How to determine the thermal conductivity of a sand/aluminum mixture
How to determine the thermal conductivity of a sand/aluminum mixture
(OP)
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.
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.





RE: How to determine the thermal conductivity of a sand/aluminum mixture
In 'Introduction to Composite materials Design' Barbero gives an alternative: Kcomp = Ksand * (1+eta*Vfalu)/(1-eta*Vfalu) and eta = (Kalu/Ksand-1)/(Kalu/Ksand+1). For 250 and 0.15 and 25% Vf aluminium this gives Kcomp = 0.25 W/(m.K). (At least, I think it does.)
I tend to trust Barbero, but I must admit this is my simplification of his formula for 2-direction or though-thickness conductivity of a long fibre composite.
My own googling turned up
ftp
and
http://wv
so it looks like it might be quite a bit more complicated and slightly higher Kcomp is possible, but for a reasonable real-world value 'close to the sand plus a bit' is probably good enough as an initial stab, and as usual trial and error with your actual application (whatever it is) is the most practical way forward. If it's important then measuring the Kcomp would seem quite advisable (particularly if the sand can be wet), though it would quite awkward to do well. Let's hope someone with a more practical or aerothermal-type background is prompted to contribute.
RE: How to determine the thermal conductivity of a sand/aluminum mixture
You also have this posted in heat transfer and thermodynamics engineering.
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