Exploring the Biot Number and Characteristic Lengths

In summary, according to this article, the characteristic length for a slab, sphere, and cylinder is the volume of the body divided by its surface area. If the body's biot number is less than 0.1, then the characteristic length is typically the volume of the body divided by its surface area. If the body's biot number is greater than 0.1, then the characteristic length is typically the surface area of the body divided by its volume.
  • #1
gfd43tg
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Hello

I confused about the equation for the biot number

Bi = hLc/k

For a slab, sphere, and cylinder, what are the characteristic lengths?
 
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  • #2
Maylis said:
Hello

I confused about the equation for the biot number

Bi = hLc/k

For a slab, sphere, and cylinder, what are the characteristic lengths?

According to this article:

http://en.wikipedia.org/wiki/Biot_number

the characteristic length Lc is usually the volume of the body divided by its surface area, or

Lc = Vbody/Asurface
 
  • #3
I think that is for biot numbers less than 0.1
 
  • #4
Maylis said:
I think that is for biot numbers less than 0.1

If you read the quoted article, it discusses what the implications are for Biot Nos. < 0.1 and Biot Nos. > 0.1 of an object in terms of heat transfer. It does not, however, indicate that Lc is modified depending on the value of the Biot No., as you could never tell if you are calculating the correct Biot No. with such a definition.

If the Wiki definition is not satisfactory, try this one:

http://www.tufts.edu/as/tampl/en43/lecture_notes/ch4.html

or this one:

http://ocw.mit.edu/courses/chemical...ng-spring-2007/lecture-notes/biot_numbers.pdf
 
  • #5
Yes, the tufts article is where I am getting the 0.1 figure from. I'm just confused because our professor told us something contradictory, basically the the characteristic length is one half the diameter
 
  • #6
"Characteristic lengths" in fluid dynamics are not an exact science. In the Tufts article, the behavior of the system doesn't suddenly change to something completely different when the non-dimensional parameter changes from 0.0999 to 0.1001. The important thing is the physical interpretation i.e. the "resistance" to heat flow across the surface, compared with the "resistance" inside the body, and what that means for the way the temperature varies with time. At one extreme, the surface temperature stays almost constant. At the other extreme, the internal temperatures stay almost uniform.
 
  • #7
See how McAdams defines the Biot number for various shapes. Also, check out how Bird et al do it.

Chet
 
  • #8
It turns out that we use the radius because the charts given to us use that as the characteristic length
 

1. What is the Biot Number and why is it important in scientific research?

The Biot Number is a dimensionless number that describes the ratio of convective heat transfer to conductive heat transfer. It is important in scientific research because it helps determine the dominant mode of heat transfer in a system and can be used to analyze and optimize heat transfer processes.

2. How is the Biot Number calculated?

The Biot Number is calculated by dividing the characteristic length of a system by the thermal diffusion length. The characteristic length is the length scale of the system, while the thermal diffusion length is the distance that heat can travel in a material over a given time period.

3. What are characteristic lengths and how are they determined?

Characteristic lengths are specific dimensions or length scales used to describe a system. They can be determined by analyzing the geometry and dimensions of the system, as well as the material properties and boundary conditions.

4. How does the Biot Number affect heat transfer processes?

The Biot Number plays a crucial role in determining the dominant mode of heat transfer in a system. A low Biot Number indicates that conductive heat transfer is dominant, while a high Biot Number indicates that convective heat transfer is dominant. This information can be used to optimize heat transfer processes and improve efficiency.

5. Can the Biot Number be applied to systems other than heat transfer?

While the Biot Number is most commonly used in heat transfer analysis, it can also be applied to other types of transport phenomena, such as mass transfer. In these cases, the Biot Number describes the ratio of convective mass transfer to diffusive mass transfer.

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