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Research Papers: Conduction

# Simultaneous Estimation of Principal Thermal Conductivities of an Anisotropic Composite Medium: An Inverse Analysis

[+] Author and Article Information
C. Balaji

e-mail: balaji@iitm.ac.in

S. P. Venkateshan

Heat Transfer and Thermal Power Laboratory,
Department of Mechanical Engineering,
Indian Institute of Technology Madras,
Chennai 600 036, India

V. Ramakrishnan

Thermal Properties Measurement Section, TSG,
ISAC, Indian Space Research Organization,
Bangalore 560 017, India

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 23, 2012; final manuscript received July 27, 2012; published online January 4, 2013. Assoc. Editor: Frank Cunha.

J. Heat Transfer 135(2), 021301 (Jan 04, 2013) (8 pages) Paper No: HT-12-1129; doi: 10.1115/1.4007422 History: Received March 23, 2012; Revised July 27, 2012

## Abstract

This paper reports the results of an experimental study to determine the principal thermal conductivities ($kx,ky$, and $kz$) of an anisotropic composite medium using an inverse heat transfer analysis. The direct problem consists of solving the three dimensional heat conduction equation in an orthotropic composite medium with the finite difference method to generate the required temperature distribution for known thermal conductivities. The measurement technique involves dissipating a known heat flux at the central region of a square sample and allowing it to conductively transfer the heat to an aluminium cold plate sink via a square copper ring. At steady state, temperatures at 28 (19 are used for retrievals due to symmetry) discrete locations are logged and used for parameter estimation. The entire measurement process is conducted in a vacuum environment. The inverse heat conduction problem (IHCP) for retrieving the orthotropic thermal conductivity tensor(parameter estimation) is then solved using a two layer feed forward back propagation artificial neural network (ANN) trained using the Levenberg–Marquardt algorithm (LMA), with temperatures as input and thermal conductivity values $kx,ky$, and $kz$ as the output. The method is first validated against a stainless steel(SS-304) sample of known thermal properties followed by the determination of the orthotropic conductivities of the honeycomb composite material.

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## References

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## Figures

Fig. 2

Simulated temperature distribution on a line along z-axis through sensor no. 3 for q = 5 W, kx=5 W/mK,ky=4 W/mK and varying kz,h=1400 W/m2K and sink temperature of −60 °C

Fig. 5

Thermocouple sensor locations in the test sample. Numbers in parentheses show sensors at the bottom of the sample.

Fig. 1

Schematic of the problem geometry

Fig. 3

Schematic view of the complete experimental setup

Fig. 4

Exploded view of the test sample assembly

Fig. 6

Sensitivity of simulated temperatures to contact conductance (h) in one quarter of test sample, for honeycomb material, at q = 2.5 W

Fig. 7

Parity plot showing adequacy of the ANN in accomplishing the retrievals for honeycomb sample, at q = 2.5 W

## Errata

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