Thermodynamics heat loss fridge

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Discussion Overview

The discussion revolves around calculating heat loss in a fridge, specifically focusing on the appropriate surface area to use in the heat loss formula. Participants explore the implications of using either the inside or outside surface area, as well as the complexities introduced by the geometry of the fridge and the heat transmission coefficient.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question whether the inside or outside surface area should be used in the heat loss formula, noting that this choice significantly impacts the outcome, especially with thick walls.
  • Concerns are raised about the uncertainty in values such as the heat transmission coefficient (k), temperature difference (ΔT), and surface areas (Ain, Aout, Agasket).
  • One participant suggests that a 1D heat conduction analysis may not be adequate due to the complexities of the fridge's geometry, proposing that a 2D analysis might be necessary.
  • Another participant points out that k is a constant that encompasses various factors, implying that its definition must be clarified by the source providing it.
  • There is a mention of the challenges posed by corners in the geometry, with one participant expressing skepticism about the feasibility of solving the problem analytically.
  • Some participants propose that numerical methods, such as finite element analysis, could be used to handle heat transfer in complicated geometries.
  • One participant reflects on the difficulty of performing a 2D analysis by hand, suggesting that it may be more practical to use software for such calculations.
  • There is a discussion about whether the heat flow in the corners is negligible, with a suggestion that if it is, the inside surface area could be used.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate surface area to use in the heat loss calculation, and there is no consensus on how to handle the complexities introduced by the fridge's geometry. The discussion remains unresolved regarding the best approach to take.

Contextual Notes

Participants highlight limitations related to assumptions about the geometry and the treatment of corners, as well as the dependence on the definitions of the heat transmission coefficient and surface areas. The discussion reflects uncertainty about the adequacy of 1D versus 2D analyses.

mrquestion123
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Hello

To calculate the heat loss of a fridge, do I need to take the surface area of the in- or outside of the fridge?

Heat loss formula = k * delta T * A

k = heat transmission coefficient
A = surface area
 
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What's the uncertainty in the value of "k?" In ΔT? In Ain? In Aout? In Agasket? What are contributions at the edges for both inside and outside cases? And, how small an uncertainty can you stand in your calculation?
 
Let's just say there is no uncertainty, because the values are given. If you take the in- or the outside surface area, it has a large impact on the outcome. Especially with thick walls. So my question is, in this formula, should the in- or the outside surface area be used?
 
mrquestion123 said:
Let's just say there is no uncertainty, because the values are given. If you take the in- or the outside surface area, it has a large impact on the outcome. Especially with thick walls. So my question is, in this formula, should the in- or the outside surface area be used?
If you feel that it really matters that much, then you can't use the 1D heat conduction equation. A 1D analysis of the heat conduction will not not be adequate. You will need to solve the 2D heat conduction equation within the walls of the frig.

Chet
 
Since k is a rolled-up constant that includes a number of factors, such as internal and external convection and internal conduction, the answer to what k means must be provided by whomever provided k.
 
mrquestion123 said:
Let's just say there is no uncertainty, because the values are given. If you take the in- or the outside surface area, it has a large impact on the outcome. Especially with thick walls. So my question is, in this formula, should the in- or the outside surface area be used?
Neither.
The corners complicate things to the point to where I don't think even the guru's of the highest levels of PF's maths forums would spend their time on such a problem.
Though, I may attempt a solution in the morning.
But don't hold your breath.

I did earlier google "heat transfer rate through an isosceles trapezoidal object", but got very bored, as, after 10 minutes of scrolling, it appeared that no one in the history of the planet has attempted to solve the problem.
 
Last edited:
Heat transfer problems in complicated geometries are routinely handled using finite element (numerical) analysis. Even with finite difference analysis, heat transfer in an isosceles trapezoidal object seems pretty simple if the trapazoid is mathmatically mapped onto a rectangle by transformation of the spatial independent variables.

Chet
 
Chestermiller said:
Heat transfer problems in complicated geometries are routinely handled using finite element (numerical) analysis. Even with finite difference analysis, heat transfer in an isosceles trapezoidal object seems pretty simple if the trapazoid is mathmatically mapped onto a rectangle by transformation of the spatial independent variables.

Chet
I stand corrected.
But what for you "seems pretty simple", would take me most of tomorrow to figure out.
Or were you going to use software for the analysis? I was going to do it by hand.

ps. mrquestion123, do not bother holding your breath.
 
Thank you all for your replies,

@MR chestermiller it seems pretty complicated to do.a 2d analysis.
@Russ waters, yes maybe i should just ask the questioner. The book writes K is transport through a flat wall with a surface area, which does not answer my question yet. The previous question is to calculate the interior volume (for heat loss opening the door) and the exterior size, which why I assume they mean the outside surface area should be used.
@OmCheeto, hmm they do not expect me to calculate the corners. This should be covered with the in- or outside surface area.
 
  • #10
mrquestion123 said:
Thank you all for your replies,

@MR chestermiller it seems pretty complicated to do.a 2d analysis.
@Russ waters, yes maybe i should just ask the questioner. The book writes K is transport through a flat wall with a surface area, which does not answer my question yet. The previous question is to calculate the interior volume (for heat loss opening the door) and the exterior size, which why I assume they mean the outside surface area should be used.
@OmCheeto, hmm they do not expect me to calculate the corners. This should be covered with the in- or outside surface area.
If the heat flow in the corners is negligible, then you use the inside area.

Chet
 
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