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.
Issue Section:
Heat and Mass Transfer
References
1.
Balakrishnan
, V.
, Phan
, H.-P.
, Dinh
, T.
, Dao
, D. V.
, and Nguyen
, N.-T.
, 2017
, “Thermal Flow Sensors for Harsh Environments
,” Sensors
, 17
(9
), p. 2061
.2.
Dinh
, T.
, Phan
, H.-P.
, Qamar
, A.
, Woodfield
, P.
, Nguyen
, N.-T.
, and Dao
, D. V.
, 2017
, “Thermoresistive Effect for Advanced Thermal Sensors: Fundamentals, Design Considerations, and Applications
,” J. Microelectromech. Syst.
, 26
(5
), pp. 966
–986
.3.
Nguyen
, N.
, Bochnia
, D.
, Kiehnscherf
, R.
, and Dötzel
, W.
, 1996
, “Investigation of Forced Convection in Microfluid Systems
,” Sens. Actuators A
, 55
(1
), pp. 49
–55
.4.
Ali
, S. Z.
, Udrea
, F.
, Milne
, W. I.
, and Gardner
, J. W.
, 2008
, “Tungsten-Based SOI Microhotplates for Smart Gas Sensors
,” J. Microelectromech. Syst.
, 17
(6
), pp. 1408
–1417
.5.
Dibbern
, U.
, 1990
, “A Substrate for Thin-Film Gas Sensors in Microelectronic Technology
,” Sens. Actuators B
, 2
(1
), pp. 63
–70
.6.
Suehle
, J. S.
, Cavicchi
, R. E.
, Gaitan
, M.
, and Semancik
, S.
, 1993
, “Tin Oxide Gas Sensor Fabricated Using CMOS Micro-Hotplates and In-Situ Processing
,” IEEE Electron Device Lett.
, 14
(3
), pp. 118
–120
.7.
Horrillo
, M.
, Sayago
, I.
, Arés
, L.
, Rodrigo
, J.
, Gutiérrez
, J.
, Götz
, A.
, Gracia
, I.
, Fonseca
, L.
, Cané
, C.
, and Lora-Tamayo
, E.
, 1999
, “Detection of Low NO2 Concentrations With Low Power Micromachined Tin Oxide Gas Sensors
,” Sens. Actuators B
, 58
(1
), pp. 325
–329
.8.
Chan
, P. C.
, Yan
, G.-Z.
, Sheng
, L.-Y.
, Sharma
, R. K.
, Tang
, Z.
, Sin
, J. K.
, Hsing
, I.-M.
, and Wang
, Y.
, 2002
, “An Integrated Gas Sensor Technology Using Surface Micro-Machining
,” Sens. Actuators B
, 82
(2
), pp. 277
–283
.9.
Elmi
, I.
, Zampolli
, S.
, Cozzani
, E.
, Passini
, M.
, Cardinali
, G.
, and Severi
, M.
, 2006, “Development of Ultra Low Power Consumption Hotplates for Gas Sensing Applications
,” Fifth IEEE
Conference on Sensors,
Daegu, South Korea, Oct. 22–25, pp. 243
–246
.10.
Fürjes
, P.
, Dücső
, C.
, Ádám
, M.
, Zettner
, J.
, and Bársony
, I.
, 2004
, “Thermal Characterisation of Micro-Hotplates Used in Sensor Structures
,” Superlattices Microstruct.
, 35
(3
), pp. 455
–464
.11.
Yadav
, J.
, Mishra
, V. V.
, and Prasad
, M.
, 2014
, “Design and Partial Fabrication of Low Power Pt-Based Microheater for Gas Sensing Application
,” INROADS Int. J. Jaipur Natl. Univ.
, 3
(1 s
), pp. 261
–265
.12.
Harley-Trochimczyk
, A.
, Chang
, J.
, Zhou
, Q.
, Dong
, J.
, Pham
, T.
, Worsley
, M. A.
, Maboudian
, R.
, Zettl
, A.
, and Mickelson
, W.
, 2015
, “Catalytic Hydrogen Sensing Using Microheated Platinum Nanoparticle-Loaded Graphene Aerogel
,” Sens. Actuators B
, 206
, pp. 399
–406
.13.
Glaninger
, A.
, Jachimowicz
, A.
, Kohl
, F.
, Chabicovsky
, R.
, and Urban
, G.
, 2000
, “Wide Range Semiconductor Flow Sensors
,” Sens. Actuators A
, 85
(1
), pp. 139
–146
.14.
Bedö
, G.
, Fannasch
, H.
, and Müller
, R.
, 2000
, “A Silicon Flow Sensor for Gases and Liquids Using AC Measurements
,” Sens. Actuators A
, 85
(1
), pp. 124
–132
.15.
Hung
, S.-T.
