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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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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