Rate of thermal conduction in various copper structures

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Discussion Overview

The discussion revolves around the rate of thermal conduction in various configurations of copper within a cylindrical structure, specifically comparing solid copper, copper powder, small diameter copper rods, small diameter copper tubes, and a honeycomb structure surrounded by air. The focus is on theoretical implications of these configurations on thermal conductivity under continuous heat application.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant outlines a scenario with a cylinder made of different copper structures and queries how the rate of thermal conduction would differ among them.
  • Another participant suggests that thermal conductivity is proportional to cross-sectional area and inversely proportional to length, indicating that cases with solid copper and certain configurations should be straightforward to analyze.
  • Concerns are raised about the complexities in calculating thermal conductivity for configurations with voids, such as copper powder and honeycomb structures, suggesting that these would likely have lower conductivity than solid copper.
  • A hypothesis is presented that in materials with small pores, thermal energy may be transferred more effectively to the conducting copper walls rather than through the air in the pores, potentially increasing conductivity for copper powder compared to the honeycomb structure.
  • One participant introduces the idea that increased surface area in configurations d) and e) could reduce propagation time for infrared energy, questioning the validity of this perspective.
  • Another participant counters that copper is opaque to infrared and suggests that conduction typically dominates over radiation unless there is a significant temperature difference.

Areas of Agreement / Disagreement

Participants express differing views on the impact of surface area and voids on thermal conductivity, with no consensus reached on the validity of the infrared propagation argument or the comparative conductivity of the various configurations.

Contextual Notes

Participants acknowledge the complexities involved in calculating thermal conductivity for non-uniform structures, particularly those with voids, and the potential influence of temperature differences on conduction versus radiation.

Who May Find This Useful

This discussion may be of interest to those studying thermal conductivity in materials science, engineering applications involving heat transfer, and theoretical physics related to thermal dynamics.

steveh721
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A cylinder is constructed from a super insulator. The dimensions of the cylinder are Length L: 1 M; inside diameter i.d.: 12 mm. The entire Length of the cylinder contains copper (cases described below).

Heat (T > 100C) is continuously applied to the copper on one end of the cylinder. There is a heat sink attached to the copper at the opposite end of the cylinder--it can dissipate the heat at or above the rate of heat absorption.

What will be the difference in rate of conduction, if any, for:

a) the cylinder contains solid copper (12mm dia. X L)

b) the cylinder is packed with copper powder (say, 30 microns)

c) the cylinder is packed with small diameter copper rods (say, 1mm dia. X L)

d) the cylinder is packed with small diameter copper tubes (say, 5mm o.d., 4m i.d. X L)

e) the cylinder contains a uniform copper lattice (honeycomb X L) structure surrounded by air

If there's a difference, which case results in the highest conduction rate and why? Lowest?
 
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The thermal conductivity will be proportional to cross sectional area and inversely proportional to length. So cases a) c) and d) should be easy enough.

Case b) and e) is tricky because instead of having a uniform cross section you have lots of voids in three dimensions. I'm not sure how you go about calculating the thermal conductivity but it will obviously be lower than for case a) which is a solid rod.

In a material with small pores the mean free path of air molecules (eg Nitrogen) might be less than the pore size. So they are more likely to collide with the walls of the pore than each other. So the thermal energy will be transferred to the conducting copper pore walls rather than travel through the air in the pores. I think this means b) is likely to have increased conductivity compared to e). Edit: and perhaps quite close to that of a).
 
Last edited:
Thank you for your comments.

I was anticipating responses would be more toward d) and/or e) because the infrared spectrum is short wavelength/high frequency electro-magnetic energy. And, at least in the RF spectrum, high frequency energy propagates on the surface--and increased surface area has reduced impedance. Consequently, I imagined that more surface area would also result in reduced propagation time for infrared, too.

Could there be any validity to this idea?
 
Pretty sure copper is opaque to infrared :-)

Conduction usually beats radaition unless the temperature difference is very high.
 

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