Determining the effective thermal conductivity of a sand/aluminum mix

[viderde]

Problem:
This should be a very simple problem, I just want to make sure I am doing it correctly. I have a box of sand. I am adding aluminum shavings to it. How do I determine the effective thermal conductivity of the mixture.

Known:
Density of sand and aluminum
Mass of sand and aluminum in box
K values of sand and aluminum

I have seen several methods online how to do this so I want someones expert advice on the correct way to figure out the theoretical effective thermal conductivity of the mixture.

 

[berkshire]

Mix and measure,
Re- mix re-measure.
Re-iterate until you have a chart.


The good engineer does not need to memorize every formula; he just needs to know where he can find them when he needs them. Old professor

 

[IRstuff]

I don't think this is a "simple" problem. The relative proportions of the materials, their relative sizes, the degree of compaction, etc. all enter into the resultant conductivity.

TTFN
faq731-376

 

[Compositepro]

Your neglecting the ingredient that that has the greatest effect - air.

 

[viderde]

@Berkshire
I need to know the theoretical k so that I can compare it to an experimental value.

@IRstuff
I know the proportions of the sand and aluminum, and I will be assuming the sand and aluminum particles are the same size (not true, but the shavings are very small so it will be close enough)

@Compositepro
I will be finding the theoretical k of several different mixtures with different percentages of aluminum in the mixture. These will be compared to each other and to the k of sand by itself, so the k value of air is irrelevant. Explain if you think otherwise.

 

[berkshire]

viderde,
Here is a link to theroretical K values of common elements
But I think you said you already had this.

http://www.engineeringtoolbox.com/thermal-conductivity-d_429.html

I am looking at your experiment and wondering how you are going to determine that your mixture is homogenous.
B.E.

The good engineer does not need to memorize every formula; he just needs to know where he can find them when he needs them. Old professor

 

[moltenmetal]

You also may be forgetting another key component: water. If the sand is moist at all, you're talking about a totally different problem.

If you do figure it out, and get experimental data to back it up, please make sure you come back here and post the results. This is not a trivial problem by any stretch of the imagination.

 

[CastMetal]

The compaction and moisture content of the sand has a dramatic effect on the thermal conductivity of sand in and of itself as others have said.

This paper is probably worth a read to see the effects these two variables can have.

http://hydrologydays.colostate.edu/Papers_2009/Smits_paper.pdf

Comprehension is not understanding. Understanding is not wisdom. And it is wisdom that gives us the ability to apply what we know, to our real world situations