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Volume 3,     Number 3,     Summer 1995

 

SOLUTION OF THE TRANSIENT HOT-WIRE PROBLEM
FOR A CYLINDRICAL CELL OF FINITE LENGTH
A.A. KOLYSHKIN, E.G.OKOULICH-KAZARIN 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 gas-filled 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 first-order approximate formula includes all corrections, except convection, to the ideal continuous-line 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.R1, and finite length, l, situated coaxially in a gas-filled cylindrical cavity of radius R2 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 = R1/R2, in view of determining the region of experimental measurement of the thermal conductivity and diffusivity of gases. This first-order approximate formula includes all corrections, except convection, to the ideal continuous-line 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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