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Research Papers: Heat and Mass Transfer

Application of Hybrid Monte Carlo Algorithm in Heat Transfer

[+] Author and Article Information
S. Reetik Kumar, B. Konda Reddy

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

C. Balaji

Heat Transfer and Thermal Power Laboratory,
Department of Mechanical Engineering,
Indian Institute of Technology Madras,
Chennai 600 036, India
e-mail: balaji@iitm.ac.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 17, 2015; final manuscript received February 24, 2017; published online April 19, 2017. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 139(8), 082004 (Apr 19, 2017) (12 pages) Paper No: HT-15-1200; doi: 10.1115/1.4036153 History: Received March 17, 2015; Revised February 24, 2017

This article presents a new method of estimation of thermophysical parameters using the hybrid Monte Carlo (HMC) algorithm that synergistically combines the advantages of a Markov chain Monte Carlo (MCMC) method and molecular dynamics. The advantages of this technique over the conventional MCMC are elucidated by considering the multiparameter estimation in heat transfer. Four situations were analyzed. The first two involve a two- and a three-parameters estimation in a lumped capacitance model, third involves estimation in a distributed system, and the fourth involves estimation in a fin system. The goal is to establish the potency and usefulness of the HMC method for a wide class of engineering problems.

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Figures

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Fig. 1

Flowchart of the estimation of a parameter using the Bayesian inference and the hybrid Monte Carlo algorithm

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Fig. 2

Geometry of the distributed system and boundary conditions

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Fig. 3

Parity plot of the surrogate temperature versus the temperature obtained from the retrieved parameters using the HMC and the MCMC techniques at various noise levels for spatially distributed system

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Fig. 4

Evolution of initial temperature Tini parameter with iterations in HMC and MCMC for the lumped capacitance system; target: Tini = 101.7 °C

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Fig. 5

Evolution of heat generation Qgen parameter with iterations in HMC and MCMC for the lumped capacitance system; target: Qgen = 500 W

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Fig. 6

Evolution of time constant τc parameter with iterations in HMC and MCMC for the lumped capacitance system; target: τc = 100 s

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Fig. 7

Evolution of thermal conductivity k parameter with iterations in HMC and MCMC for the spatially distributed system; target: k = 25 W/m K

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Fig. 8

Evolution of heat transfer coefficient h parameter with iterations in HMC and MCMC for the spatially distributed system; target: h = 10 W/m2 K

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Fig. 9

Evolution of nondimensional parameter a with iterations in HMC and MCMC for the one-dimensional fin system

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Fig. 10

Evolution of thermal diffusivity α with iterations in HMC and MCMC for the one-dimensional fin system

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