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ISSN Online: 2688-7231

ISBN Online: 978-1-56700-524-0

Proceedings of the 26thNational and 4th International ISHMT-ASTFE Heat and Mass Transfer Conference December 17-20, 2021, IIT Madras, Chennai-600036, Tamil Nadu, India
December, 17-20, 2021, IIT Madras, Chennai, India

Thermal parameter estimation in a two-dimensional irregular heat conducting body using the Bayesian approach

Get access DOI: 10.1615/IHMTC-2021.1270
pages 847-852

Abstract

In this study, the Metropolis-Hastings Markov Chain Monte Carlo (MH-MCMC) algorithm is used to estimate heat transfer parameters for a two-dimensional irregular heat conducting body. The forward model of the two-dimensional steady-state heat conduction equation with Neumann and Robin boundary conditions is solved using COMSOL Multiphysics. Synthetically generated temperatures using the assumed values of the parameters to be estimated are taken as the measured temperatures. Artificial Neural Networks (ANN) based approach is implemented to develop a surrogate model. Thermal conductivity (k), convective heat transfer coefficient (h), and heat flux (q) are estimated. Cases involving simultaneous estimation of two and three parameters and estimation of temperature-dependent h and q are studied. The problem being ill-posed, estimation of three parameters without the prior knowledge of k is a challenging task. Using Gaussian prior for k, the prediction error of less than 5% is observed using the MH-MCMC algorithm. The usefulness of priors in improving the estimates of parameters, the effect of location, and the number of probes used for the measurement is studied for the different combinations of initial guess values. It is concluded that independent of the parameters to be retrieved, the estimation can be done using the MH-MCMC algorithm using temperature probes at any location on the surface of the body.
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