Cu vs Al Heat Transfer Debate: Specific Heat vs Thermal Conductivity Explained

[Steve_]

I got into a discussion about heat sink materials and was beaten up for suggesting that Aluminum is better than Copper because it will transfer the heat away from itself much faster than copper.
Copper has about half the specific heat and about twice the thermal conductivity over Aluminum.
Am I incorrect in the notion that the specific heat not the thermal conductivity will dominate the calculation of heat transfer to a gas like air from a metal fin?
I took thermo about 30 years ago and didn't really like it much or make a stellar showing. However, I recall that the specific heat is very important when condidering the flux of heat. I also keep thinking about how fast Al will cool down compared to Cu.

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May your world be linear, Gaussian, and steady state.

 

[ZapperZ]

I got into a discussion about heat sink materials and was beaten up for suggesting that Aluminum is better than Copper because it will transfer the heat away from itself much faster than copper.
Copper has about half the specific heat and about twice the thermal conductivity over Aluminum.
Am I incorrect in the notion that the specific heat not the thermal conductivity will dominate the calculation of heat transfer to a gas like air from a metal fin?
I took thermo about 30 years ago and didn't really like it much or make a stellar showing. However, I recall that the specific heat is very important when condidering the flux of heat. I also keep thinking about how fast Al will cool down compared to Cu.

----------------------------
May your world be linear, Gaussian, and steady state.

I hope you didn't have a bet, because you are wrong here.

Specific heat simply tells you how much heat you need to supply to raise a unit mass of the object by 1 degree C (or K). It doesn't say how fast the heat moves through the material, which is something you get from thermal conductivity coefficient.

In fact, with Cu having a smaller specific heat means that it not only can it increase its temperature faster and conducts heat faster, but it can also lose heat easier. This means that if one end of it is in a cold bath, it will lose the heat that it is conducting much more efficiently.

So I would certainly use Cu as a heat sink material to "suck" away the heat.

Zz.

 

[Phrak]

In fact, with Cu having a smaller specific heat means that it not only can it increase its temperature faster and conducts heat faster, but it can also lose heat easier. This means that if one end of it is in a cold bath, it will lose the heat that it is conducting much more efficiently.
Zz.

I don't get that last part, Zapper. As I'v learned it, the thermal resistance of a chunck of heat sink from region A to region B is all you need to know in selecting a heat sink. As far as I know this is determined soley by geometry and the thermal conductivity of the material.

Perhaps you mean that Cu can lose its temperature (rather than heat) easier, due to it's lower specific heat.

 

[mgb_phys]

Zapper is only correct for the case where the input power is removed, the copper will cool more quickly - but that is a bit unusual. In the steady state the heat capacity of the heat sink is irrelevant.

It might matter for some transient cases where there are rapid changes in the temperature of the heat source and you want the heatsink to be able to follow it without there being too much of a temperature difference which could lead to mechanical stress.

For gases the heat capacity is much more important, that is why you use Helium for heat transfer and Argon for insulation.

 

[ZapperZ]

I don't get that last part, Zapper. As I'v learned it, the thermal resistance of a chunck of heat sink from region A to region B is all you need to know in selecting a heat sink. As far as I know this is determined soley by geometry and the thermal conductivity of the material.

Perhaps you mean that Cu can lose its temperature (rather than heat) easier, due to it's lower specific heat.

If you are using something merely to absorb and retain the heat, then Cu isn't the right one. But if you are hoping to conduct the heat away (that's why I said to a cold bath), then Cu would be something you want to use due to the two properties that you had mentioned. The "geometry" is simply to increase the surface area of contact with the heat source. The thermal conductivity is how efficiently that material can move that heat to other parts of its bulk volume. However, if it doesn't have a low specific heat, then it doesn't give off that heat easily and at some point, its temperature will go up. If we take a naive model of heat transfer and Newton's Law of Cooling, then there will be a drop in the temperature gradient and thus, a decrease in the rate of heat flow in the material, making it less efficient at conducting the heat away.

Zz.

 

[Mapes]

Several people, including the original poster, have mentioned the "speed" at which something heats or cools. The figure of merit here is the thermal diffusivity

[tex]\alpha=\frac{k}{\rho c}[/itex]

where $k$ is the thermal conductivity, $\rho$ is the density, and $c$ is the specific heat capacity. This value is about 20% higher for copper than alumunum. So copper wins the speed metric.

(Edited, used molar specific heats the first time and got the opposite answer.)

 

[ZapperZ]

Several people, including the original poster, have mentioned the "speed" at which something heats or cools. The figure of merit here is the thermal diffusivity

[tex]\alpha=\frac{k}{\rho c}[/itex]

where $k$ is the thermal conductivity, $\rho$ is the density, and $c$ is the specific heat capacity. This value is about twice as high for aluminum due to copper's large density.

The original poster is technically right ("Aluminum...will transfer the heat away from itself much faster than copper") but for the wrong reason. Also, note that aluminum is faster, but less energy is being transferred because of its lower thermal conductivity. Speed isn't everything!

Ah, of course! Thanks for bringing this up. I had neglected to consider this aspect of it.

Zz.

 

[Mapes]

But please note my correction above.

 

[ZapperZ]

But please note my correction above.

That's fine. I just forgot to include diffusivity into the whole thing and thought the conductivity was sufficient. Either way, Cu still wins. :)

Zz.

 

[Steve_]

Thanks all for the replys. My perception was inaccurate and I am corrected.

I went looking for the math that might help me understand the relationship of Cp and k to temperature.
(This is from the Handbook of Physics, Springer 2006, pp753.)
dQ/dt for a mass cooling while submersed in another material has this solution:

T(t) = (T0-TM) * e ^-(k*A/(Cp*m))*t + TM
Cp of the cooling medium >> Cp of material

As pointed out, for fast cooling we want low Cp and high k. Now I am thinking about doing an experiment to see how well this model will agree with reality.

 

[russ_watters]

T(t) = (T0-TM) * e ^-(k*A/(Cp*m))*t + TM
Cp of the cooling medium >> Cp of material

As pointed out, for fast cooling we want low Cp and high k. Now I am thinking about doing an experiment to see how well this model will agree with reality.

Just to clarify here, are you talking about having the object cool itself or cool something else. Those are two different processes with two different requirements.

 

[Steve_]

Russ, sorry this took a while, I was without internet the last few days.
The problem was the transport of heat from a hot elelctronic part to the air. But I was just asking about the part where a hot mass is submersed in a cool mass. Like a single fin in air or water. It looks like the total heat transfer problem is not trivial but I think I have a handle on the way Cp and k effect the cooling rate for a simple case.

Thanks again.