, Wong
, S.-C.
, and Fang
, W.
, 2000
, “The Development and Application of Microthermal Sensors With a Mesh-Membrane Supporting Structure
,” Sens. Actuators A
, 84
(1
), pp. 70
–75
.16.
Robadey
, J.
, Paul
, O.
, and Baltes
, H.
, 1995
, “Two-Dimensional Integrated Gas Flow Sensors by CMOS IC Technology
,” J. Micromech. Microeng.
, 5
(3
), p. 243
.17.
Dai
, C.-L.
, 2007
, “A Capacitive Humidity Sensor Integrated With Micro Heater and Ring Oscillator Circuit Fabricated by CMOS–MEMS Technique
,” Sens. Actuators B
, 122
(2
), pp. 375
–380
.18.
Dai
, C.-L.
, Liu
, M.-C.
, Chen
, F.-S.
, Wu
, C.-C.
, and Chang
, M.-W.
, 2007
, “A Nanowire WO 3 Humidity Sensor Integrated With Micro-Heater and Inverting Amplifier Circuit on Chip Manufactured Using CMOS-MEMS Technique
,” Sens. Actuators B
, 123
(2
), pp. 896
–901
.19.
Wang
, B.
, 2012
, “MEMS-Based Temperature-Dependent Characterization of Biomolecular Interactions,” Ph.D., thesis
, Columbia University, New York.20.
Placinta
, M.
, Shen
, M.-C.
, Achermann
, M.
, and Karlstrom
, R. O.
, 2009
, “A Laser Pointer Driven Microheater for Precise Local Heating and Conditional Gene Regulation In Vivo. Microheater Driven Gene Regulation in Zebrafish
,” BMC Dev. Biol.
, 9
(1
), p. 73
.21.
Hwang
, W.-J.
, Shin
, K.-S.
, Roh
, J.-H.
, Lee
, D.-S.
, and Choa
, S.-H.
, 2011
, “Development of Micro-Heaters With Optimized Temperature Compensation Design for Gas Sensors
,” Sensors
, 11
(3
), pp. 2580
–2591
.22.
Balakrishnan
, V.
, Dinh
, T.
, Phan
, H.-P.
, Kozeki
, T.
, Namazu
, T.
, Dao
, D. V.
, and Nguyen
, N.-T.
, 2017
, “Steady-State Analytical Model of Suspended p-Type 3C–SiC Bridges Under Consideration of Joule Heating
,” J. Micromech. Microeng.
, 27
(7
), p. 075008
.23.
Belmonte
, J. C.
, Puigcorbe
, J.
, Arbiol
, J.
, Vila
, A.
, Morante
, J.
, Sabate
, N.
, Gracia
, I.
, and Cane
, C.
, 2006
, “High-Temperature Low-Power Performing Micromachined Suspended Micro-Hotplate for Gas Sensing Applications
,” Sens. Actuators B
, 114
(2
), pp. 826
–835
.24.
Tsamis
, C.
, Nassiopoulou
, A.
, and Tserepi
, A.
, 2003
, “Thermal Properties of Suspended Porous Silicon Micro-Hotplates for Sensor Applications
,” Sens. Actuators B
, 95
(1
), pp. 78
–82
.25.
Afridi
, M. Y.
, Suehle
, J. S.
, Zaghloul
, M. E.
, Berning
, D. W.
, Hefner
, A. R.
, Cavicchi
, R. E.
, Semancik
, S.
, Montgomery
, C. B.
, and Taylor
, C. J.
, 2002
, “A Monolithic CMOS Microhotplate-Based Gas Sensor System
,” IEEE Sens. J.
, 2
(6
), pp. 644
–655
.26.
Zhou
, Q.
, Sussman
, A.
, Chang
, J.
, Dong
, J.
, Zettl
, A.
, and Mickelson
, W.
, 2015
, “Fast Response Integrated MEMS Microheaters for Ultra Low Power Gas Detection
,” Sens. Actuators A
, 223
, pp. 67
–75
.27.
Phan
, H.-P.
, Dinh
, T.
, Kozeki
, T.
, Qamar
, A.
, Namazu
, T.
, Dimitrijev
, S.
, Nguyen
, N.-T.
, and Dao
, D. V.
, 2016
, “Piezoresistive Effect in p-Type 3C-SiC at High Temperatures Characterized Using Joule Heating
,” Sci. Rep.
, 6
, p. 28499
.28.
Briand
, D.
, Heimgartner
, S.
, Grétillat
, M.-A.
, van der Schoot
, B.
, and de Rooij
, N. F.
, 2002
, “Thermal Optimization of Micro-Hotplates That Have a Silicon Island
,” J. Micromech. Microeng.
, 12
(6
), p. 971
.29.
Dumitrescu
, M.
, Cobianu
, C.
