The use of potential drop measurements to predict the temperature distribution in a thin wire with current flowing throu
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TECHNICAL PAPER
The use of potential drop measurements to predict the temperature distribution in a thin wire with current flowing through it Hironori Tohmyoh1
•
Kyohei Hiwatashi1
Received: 11 November 2019 / Accepted: 22 September 2020 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract When a current is supplied to a thin wire having smaller heat capacity, the temperature of the wire easily increases due to the principle of Joule heating. The temperature distribution in the wire has constituted an important issue for thin wire application. This paper reports a method to predict the temperature distribution in a thin wire through which current is flowing. The potential drops at the surfaces of thin Cu wires with diameters of 25 lm and 100 lm were measured. For these measurements the points of contact were close together, enabling us to measure the temperature dependency of the electrical resistivity of the wire. On the other hand, potential drop measured between the points of contact much further apart provided the information on the temperature distribution in the wire. By assuming the symmetric and parabolic temperature distribution, the temperature distributions in the Cu wires of 25 lm and 100 lm thick were predicted using the potential drop measurements made with the points of contact much further apart. The temperature distributions predicted were in good agreement with those measured by infrared thermography. The validity of the proposed method was also verified by conducting a similar experiment on Fe wire having a diameter of 100 lm. Nomenclature A Cross-sectional area (m2) c Specific heat (J kg-1 K-1) d Diameter (m) f An index describing the thermal boundary conditions around the wire with flowing the current I Current (A) Im Current requires to Tc reaches Tm (A) Im’ Current requires to Tc reaches Tm in case that the wire is covered with black body paint (A) (Im)0 Current requires to (Tc)0 reaches Tm (A) K Thermal conductivity (W m-1 K-1) l Length for the current supply (m) N Number Q Diameter of the terminals for potential drop measurements (m) R2 Coefficient of correlation T Temperature (K) t Time (s) T0 Reference temperature (K)
Ta Tc Te Tm (Tc)0
(Tc)IR (Tx)0
2u V0
X x
& Hironori Tohmyoh [email protected] 1
Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan
b DI
Ambient temperature (K) Temperature at the midpoint of the wire (K) Temperature at the ends of the wire (K) Prescribed temperature (K) Temperature at the midpoint of the wire under the thermal boundary conditions where no heat transfer from the wire surface and the temperature at both ends for current supply is constant at Ta (K) Temperature at the midpoint of the wire measured by the infrared thermography (K) Temperature at the position x in the wire under the thermal boundary conditions where no heat transfer from the wire surface and the temperature at both ends for current supply is constant at Ta (K) Terminal spacing for potential dr
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