Volume 3, Number 3, Summer 1995
SOLUTION OF THE TRANSIENT HOTWIRE PROBLEM
FOR A CYLINDRICAL CELL OF FINITE LENGTH
A.A. KOLYSHKIN, E.G.OKOULICHKAZARIN AND R. VAILLANCOURT
Abstract. An analytical solution to the heat problem is
found for a metal wire of small radius, An analytical solution to the heat problem is
found for a metal wire of small radius, R1, and finite length, I ,
situated coaxially in a gasfilled cylindrical cavity of radius R2
and same length 1. A simplified formula for the average temperature
of the wire is obtained in the realistic case of a small
ratio, R = R1/R2, in view of determining the region of experimental
measurement of the thermal conductivity and diffusivity
of gases. This firstorder approximate formula includes
all corrections, except convection, to the ideal continuousline
source solution and gives the difference between the ideal solution
and the experimental line source, except at very short
times. Computations show that R and 1 are the most important
parameters. Theoretical values are compared satisfactorily
with experimental data found in the literature.R_{1}, and finite length, l,
situated coaxially in a gasfilled cylindrical cavity of radius R_{2}
and same length l. A simplified formula for the average temperature
of the wire is obtained in the realistic case of a small
ratio, R = R_{1}/R_{2}, in view of determining the region of experimental
measurement of the thermal conductivity and diffusivity
of gases. This firstorder approximate formula includes
all corrections, except convection, to the ideal continuousline
source solution and gives the difference between the ideal solution
and the experimental line source, except at very short
times. Computations show that R and l are the most important
parameters. Theoretical values are compared satisfactorily
with experimental data found in the literature.
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