 27°C. Insulation costs $200x per meter, where x is thickness in meters. The solution finds the optimum thickness as 10.442cm, with an insulating surface temperature of 39.9040C.

1. CHE 216: Optimization Problems Agustin, Joanna Dannela Enal, Jr. Hernando Medriano, Carl Angelo Uy, Debbie Ann

2. Statement of the Problem 6. 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.

3. 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:

4. Solution

8. Summary For question number 6, the optimum economic thickness of insulation that should be used was computed to be 10.442 cm . Also, surface temperature of the insulating material was found out to be 39.904⁰C .