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The use of potential drop measurements to predict the temperature distribution in a thin wire with current flowing through it

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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 µm and 100 µm 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 µm and 100 µm 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 µm.

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Abbreviations

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)

I m :

Current requires to Tc reaches Tm (A)

I m’:

Current requires to Tc reaches Tm in case that the wire is covered with black body paint (A)

(I m)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)

R 2 :

Coefficient of correlation

T :

Temperature (K)

t :

Time (s)

T 0 :

Reference temperature (K)

T a :

Ambient temperature (K)

T c :

Temperature at the midpoint of the wire (K)

T e :

Temperature at the ends of the wire (K)

T m :

Prescribed temperature (K)

(T c)0 :

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)

(T c)IR :

Temperature at the midpoint of the wire measured by the infrared thermography (K)

(T x)0 :

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)

2u :

Terminal spacing for potential drop measurements (m)

V 0 :

Potential drop without the effect of the heat conduction from the wire surface to the terminals for the potential drop measurements (V)

X :

Position in the wire and its origin is located at the midpoint of the wire (m)

x :

Position in the wire and its origin is located at the left end for the current supply (m)

β :

Constant related to the temperature distribution in the wire (K m−2)

ΔI :

Increment of current (A)

ΔV :

Potential drop (V)

δ :

Coefficient for calibrating the effect of black body paint

ρ e :

Electrical resistivity (Ω m)

κ :

Thermal diffusivity (m2 s−1)

υ :

Heat transfer coefficient (W m−2 K−1)

ρ m :

Mass density (kg m−3)

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Acknowledgements

The authors would like to acknowledge Professor M. Saka for his valuable discussions throughout this work, and Mr. S. Hoshi for his contribution in starting this research works. This work was supported by JSPS KAKENHI (Grant Number 18H01331).

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Authors and Affiliations

  1. Department of Finemechanics, Tohoku University, Sendai, 980-8579, Japan

    Hironori Tohmyoh & Kyohei Hiwatashi

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  1. Hironori Tohmyoh
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  2. Kyohei Hiwatashi
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Correspondence to Hironori Tohmyoh.

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Tohmyoh, H., Hiwatashi, K. The use of potential drop measurements to predict the temperature distribution in a thin wire with current flowing through it. Microsyst Technol 27, 639–648 (2021). https://doi.org/10.1007/s00542-020-05043-w

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  • DOI: https://doi.org/10.1007/s00542-020-05043-w

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