Experiment to measure the thermal conductivity of a material

[matt621]

We have a customer asking us for the thermal conductivity of a product we sell.

None of the engineers have that number.

I can think of a simple experiment that might do it, but I don't know the math.

I want to take a piece of this material (it's a 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 one of those infared temp sensors.

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.

If you can help a big thanks!

 

[Rap]

I'll try to find the equations for this. I think you want to run hot water thru the pipe as fast as you can, instead of capping it and pouring hot water in. That way you know the temperature at the inner radius and don't have to worry about how much the pipe cools the water. I think you will also have to know the specific heat of the plastic - how much heat you have to put into it in order to raise its temperature one degree. Do you have that number?

 

[matt621]

No, we don't have any engineering specs on it at all. It's kind of a hybrid material.

 

[Rap]

If you measure the temperature of the wall, its a function of k/c where k is the thermal conductivity, and c is the heat capacity of the material. You can avoid worrying about the heat capacity if you can measure the heat given off at the wall, rather than the temperature. If you can run water at a fixed high temperature through the pipe, and then enclose it in a larger pipe, and recirculate cold water through the outer pipe, and measure the temperature of the cold water as it warms up, that would be better.

 

[matt621]

Yes, I see what you mean. I could rig up something.

It'll depend on the order size to see if it's worth going thru all that.

So if we run constant known temp in the inside and the monitor the temp of the water enclosed on the outside, I'm assuming we plot temp v time. And from there we do I get the thermal conductivity for the pipe?

thanks

 

[Rap]

Yes, I see what you mean. I could rig up something.

It'll depend on the order size to see if it's worth going thru all that.

So if we run constant known temp in the inside and the monitor the temp of the water enclosed on the outside, I'm assuming we plot temp v time. And from there we do I get the thermal conductivity for the pipe?

thanks

Sorry, tex is really flaky so I have to write the equations in text

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)

I didn't bother with units, but if you need those spelled out, let me know.

 

[Studiot]

Why don't you just do a conventional thin slice test?

Sandwich a thin disk of your material between two (polished) steel plates, heat one plate and measure the rate of temperature rise on the other.

Accuracy is good because the edges are small compared to the transfer area.

 

[matt621]

Thanks to all. At least I know i can give a reasonably accurate no. if we get to that point.

Thanks you to all!

 

[Rap]

Why don't you just do a conventional thin slice test?

Sandwich a thin disk of your material between two (polished) steel plates, heat one plate and measure the rate of temperature rise on the other.

Accuracy is good because the edges are small compared to the transfer area.

That would be good if you can get a thin slice of the material, if you are not restricted to using the pipe itself. You would have to know the heat capacity of the steel, though, right?

 

[Studiot]

If matt's company manufactures pipe, they must have sheets of the stuff. What about the end caps?