Does Figure C Show A Constant Temperature Profile for Plane Wall Heat Transfer?

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Discussion Overview

The discussion revolves around the temperature profile for plane wall heat transfer as depicted in a series of figures. Participants explore the implications of different boundary conditions on temperature distribution, specifically focusing on a steady state scenario and the characteristics of heat transfer in various configurations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that figure A shows a constant temperature distribution, while figure B indicates a linear temperature gradient due to heat entering the wall.
  • Another participant questions the meaning of "no condition" and seeks clarification on the constraints affecting the temperature gradient in figure A.
  • A participant proposes that in figure C, the temperature distribution could vary depending on whether heat is leaving or entering the wall from the right-hand side.
  • One participant challenges the idea that heat can move into the wall in figure B, arguing that a temperature gradient must exist according to Fourier's Law, and posits that without a place for heat to dissipate, the temperature would increase indefinitely.

Areas of Agreement / Disagreement

Participants express differing views on the temperature profiles associated with the figures, particularly regarding the conditions under which heat enters or leaves the wall. The discussion remains unresolved, with no consensus on the implications of the figures.

Contextual Notes

Participants have not fully clarified the temperature constraints for the figures, and there are unresolved assumptions about the heat transfer conditions in each scenario.

no183
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Refer to the attached picture,
condition : assume steady state
legend : red : insulated (adiabatic)
black : no condition
Green : Temperature distribution, T(X)
I started with figure A, from heat equation, A u will get the distribution with is just a constant temperature..
For B, u will get a linear temperature gradient as shown in the figure, how bout C?
 

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What do you mean by "no condition"?
 
mean, just a normal wall.. non-insulated
 
Then why would there be a temperature gradient in part (a)? Is there another constraint that the temperature is held at certain (different) values on the left and right sides? If so, what are the temperature constraints in part (c)?
 
ok, let's say heat is LEAVING from figure A RIGHT HAND SIDE (BLACK) so i will get the temperature distribution
While on B, heat is MOVING IN TO THE WALL from RIGHT HAND SIDE (BLACK) and i will get the temperature distribution
lastly C, what i will get if
a) heat LEAVING the wall on the right hand side
b) heat ENTERING the wall on the right hand side
 
no183 said:
While on B, heat is MOVING IN TO THE WALL from RIGHT HAND SIDE (BLACK) and i will get the temperature distribution

I don't think so, for a couple reasons. First, heat flux is always coupled to a temperature gradient (this is Fourier's Law), so the temperature profile wouldn't be flat. Second, there's nowhere for this heat to go. Therefore, there won't be any steady state condition; the temperature will just keep increasing indefinitely.
 

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