What Are the Characteristic Lengths for the Biot Number in Different Shapes?

[gfd43tg]

Hello

I confused about the equation for the biot number

Bi = hLc/k

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

 

[SteamKing]

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

 

[gfd43tg]

I think that is for biot numbers less than 0.1

 

[SteamKing]

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

 

[gfd43tg]

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

 

[AlephZero]

"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.

 

[Chestermiller]

See how McAdams defines the Biot number for various shapes. Also, check out how Bird et al do it.

Chet

 

[gfd43tg]

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