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

• Urmi Roy
In summary, the ln(Θ)=exp(-hAt/ρVc) equation is used in lumped parameter systems for non-dimensional temperature, with 't' representing time. The Biot number does not determine if a problem is transient or steady state, but the Fourier number does. At long times, θ approaches 0 instead of 1.
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?

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.

1 person
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!

## 1. What is the Biot number?

The Biot number is a dimensionless number used in heat transfer analysis that compares the rate of heat transfer within a solid to the rate of heat transfer at its surface. It represents the ratio of internal thermal resistance to external thermal resistance.

## 2. How is the Biot number calculated?

The Biot number is calculated by dividing the thermal conductivity of the solid by the product of its heat transfer coefficient and characteristic length. The characteristic length is typically the length or diameter of the solid, depending on the configuration of the problem.

## 3. Can the Biot number determine if a problem is transient or steady state?

Yes, the Biot number can provide information about whether a problem is transient or steady state. A Biot number less than 0.1 indicates a transient problem, while a Biot number greater than 10 indicates a steady state problem. A Biot number between 0.1 and 10 indicates a problem with both transient and steady state characteristics.

## 4. What is the significance of a high Biot number?

A high Biot number indicates that the internal thermal resistance of the solid is much larger than the external thermal resistance. This means that heat will transfer more slowly within the solid than at its surface, and the temperature distribution within the solid will be more significant.

## 5. Is the Biot number applicable to all heat transfer problems?

No, the Biot number is primarily used for problems involving conduction heat transfer in solids. It is not applicable to problems involving convection or radiation heat transfer. Additionally, the Biot number is only valid for problems with simple geometries and uniform properties.

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