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Research Papers

A New Thermophysical Property Estimation Approach Based on Calibration Equations and Rescaling Principle

[+] Author and Article Information
Y. Y. Chen

Department of Mechanical, Aerospace and
Biomedical Engineering,
The University of Tennessee,
1512 Middle Drive,
Knoxville, TN 37996-2210
e-mail: cyinyuan@utk.edu

M. Keyhani

Professor
Department of Mechanical, Aerospace and
Biomedical Engineering,
The University of Tennessee,
1512 Middle Drive,
Knoxville, TN 37996-2210
e-mail: keyhani@utk.edu

J. I. Frankel

Professor
Department of Mechanical, Aerospace and
Biomedical Engineering,
The University of Tennessee,
1512 Middle Drive,
Knoxville, TN 37996-2210
e-mail: jfranke1@utk.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received April 14, 2015; final manuscript received November 11, 2015; published online January 12, 2016. Assoc. Editor: Hongbin Ma.

J. Thermal Sci. Eng. Appl 8(2), 021013 (Jan 12, 2016) (10 pages) Paper No: TSEA-15-1109; doi: 10.1115/1.4032179 History: Received April 14, 2015; Revised November 11, 2015

A novel thermophysical property estimation method is proposed, which incorporates both calibration and rescaling principles for estimating both unknown thermal diffusivity and thermal conductivity of materials. In this process, temperature and heat flux calibration equations are developed, which account for temperature-dependent thermophysical property combinations. This approach utilizes a single in-depth temperature measurement and a known set of boundary conditions. To acquire both thermal diffusivity and thermal conductivity, two distinct stages are proposed for extracting these properties. The first stage uses a temperature calibration equation for estimating the unknown thermal diffusivity. This process determines the thermal diffusivity by minimizing the residual of the temperature calibration equation with respect to the thermal diffusivity. The second stage uses the estimated thermal diffusivity and a heat flux calibration equation for estimating the unknown thermal conductivity. This stage produces the desired thermal conductivity by minimizing the residual of the heat flux calibration equation with respect to the thermal conductivity. Results verify that the proposed estimation process works well even in the presence of significant measurement noise for the chosen two representative materials. The relative error between the exact properties and the estimated values is shown to be small. For both test materials (stainless steel 304 and a representative carbon composite), the maximum relative prediction error is approximately 2–3%. Finally, as an added benefit, this method does not require explicit knowledge of the slab thickness or sensor position which further reduces systematic errors.

Copyright © 2016 by ASME
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Figures

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Fig. 1

System setup for the one-dimensional heat conduction problem showing boundary conditions and the probe position

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Fig. 10

An example of the simulated noise added to the noiseless temperature with mean of 0 °C and standard deviation of 0.5 °C

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Fig. 11

The noisy temperature data T(0,t) and T(b,t) of stainless steel for the experiment with initial temperature 0 °C

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Fig. 12

Predicted thermal diffusivity for stainless steel based on noisy data

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Fig. 13

Predicted thermal diffusivity for carbon composite based on noisy data

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Fig. 14

Predicted thermal conductivity for stainless steel based on noisy data

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Fig. 15

Predicted thermal conductivity for carbon composite based on noisy data

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Fig. 7

Predicted thermal diffusivity for carbon composite corresponding to different probe positions and slab thicknesses

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Fig. 8

Predicted thermal conductivity for stainless steel corresponding to different probe positions and slab thicknesses

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Fig. 9

Predicted thermal conductivity for carbon composite corresponding to different probe positions and slab thicknesses

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Fig. 2

Time-varying input surface heat flux applied to the front surface of stainless steel and representative carbon composite

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Fig. 3

The temperature histories at uniformly distributed spatial locations for stainless steel with the slab thickness L=5 mm

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Fig. 4

The temperature histories at uniformly distributed spatial locations for carbon composite with the slab thickness L=5 mm

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Fig. 5

An example for the optimal thermal diffusivity selection: the optimal thermal diffusivity corresponds to the minimum value of residual function RN,T

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Fig. 6

Predicted thermal diffusivity for stainless steel corresponding to different probe positions and slab thicknesses

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