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Research Papers: Heat and Mass Transfer

Theoretical and Experimental Investigation of Thermal Dynamics of Steinhart–Hart Negative Temperature Coefficient Thermistors

[+] Author and Article Information
Hooman Fatoorehchi

School of Chemical Engineering,
College of Engineering,
University of Tehran,
P.O. Box 11365-4563,
Tehran 1417466191, Iran
e-mail: hfatoorehchi@ut.ac.ir

Mahdi Alidadi

School of Chemical Engineering,
College of Engineering,
University of Tehran,
P.O. Box 11365-4563,
Tehran 1417466191, Iran
e-mail: mahdi_alidadi@ut.ac.ir

Randolph Rach

The George Adomian Center for
Applied Mathematics,
316 South Maple Street,
Hartford, MI 49057-1225
e-mail: tapstrike@gmail.com

Abolfazl Shojaeian

Department of Chemical Engineering,
Hamedan University of Technology,
P.O. Box 65155-579,
Hamedan 3733165169, Iran
e-mail: shojaeian@hut.ac.ir

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 21, 2018; final manuscript received April 21, 2019; published online May 20, 2019. Assoc. Editor: Srinath V. Ekkad.

J. Heat Transfer 141(7), 072003 (May 20, 2019) (11 pages) Paper No: HT-18-1744; doi: 10.1115/1.4043676 History: Received November 21, 2018; Revised April 21, 2019

The temperature-dependent dynamics of a negative temperature coefficient (NTC) thermistor conducting variable electric current is modeled using the differential approach. The thermistor is assumed to follow the Steinhart–Hart resistance-temperature equation. The developed mathematical model consists of a nonlinear differential-algebraic equations system, and it was analyzed by the Adomian decomposition method (ADM) and its time-marching version known as the multistage Adomian decomposition method (MADM) as well as the Dormand–Prince (DP) numerical method. Five sets of experiments were conducted on five different NTC thermistors and the laboratory measurements were compared with the model predictions. It is demonstrated that the proposed model, when combined with the MADM, can accurately simulate the thermal behavior of the NTC thermistors. The MADM reproduces the experimental temperature dynamics of the five NTC thermistors with an average absolute relative error of about 2.601% while the corresponding errors for the DP method and the classic ADM are 8.122% and 51.255%, respectively. Also, it is shown that the MADM is highly efficient in terms of computational efficiency and it is approximately 6.5 times faster than the classic DP method, when tuned appropriately.

