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

[Urmi Roy]

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?

 

[Urmi Roy]

Some help?

 

[Chestermiller]

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.

 

[Urmi Roy]

Thanks. And for steady state, t (time) tends to infinity, so you just get Θ=1?

 

[Chestermiller]

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.

 

[Urmi Roy]

I agree...clumsy mistake on my part!