Research Papers

Bayesian Inference for Parameter Estimation in Transient Heat Transfer Experiments

[+] Author and Article Information
R. Renjith Raj

Assistant Professor
Department of Mechanical Engineering,
Sree Budha College of Engineering,
Alappuzha, Kerala 690529, India
e-mail: renjithrajr@hotmail.com

G. Venugopal

Associate Professor
Department of Mechanical Engineering,
Rajiv Gandhi Institute of Technology,
Kottayam, Kerala 686501, India
e-mail: gvenucet@gmail.com

M. R. Rajkumar

Assistant Professor
Department of Mechanical Engineering,
College of Engineering, Trivandrum Trivandrum,
Kerala 695014, India
e-mail: rajkumar@cet.ac.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 30, 2014; final manuscript received April 17, 2015; published online August 11, 2015. Assoc. Editor: P.K. Das.

J. Heat Transfer 137(12), 121011 (Aug 11, 2015) (7 pages) Paper No: HT-14-1361; doi: 10.1115/1.4030955 History: Received May 30, 2014

In this study, an inverse heat transfer problem of parameter estimation using Bayesian inference is considered. Single parameter (specific heat of solid material) estimation as well as simultaneous estimation of two parameters (specific heat and emissivity) is done using a methodology combining the Bayesian inference with Markov chain Monte Carlo (MCMC) based sampling method. Computation of posterior probability density function (PPDF), using Bayes formula, is central to the inverse determination of parameters using Bayesian inference approach. Maximum-a-posteriori (MAP) and posterior mean are used to report the values of the estimated parameters and the uncertainties in the estimated parameters are characterized by the variance of the PPDF. The estimated value of specific heat and emissivity is well in agreement with reported value in literature.

Copyright © 2015 by ASME
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Fig. 2

Heater plate assembly

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Fig. 1

Experimental setup

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Fig. 3

PPDF for sample size 5000

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Fig. 4

PPDF for sample size 10,000

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Fig. 11

PPDF versus emissivity

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Fig. 5

Error between measured and predicted temperature corresponding to posterior mean estimate

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Fig. 6

PPDF plotted for initial steady-state temperature 336.2 K

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Fig. 7

PPDF plotted for initial steady-state temperature 361.2

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Fig. 8

PPDF plotted for scanning interval 30 s

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Fig. 9

PPDF plotted for scanning interval 10 s

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Fig. 10

PPDF versus heat capacity




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