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References

Chen, C. , 2009, “ Evaluation of Resistance–Temperature Calibration Equations for NTC Thermistors,” Measurement, 42(7), pp. 1103–1111. [CrossRef]
Feteira, A. , 2009, “ Negative Temperature Coefficient Resistance (NTCR) Ceramic Thermistors: An Industrial Perspective,” J. Am. Ceram. Soc., 92(5), pp. 967–983. [CrossRef]
Billings, K. , and Morey, T. , 2011, Switchmode Power Supply Handbook, 3rd ed., McGraw-Hill, New York.
Wang, Y. , Zhang, X. , Wang, W. , and Xu, D. , 2015, “ Three-Stage Inrush Current Suppressed Circuit for BCM Boost Converter,” Int. J. Circuit Theory App., 43(5), pp. 684–690. [CrossRef]
Mrooz, O. , Kovalski, A. , Pogorzelska, J. , Shpotyuk, O. , Vakiv, M. , Butkiewicz, B. , and Maciak, J. , 2001, “ Thermoelectrical Degradation Processes in NTC Thermistors for InRush Current Protection of Electronic Circuits,” Microelectron. Reliab., 41(5), pp. 773–777. [CrossRef]
Park, K. , and Lee, J. K. , 2007, “ Mn–Ni–Co–Cu–Zn–O NTC Thermistors With High Thermal Stability for Low Resistance Applications,” Scr. Mater., 57(4), pp. 329–332. [CrossRef]
Muralidharan, M. N. , Rohini, P. R. , Sunny, E. K. , Dayas, K. R. , and Seema, A. , 2012, “ Effect of Cu and Fe Addition on Electrical Properties of Ni–Mn–Co–O NTC Thermistor Compositions,” Ceram. Int., 38(8), pp. 6481–6486. [CrossRef]
He, L. , Ling, Z. Y. , and Zhang, G. , 2015, “ Connectivity Between Electrical Conduction and Electrode Structure in Mn–Co–Ni–O Thick-Film Thermistors,” Appl. Phys. A: Mater., 118(1), pp. 177–182. [CrossRef]
Vaegae, N. K. , Komanapalli, V. L. N. , and Annepu, B. R. , 2016, “ Design and Modeling of an Intelligent Temperature to Frequency Converter,” Measurement, 85, pp. 54–64. [CrossRef]
Steinhart, J. S. , and Hart, S. R. , 1968, “ Calibration Curves for Thermistors,” Deep-Sea Res. Oceanogr. Abstr., 15(4), pp. 497–503. [CrossRef]
Childs, P. R. N. , 2001, Practical Temperature Measurement, Butterworth-Heinemann, Boston, MA.
Fraden, J. , 2010, Handbook of Modern Sensors: Physics, Designs, and Applications, Springer, New York.
Kerlin, T. W. , and Shepard, R. L. , 1982, Industrial Temperature Measurement, International Society of Automation (ISA) Press, Research Triangle Park, NC.
Eke, R. , Kavasoglu, A. S. , and Kavasoglu, N. , 2012, “ Design and Implementation of a Low-Cost Multi-Channel Temperature Measurement System for Photovoltaic Modules,” Measurement, 45(6), pp. 1499–1509. [CrossRef]
Keskin, A. Ü. , 2005, “ A Simple Analog Behavioural Model for NTC Thermistors Including Selfheating Effect,” Sens. Actuators, A, 118(2), pp. 244–247. [CrossRef]
Wang, L. M. , Deng, Y. F. , Zhao, X. L. , and Liu, B. L. , 2008, “ A Neural Network Approach for Creating a NTC Thermistor Model Library for PSpice,” IEEE International Conference on Cybernetics and Intelligent Systems, Chengdu, China, Sept. 21–24, pp. 1133–1137.
Fowler, A. C. , Frigaard, I. , and Howison, S. D. , 1992, “ Temperature Surges in Current-Limiting Circuit Devices,” SIAM J. Appl. Math., 52(4), pp. 998–1011. [CrossRef]
Khani, F. , Ahmadzadeh Raji, M. , and Hamedi Nejad, H. , 2009, “ Analytical Solutions and Efficiency of the Nonlinear Fin Problem With Temperature-Dependent Thermal Conductivity and Heat Transfer Coefficient,” Commun. Nonlinear Sci. Numer. Simul., 14(8), pp. 3327–3338. [CrossRef]
Singh, S. , Kumar, D. , and Rai, K. N. , 2014, “ Convective-Radiative Fin With Temperature Dependent Thermal Conductivity, Heat Transfer Coefficient and Wavelength Dependent Surface Emissivity,” Propul. Power Res., 3(4), pp. 207–221. [CrossRef]
Sun, Y. , Ma, J. , Li, B. , and Guo, Z. , 2016, “ Predication of Nonlinear Heat Transfer in a Convective-Radiative Fin With Temperature-Dependent Properties by the Collocation Spectral Method,” Numer. Heat Transfer, Part B, 69(1), pp. 68–83. [CrossRef]
Coughanowr, D. R. , and Leblanc, S. E. , 2009, Process Systems Analysis and Control, 3rd ed., McGraw-Hill, New York.
Adomian, G. , and Rach, R. , 1983, “ Inversion of Nonlinear Stochastic Operators,” J. Math. Anal. Appl., 91(1), pp. 39–46. [CrossRef]
Adomian, G. , 1994, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic, Dordrecht, The Netherlands.
