Heat Flow Rate through Thin Metallic Plates: Air vs. Vacuum

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Discussion Overview

The discussion revolves around the heat flow rate through two parallel thin metallic plates with a gap between them, specifically comparing scenarios where the gap is filled with air versus a vacuum. Participants explore the mechanisms of heat transfer in these cases, including radiation and conduction, and consider the implications of different materials filling the gap.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that energy transfer will occur primarily through blackbody radiation, proposing a formula involving the fourth power of the temperature difference.
  • Another participant questions the correct formulation of the temperature difference in the radiation equation, asking whether it should be (dT)^4 or d(T^4).
  • Concerns are raised about the effect of the gap size on heat transfer, noting that if the gap is large enough to allow for air convection, the situation becomes significantly more complex.
  • A participant mentions that if the gap were filled with wood, heat transfer would occur via conduction, providing a different equation that incorporates thermal conductivity.
  • There is a correction made regarding the formulation of the radiation equation, clarifying the notation used for the temperature difference.

Areas of Agreement / Disagreement

Participants express differing views on the primary mechanisms of heat transfer in the scenarios discussed, particularly regarding the role of convection in air and the implications of using different materials. No consensus is reached on the correct formulation of the equations or the impact of gap size.

Contextual Notes

Participants highlight the dependence of heat transfer on the gap size and the material properties, indicating that assumptions about the conditions may affect the outcomes. The discussion remains open regarding the specific effects of air versus vacuum and the implications of using wood as a filler.

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Two parallel thin metallic plates with a gap between them are used as a heat insulator. How does the heat flow rate through this device depend on the temperatures on its two sides in the following two cases?

Case 1: The gap is filled with air.
Case 2: There is a vacuum in the gap.
 
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Energy transfer will be by blackbody radiation.

E= σ(ΔT)4

σ=5.67e-8 (Wm-2C-4)
(ΔT)= Temperature difference between the plates.

Air or vacuum will have little effect as long as the gap is small. If the gap is large enough to allow air convection then all bets are off. It is a very different and difficult problem.
 
1. Should it be (dT)^4 or d(T^4)?
2. What would be the answer if the gap were filled with wood?
 
That is
(ΔT)= Temperature difference between the plates.

The energy transfer is proportional to the fourth power of the temperature difference


If the gap were wood heat transfer would be by conduction.

E= kAΔT/L

k = Thermal conductivity of Wood (will depend upon the type of wood)
A = Area
L= Length
 
That should be

E = σΔ(T4)

Sorry I missed that the first time!
 

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