3. Insulation of a steam pipe for safety of the students

In a chemical engineering lab, the students are working with a steam engine that is fed by steam

pipes. One of the students reaches over to make an adjustment and burns herself by bumping her

arm on the exposed steam pipe. This prompts the lab coordinator to buy foam to cover the steam

pipes, but first he needs to calculate how thick the foam needs to be. The lab coordinator measures

the outside of the bare pipe, which has an outer diameter of 10 cm and is 2 m tall, to be 106°C. The

lab coordinator also knows that the pipe is stainless steel, and the conductivity is 17.3 W/m-K. There

needs to be at least enough insulation that the outside temperature is 50°C or less. The lab is

uncomfortably warm at 27°C, so a fan is positioned next to the steam engine and blows air at 7 m/s.

The steam inside the pipe is at 107°C and is flowing at 10 m/s. Use Appendix I in Welty et al. for

all physical properties of liquids and gases.

A. How thick does the insulation have to be if expanded polyethylene foam, which has a

conductivity of 0.3 W/m-K, is used? Hint: Excel Solver is your friend!

B. What is the inner diameter of the steam pipe?