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Fourier heat trans equation problem

Fourier heat trans equation problem

Fourier heat trans equation problem

(OP)
i'm checking some calculations, i can't figure out how they got the following equation from fouriers law:

q = (4)(pi)(k)(delta T) / (ln(t1/t2))

for a long wire
---------------

fouriers law is q = (k)(A)(delta T) / L

are they using characteristic length instead of wire length?
i'm not sure about the natural log of time either

RE: Fourier heat trans equation problem

Not the right forum

http://www.eng-tips.com/threadminder.cfm?pid=391

Anyway...

First of all who are "they"?

Integrating Fourier's law for an hollow cylinder of internal radius t1 and external radius t2 and considering a unitary length

Q = 2*PI*k*deltaT/ln(t2/t1)
 

RE: Fourier heat trans equation problem

(OP)
'they' are the people's work i am checking, employees.  

the equation they have is correct, it is an equation used for a probe method of measuring thermal conductivity.  the 4 pi has to do with boundary conditions. thanks

RE: Fourier heat trans equation problem

Sorry for having miuntepreted...

Carslaw, H. S. and Jaeger, J. C, Conduction of Heat in Solids, Oxford Press, 2nd ed., 1964, pp. 58-60, 344-345

RE: Fourier heat trans equation problem

hacksaw,

Google "measurement of apparent  thermal conductivity probe method" and you'll see the equation reported in the OP is correct, as confirmed by PEinOHIO in his/her second post

RE: Fourier heat trans equation problem

Looking at the paper ione posted, I think the simplest explanation is that the heat flux related to 2.Pi..etc relates to a heat transfer boundary condition on a cylindrical surface, whereas the 4.Pi..etc. relates to the solution of the transient heat transfer equation for relatively small r, which the thermal probe within the medium is assumed to be.

Tata  

RE: Fourier heat trans equation problem

amazing forum always something to learn

RE: Fourier heat trans equation problem

(OP)
yep, that is the same reference i found.  i too thought the 4pi should have been 2pi, but i learned something haha.  thanks for the help everyone!

happy friday

RE: Fourier heat trans equation problem

1) Wire length as measured,
2) Natural Log, not base 10.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

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