Adomian, G. , 1990, “ A Review of the Decomposition Method and Some Recent Results for Nonlinear Equations,” Math. Comput. Model., 13(7), pp. 17–43. [CrossRef]
Abbasbandy, S. , 2003, “ Improving Newton-Raphson Method for Nonlinear Equations by Modified Adomian Decomposition Method,” Appl. Math. Comput., 145(2–3), pp. 887–893.
Chiu, C.-H. , and Chen, C.-K. , 2003, “ Application of Adomian's Decomposition Procedure to the Analysis of Convective-Radiative Fins,” ASME J. Heat Transfer, 125(2), pp. 312–316. [CrossRef]
Fatoorehchi, H. , and Abolghasemi, H. , 2014, “ Approximating the Minimum Reflux Ratio of Multicomponent Distillation Columns Based on the Adomian Decomposition Method,” J. Taiwan Inst. Chem. Eng., 45(3), pp. 880–886. [CrossRef]
Fatoorehchi, H. , and Abolghasemi, H. , 2016, “ Series Solution of Nonlinear Differential Equations by a Novel Extension of the Laplace Transform Method,” Int. J. Comput. Math., 93(8), pp. 1299–1319. [CrossRef]
Fatoorehchi, H. , Abolghasemi, H. , and Rach, R. , 2015, “ A New Parametric Algorithm for Isothermal Flash Calculations by the Adomisan Decomposition of Michaelis-Menten Type Nonlinearities,” Fluid Phase Equilib., 395(15), pp. 44–50. [CrossRef]
Makinde, O. D. , and Sibanda, P. , 2008, “ Magnetohydrodynamic Mixed-Convective Flow and Heat and Mass Transfer Past a Vertical Plate in a Porous Medium With Constant Wall Suction,” ASME J. Heat Transfer, 130(11), p. 112602. [CrossRef]
Fatoorehchi, H. , Gutman, I. , and Abolghasemi, H. , 2015, “ A Combined Technique for Computation of Energy-Effect of Cycles in Conjugated Molecules,” J. Math. Chem., 53(4), pp. 1113–1125. [CrossRef]
Fatoorehchi, H. , Rach, R. , Tavakoli, O. , and Abolghasemi, H. , 2015, “ An Efficient Numerical Scheme to Solve a Quintic Equation of State for Supercritical Fluids,” Chem. Eng. Commun., 202(3), pp. 1113–1125. [CrossRef]
Fatoorehchi, H. , and Abolghasemi, H. , 2013, “ Improving the Differential Transform Method: A Novel Technique to Obtain the Differential Transforms of Nonlinearities by the Adomian Polynomials,” Appl. Math. Model., 37(8), pp. 6008–6017. [CrossRef]
Kundu, B. , and Miyara, A. , 2009, “ An Analytical Method for Determination of the Performance of a Fin Assembly Under Dehumidifying Conditions: A Comparative Study,” Int. J. Refrig., 32(2), pp. 369–380. [CrossRef]
Bhanja, D. , and Kundu, B. , 2012, “ Radiation Effect on Optimum Design Analysis of a Constructal T-Shaped Fin With Variable Thermal Conductivity,” Heat Mass Transfer, 48(1), pp. 109–122. [CrossRef]
Duan, J.-S. , 2011, “ Convenient Analytic Recurrence Algorithms for the Adomian Polynomials,” Appl. Math. Comput., 217(13), pp. 6337–6348.
Kundu, B. , and Lee, K.-S. , 2011, “ Decomposition Method for Thermal Design Analysis of Vertical Straight Fins Under Condensation of Quiescent and Flowing Steam,” Heat Mass Transfer, 47(10), pp. 1261–1274. [CrossRef]
Ayoobi, A. , and Ramezanizadeh, M. , 2013, “ Analytical Investigation of Gaussian Roughness Effects on the Thermal Performance of Conical Microfins,” ASME J. Heat Transfer, 135(3), p. 031901. [CrossRef]
Duan, J.-S. , Wang, Z. , Fu, S.-Z. , and Chaolu, T. , 2013, “ Parametrized Temperature Distribution and Efficiency of Convective Straight Fins With Temperature-Dependent Thermal Conductivity by a New Modified Decomposition Method,” Int. J. Heat Mass Transfer, 59, pp. 137–143. [CrossRef]
Rèpaci, A. , 1990, “ Nonlinear Dynamical Systems: On the Accuracy of Adomian's Decomposition Method,” Appl. Math. Lett., 3(4), pp. 35–39. [CrossRef]
Fatoorehchi, H. , Abolghasemi, H. , and Zarghami, R. , 2015, “ Analytical Approximate Solutions for a General Nonlinear Resistor-Nonlinear Capacitor Circuit Model,” Appl. Math. Model., 39(19), pp. 6021–6031. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

The remainder error E(φ(t¯)) versus dimensionless time t¯. The approximants φm+1(t¯), with m=4, 10, and 15, are obtained from MADM with identical interval subdivision δ=10.

Grahic Jump Location
Fig. 2

The transient temperature variations of different NTC thermistors as obtained from experiments and numerical simulations. In the legends, we denote φ16(t¯), given by the MADM with subdivision interval 5 by MADM (16,5).

Grahic Jump Location
Fig. 3

The simulink model of the studied system

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