Biot number-does it tell us if a problem is transient or steady state?

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Discussion Overview

The discussion revolves around the relationship between the Biot number and the nature of heat transfer problems, specifically whether they are transient or steady state. It includes theoretical considerations and mathematical expressions related to heat transfer in lumped parameter systems.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that the presence of time 't' in the equation ln(Θ)=exp(-hAt/ρVc) indicates that it is applicable only to transient problems.
  • Another participant asserts that the Biot number does not indicate whether a problem is transient or steady state, but rather describes the ratio of heat transfer resistances inside and outside an object.
  • A participant points out that the Fourier number is what indicates transient behavior, and notes that the equation involves both the Biot number and Fourier number in the context of transient heat transfer.
  • There is a discussion about the behavior of Θ as time approaches infinity, with one participant suggesting it approaches 1 for steady state, while another counters that it approaches 0 instead.
  • A later reply acknowledges a mistake regarding the interpretation of steady state conditions.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the Biot number regarding transient versus steady state problems, indicating that multiple competing views remain unresolved.

Contextual Notes

Participants discuss the implications of time in the equations and the conditions under which the Biot and Fourier numbers apply, but do not resolve the nuances of these relationships.

Urmi Roy
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So in a lumped parameter system, we use the ln(Θ)=exp(-hAt/ρVc), where Θ is non-dimensional temperature.

This expression has 't' i.e. time in it. So does this mean it is used only for transient problems?

Also, does the Biot number Bi tell us anything about whether a problem is in transient or steady state, or is that entirely determined by Fourier number Fo?
 
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Some help?
 
The Biot number does not tell you whether the problem is transient or steady state. It only tells you the ratio of the resistance to heat transfer outside the object divided by the resistance to heat transfer inside the object. The Fourier number tells you that it is transient. The equation you wrote involves the product of the biot number and the Fourier number, and describes the transient heat transfer in a system where the dominant resistance to heat transfer resides outside the object.
 
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Thanks. And for steady state, t (time) tends to infinity, so you just get Θ=1?
 
Urmi Roy said:
Thanks. And for steady state, t (time) tends to infinity, so you just get Θ=1?
No. From the equation you wrote, at long times, θ→0.
 
I agree...clumsy mistake on my part!
 

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