Two competitor companies have been developing novel materials for use in a varie

Question

• Two competitor companies have been developing novel materials for use in a variety of sectors (energy, healthcare, aviation, etc.). The materials conduct heat, but the extent of this is unknown. You have been contacted by one of the companies to help them identify the thermal conductivity of the materials. In conversations with your peers, the company recognizes that you have the technical skill set needed to help them, but in this competitive environment, the company is also interested in greatly accelerating its pace of technological innovation and before giving you the job wants to access your level of creativity and your ability to solve problems. Thus, the company has first asked you to convince it that you can make such measurements using a limited cadre of supplies/equipment. You understand that scale (nano vs. micro vs. macro) likely plays a role with these materials, but for the purposes of this challenge, these aspects can be neglected. Devise an experimental strategy for how you would address this challenge.
• You have the following items at your disposal:
• ? Electrical power from the local power service (e.g., TVA) ? Heat plates with magnetic stirrers and stir bars ? A variety of glass beakers ? Water ? Ring stands and clamps ? Thermometers ? Thermocouples ? Foam padding ? Boiled eggs ? Three metallic rods: one made of plain carbon steel with a known thermal conductivity (see Table A.1 in the text); and two other rods provided by the company and made of materials that are known but not disclosed to you nor can you tell what they are by simple observation. Upon request, the company will reveal material properties for one of the materials that it provides
• please explain it for me with some examples

Explanation / Answer

I want to take a piece of this material (make it into a small pipe), put a cap on the bottom, then fill it with boiling water, then cap the top. Hang it in a room of constant temp and measure the temp of the outside wall of the pipe using thermometers and thrermocouples

I figure if I use a small pipe (1" ID) the mass of the water will be small enough that it might take some time to work it's way thru. (it's plastic pipe.)

I will know the mass/volume of the water and it's temp. The surface area of the pipe and a temp over time graph. Is there a way to calculate the thermal conductivity of the material the pipe is made of using this data?

One thing I'm also not sure of is the surface area of the ID of the pipe which will be in contact with the water will be less than the radiating surface area of the pipe which is based on the OD of the pipe. So I'm not sure how I should consider that.


The equation is

dQ/dt = -k A dT/dr

where

A is the outer area of the pipe 2 pi ro L
k is the thermal conductivity (power/degree/length)
t is time
ro is outer diameter of the inner pipe
L is the length of the inner pipe

dT/dr is the rate of change of temperature across the pipe wall, (Ti-To)/(ri-ro) is a good approximation, where

Ti is the inner water temperature
To is the outer water temperature
ri is the inner diameter of the inner pipe

dQ/dt is the rate of heat transfer to the outer water. dQ/dt=c V dTo/dt where

c is the heat capacity of water (1 calorie per degree centigrade per cc, I think)
V is the volume of the outer water

so what you want to measure is the time rate of change of temperature of the outer water and solve for k.

k=(dQ/dt)/(A dT/dr)

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