Research Papers: Heat and Mass Transfer

A Generalized Analytical Model for Joule Heating of Segmented Wires

[+] Author and Article Information
Vivekananthan Balakrishnan

Queensland Micro- and Nano Technology Centre,
Griffith University,
Brisbane 4111, Queensland, Australia
e-mail: vivekananthan.balakrishnan@griffithuni.edu.au

Toan Dinh

Queensland Micro- and Nano Technology Centre,
Griffith University,
Brisbane 4111, Queensland, Australia
e-mail: toan.dinh@griffithuni.edu.au

Hoang-Phuong Phan

Queensland Micro- and Nano Technology Centre,
Griffith University,
Brisbane 4111, Queensland, Australia
e-mail: hoangphuong.phan@griffithuni.edu.au

Dzung Viet Dao

Queensland Micro- and Nano Technology Centre,
Griffith University,
Brisbane 4111, Queensland, Australia
e-mail: d.dao@griffith.edu.au

Nam-Trung Nguyen

Queensland Micro- and Nano Technology Centre,
Griffith University,
Brisbane 4111, Queensland, Australia
e-mail: nam-trung.nguyen@griffith.edu.au

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 8, 2017; final manuscript received October 31, 2017; published online March 30, 2018. Assoc. Editor: George S. Dulikravich.

J. Heat Transfer 140(7), 072001 (Mar 30, 2018) (10 pages) Paper No: HT-17-1258; doi: 10.1115/1.4038829 History: Received May 08, 2017; Revised October 31, 2017

This paper presents an analytical solution for the Joule heating problem of a segmented wire made of two materials with different properties and suspended as a bridge across two fixed ends. The paper first establishes the one-dimensional (1D) governing equations of the steady-state temperature distribution along the wire with the consideration of heat conduction and free-heat convection phenomena. The temperature coefficient of resistance of the constructing materials and the dimension of the each segmented wires were also taken into account to obtain analytical solution of the temperature. COMSOL numerical solutions were also obtained for initial validation. Experimental studies were carried out using copper and nichrome wires, where the temperature distribution was monitored using an IR thermal camera. The data showed a good agreement between experimental data and the analytical data, validating our model for the design and development of thermal sensors based on multisegmented structures.

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Grahic Jump Location
Fig. 1

Schematic layout of the segmented heating wire

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Fig. 2

Electric potential distribution along the bridge: (a) fixed current and varying segment length ratio (α) and (b) fixed α and varying current

Grahic Jump Location
Fig. 3

(a) Influence of thermal conductivity of nichrome heater on temperature distribution and (b) influence of thermal conductivity of copper wire on temperature distribution

Grahic Jump Location
Fig. 4

(a) Influence of electrical resistivity of nichrome heater on temperature distribution and (b) influence of electrical resistivity of copper wire on temperature distribution

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Fig. 5

(a) Influence of wire diameter on the temperature distribution and (b) influence of convective heat transfer coefficient (h) on the temperature distribution

Grahic Jump Location
Fig. 6

Analytical and numerical simulation results: temperature distribution along the heater bridge for various segment length ratios and currents: (a) α=0.15, (b) α=0.2, (c) α=0.25, (d) α=0.3, and (e) α=0.35

Grahic Jump Location
Fig. 7

Analytical and numerical simulation results: maximum temperature at the center versus current characteristics for different heater bridges

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Fig. 8

(a) Experimental prototype, (b) simplified experimental setup for the measurement of temperature and resistance, and (c) transmission line method to measure the contact resistance of the wire

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Fig. 9

Analytical and experimental results: temperature distribution along the heater bridge for various segment length ratios and currents: (a) α=0.15, (b) α=0.2, (c) α=0.25, (d) α=0.3, and (e) α=0.35

Grahic Jump Location
Fig. 10

Temperature distribution along the heater bridge for different α values and with a fixed current of 3A (a) analytical results and (b) experimental results

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Fig. 11

Analytical and experimental results: electrical characteristics of different heater bridges (a) V–I characteristics and (b) P–I characteristics

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Fig. 12

Experimental data: maximum temperature at the center versus current characteristics for different heater bridges



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