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
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
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
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
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
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RE: Fourier heat trans equation problem
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
To make you surer I've not invented the reference above, you can take a look at equation 1.1 of the attached paper (page 3)
RE: Fourier heat trans equation problem
Tata
RE: Fourier heat trans equation problem
RE: Fourier heat trans equation problem
happy friday
RE: Fourier heat trans equation problem
2) Natural Log, not base 10.
Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada