The Significance of Fourier Number: Understanding Heat Conduction in Solids

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Discussion Overview

The discussion centers around the Fourier number, its definition, and its significance in the context of heat conduction in solids. Participants explore its role in determining the lumped heat capacity and the implications of its value in thermal analysis.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant asks for a clear definition of the Fourier number and its meaning, expressing confusion despite knowing its formula.
  • Another participant provides a link to Wikipedia, suggesting it as a resource for understanding the Fourier number.
  • A participant expresses frustration with the Wikipedia explanation, stating it only describes the terms involved and does not clarify the significance of the Fourier number in practical terms.
  • One participant mentions that when the Fourier number is much larger than one, it indicates that the conduction process has reached a steady state, which may address the initial query about its significance.
  • A participant presents a detailed breakdown of the Fourier number's formula, showing its relationship to heat conduction and thermal energy storage rates.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the significance of the Fourier number, with some expressing confusion and others attempting to clarify its implications in heat conduction. Multiple viewpoints regarding its interpretation and relevance remain present.

Contextual Notes

Participants have not fully resolved the significance of the Fourier number, and there are indications of differing interpretations of its practical applications in heat conduction.

New2thermodyn
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What is Fourier number??

What exactly is Fourier number? I kno its Thermal diffusivity*time/square of radius. But what exactly is the meaning of Fourier number?

For eg: Why do we calculate Fourier number for finding out the lumped heat in solids?
 
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mathman said:

Thanks Mathman, and yes,Of course iv checked wikipedia b4 posting that question! In wiki it is just the explanation of the terms involved, ie"the ratio of the heat conduction rate to the rate of thermal energy storage", is not that pretty obvious just looking at the equation? but what i want to know is the significance of the equation
 


Sorry - I can't help you any more.
 


When the Fourier number is much larger than one, the conduction process is predicted to have reached steady state. Does this answer your question?
 


New2thermodyn said:
Thanks Mathman, and yes,Of course iv checked wikipedia b4 posting that question! In wiki it is just the explanation of the terms involved, ie"the ratio of the heat conduction rate to the rate of thermal energy storage", is not that pretty obvious just looking at the equation? but what i want to know is the significance of the equation

Fo = (Heat conduction rate)/(thermal energy storage rate)
Fo = [k A [STRIKE]dT[/STRIKE]/dx]/[(dm/dt)*Cp*[STRIKE]dT[/STRIKE]] -------------> dx = L
Fo = [kA/L]/[ρ*Cp*Q] -----------------------> A/Q = t/L
Fo = [kt]/[ρ*Cp*(L2)]---------------------->k/ρ*Cp = α
Fo = αt/L2
 

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