Influence of thermal expansion on thermal conductivity

In summary, the conversation discusses the convention for solving heat conduction problems and whether thermal expansion should be taken into account. While for basic problems it may be easier to adjust the thermal conductivity to account for thermal expansion, for more complicated problems with elastic and plastic strains, thermal conductivity in the deformed frame may be more accurate. However, the change in thermal conductivity with temperature often has a greater impact on the calculation than thermal expansion. Therefore, it is typically sufficient to use data for thermal conductivity as a function of temperature without considering thermal expansion.
  • #1
Hologram0110
201
10
Hi everyone.
I was wondering if there is a convention for solving heat conduction problems. Specifically should one account for thermal expansion? The SI units for thermal conductivity are W/m/K. Does m include thermal strains already?

It seems for basic problems it would be easier to adjust the thermal conductivity. (ie decrease the conductivity with temperature to account for the fact that the geometry would actually be larger due to thermal conductivity).

For more complicated problems where there are elastic and plastic strains where you explicitly define a deformed and undeformed frames it seems like you would want thermal conductivity in the deformed frame.

I've been working assuming it is in the deformed frame but a colegue has raised concerns. Is there a well known convention?
 
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  • #2
For many materials, the change in thermal conductivity with temperature is much bigger than the effect of thermal expansion in your question, and the conductivity may either increase or decrease with increasing temperature for different materials. For example compare low alloy and high alloy steels in http://www.kayelaby.npl.co.uk/general_physics/2_3/2_3_7.html

The definition of thermal conductivity on that web page answers your question (if you read it carefully!), but in practice, the data is often not accurate enough for it to make any practical difference either way.
 
  • #3
I've never had to take into account expansion of a volume due to thermal expansion for the purpose of a thermal conduction calculation, I typically just use data for thermal conductivity as a function of temperature and call it good.

A quick analysis:

- Typical coefficients of thermal expansion are on the order of 10^-5 or 10^-6; for example Aluminum is 22.2*10^-6 m/m*K. Aluminum's thermal conductivity is 205 W/m*K at 298 K.

- Imagine analyzing conduction along a 1 m long bar of aluminum with square cross-section of 1 cm x 1 cm. Thermal resistance for conduction is Rt = L/(K*A). So at 298 K, thermal resistance of the bar is 48.780 K/W.

- Now increase the temperature of the bar to 398 K; thermal conductivity goes up to 215 W/m*K. If we ignore the volumetric effects this decreases the thermal resistance to 46.512 K/W.

- With the increase in temperature the bar also expands 22 microns in length and the cross-section area increases by 4.4*10^-9 m^2. If we take into account the increase of thermal conductivity and the volumetric changes to the bar the thermal reistance comes out to 46.511 K/W.

So the thermal expansion accounts for a 0.002% difference in the thermal conductivity (my guess well within the margin of error for the physical constants), where as the thermal conductivity increases by 4.9% just due to temperature change. So you would have to be talking about a very large coefficient of thermal expansion or very large temperature changes for it to become a significant effect.
 

1. What is thermal expansion?

Thermal expansion is the tendency of matter to change in volume in response to a change in temperature. As the temperature of a material increases, the particles within the material move faster and take up more space, resulting in an increase in volume.

2. How does thermal expansion affect thermal conductivity?

Thermal conductivity is a measure of a material's ability to transfer heat. When a material undergoes thermal expansion, the particles move farther apart, creating larger spaces between them. This can decrease the density of the material, which in turn can decrease its thermal conductivity.

3. Can thermal expansion impact the accuracy of thermal conductivity measurements?

Yes, thermal expansion can impact the accuracy of thermal conductivity measurements. If a material is undergoing thermal expansion during a measurement, the results may be skewed due to changes in the density and volume of the material. Therefore, it is important to account for thermal expansion when conducting thermal conductivity experiments.

4. Is thermal expansion a significant factor in thermal conductivity calculations?

It depends on the specific material and temperature range. Some materials have a larger coefficient of thermal expansion, meaning they experience a greater change in volume with a change in temperature. In these cases, thermal expansion can have a significant impact on thermal conductivity calculations.

5. How can thermal expansion be minimized in order to maintain accurate thermal conductivity measurements?

There are a few ways to minimize the effects of thermal expansion on thermal conductivity measurements. One method is to conduct experiments at a constant temperature and avoid temperature changes. Another approach is to use materials with a smaller coefficient of thermal expansion. Additionally, some measurement techniques, such as the transient hot-wire method, are less sensitive to the effects of thermal expansion.

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