, Lungu
, D.
, Dascalu
, D.
, Pascu
, A.
, Kolev
, S.
, and van den Berg
, A.
, 1999
, “Thermal Simulation of Surface Micromachined Polysilicon Hot Plates of Low Power Consumption
,” Sens. Actuators A
, 76
(1
), pp. 51
–56
.30.
Faglia
, G.
, Comini
, E.
, Pardo
, M.
, Taroni
, A.
, Cardinali
, G.
, Nicoletti
, S.
, and Sberveglieri
, G.
, 1999
, “Micromachined Gas Sensors for Environmental Pollutants
,” Microsyst. Technol.
, 6
(2
), pp. 54
–59
.31.
Iwaki
, T.
, Covington
, J.
, Udrea
, F.
, Ali
, S.
, Guha
, P.
, and Gardner
, J.
, 2005, “Design and Simulation of Resistive SOI CMOS Micro-Heaters for High Temperature Gas Sensors
,” J. Phys. Conf. Ser.
, 15
, pp. 27–32.32.
Swart
, N. R.
, and Nathan
, A.
, 1994
, “Coupled Electrothermal Modeling of Microheaters Using SPICE
,” IEEE Trans. Electron Devices
, 41
(6
), pp. 920
–925
.33.
Saxena
, G.
, and Paily
, R.
, 2013
, “Analytical Modeling of Square Microhotplate for Gas Sensing Application
,” IEEE Sens. J.
, 13
(12
), pp. 4851
–4859
.34.
Ansari
, M. Z.
, and Cho
, C.
, 2012
, “A Conduction–Convection Model for Self-Heating in Piezoresistive Microcantilever Biosensors
,” Sens. Actuators A
, 175
, pp. 19
–27
.35.
Khan
, U.
, and Falconi
, C.
, 2013
, “Temperature Distribution in Membrane-Type Micro-Hot-Plates With Circular Geometry
,” Sens. Actuators B
, 177
, pp. 535
–542
.36.
Kozlov
, A. G.
, 2002
, “Analytical Modelling of Steady-State Temperature Distribution in Thermal Microsensors Using Fourier Method—Part 1: Theory
,” Sens. Actuators A
, 101
(3
), pp. 283
–298
.37.
Csendes
, A.
, Szekely
, V.
, and Rencz
, M.
, 1998
, “An Efficient Thermal Simulation Tool for ICs, Microsystem Elements and MCMs: The μS-THERMANAL
,” Microelectron. J.
, 29
(4
), pp. 241
–255
.38.
Fangohr
, H.
, Chernyshenko
, D. S.
, Franchin
, M.
, Fischbacher
, T.
, and Meier
, G.
, 2011
, “Joule Heating in Nanowires
,” Phys. Rev. B
, 84
(5
), p. 054437
.39.
Xu
, S.
, Lao
, C.
, Weintraub
, B.
, and Wang
, Z. L.
, 2008
, “Density-Controlled Growth of Aligned ZnO Nanowire Arrays by Seedless Chemical Approach on Smooth Surfaces
,” J. Mater. Res.
, 23
(8
), pp. 2072
–2077
.40.
Tohmyoh
, H.
, Imaizumi
, T.
, Hayashi
, H.
, and Saka
, M.
, 2007
, “Welding of Pt Nanowires by Joule Heating
,” Scr. Mater.
, 57
(10
), pp. 953
–956
.41.
Gu
, G.
, Zheng
, B.
, Han
, W.
, Roth
, S.
, and Liu
, J.
, 2002
, “Tungsten Oxide Nanowires on Tungsten Substrates
,” Nano Lett.
, 2
(8
), pp. 849
–851
.42.
Tohmyoh
, H.
, Tanaka
, T.
, Fujimori
, M.
, and Saka
, M.
, 2013
, “Joule Heat Welding of Thin Platinum and Tungsten Wires and the Thermoelectric Effects around Bi-Metal Junctions
,” ASME J. Micro- Nano-Manuf.
, 1
(2
), p. 024501
.43.
Singh
, S.
, and Jain
, P. K.
, 2008
, “Analytical Solution to Transient Heat Conduction in Polar Coordinates With Multiple Layers in Radial Direction
,” Int. J. Therm. Sci.
, 47
(3
), pp. 261
–273
.44.
Johansson
, B. T.
, and Lesnic
, D.
, 2009
, “A Method of Fundamental Solutions for Transient Heat Conduction in Layered Materials
,” Eng. Anal. Boundary Elem.
, 33
(12
), pp. 1362
–1367
.45.
Thirumaleshwar
, M.
, 2009
, Fundamentals of Heat and Mass Transfer
, Pearson Education
, Dorling Kindersley (India) Pvt. Ltd., New Delhi, India.Copyright © 2018 by ASME
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