Faculty Publications
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Item A Markov Chain Monte Carlo-Metropolis Hastings Approach for the Simultaneous Estimation of Heat Generation and Heat Transfer Coefficient from a Teflon Cylinder(Taylor and Francis Ltd. michael.wagreich@univie.ac.at, 2018) Kumar, H.; Kumar, S.; Gnanasekaran, N.; Balaji, C.This paper reports the use of Markov Chain Monte Carlo (MCMC) and Metropolis Hastings (MH) approach, to solve an inverse heat transfer problem. Three-dimensional, steady state, conjugate heat transfer from a Teflon cylinder of dimensions 100 mm diameter and 100 mm length with uniform volumetric internal heat generation is considered. The goal is to estimate volumetric heat generation and heat transfer coefficient, given the temperature data at certain fixed location on the surface of the cylinder. The internal volumetric heat generation is specified as input and the temperature and heat transfer coefficient values are obtained by a numerical solution to the governing equation. The temperature values also depend on heat transfer coefficient which is obtained by solving Navier–Stokes equation to obtain flow information. In order to reduce the computational cost, a neural network is trained from the computational fluid dynamics simulations. This is posed as an inverse problem wherein volumetric heat generation and heat transfer coefficient are unknown but the temperature data is known by conducting experiments. The novelty of the paper is the simultaneous determination of volumetric heat generation and heat transfer coefficient for the experimentally measured steady-state temperatures from a Teflon cylinder using MCMC-MH as an inverse model in a Bayesian framework and finally, the estimates are reported in terms of mean, maximum a posteriori, and the standard deviation which is the uncertainty associated with the estimated parameters. © 2018 Taylor & Francis Group, LLC.Item A Bayesian inference approach: estimation of heat flux from fin for perturbed temperature data(Springer India, 2018) Kumar, H.; Gnanasekaran, N.This paper reports the estimation of the unknown boundary heat flux from a fin using the Bayesian inference method. The setup consists of a rectangular mild steel fin of dimensions 250×150×6 mm3 and an aluminium base plate of dimensions 250×150×8 mm3. The fin is subjected to constant heat flux at the base and the fin setup is modelled using ANSYS14.5. The problem considered is a conjugate heat transfer from the fin, and the Navier–Stokes equation is solved to obtain the flow parameters. Grid independence study is carried out to fix the number of grids for the study considered. To reduce the computational cost, computational fluid dynamics (CFD) is replaced with artificial neural network (ANN) as the forward model. The Markov Chain Monte Carlo (MCMC) powered by Metropolis–Hastings sampling algorithm along with the Bayesian framework is used to explore the estimation space. The sensitivity analysis of the estimated temperature with respect to the unknown parameter is discussed to know the dependency of the temperature with the parameter. This paper signifies the effect of a prior model on the execution of the inverse algorithm at different noise levels. The unknown heat flux is estimated for the surrogated temperature and the estimates are reported as mean, Maximum a Posteriori (MAP) and standard deviation. The effect of a-priori information on the estimated parameter is also addressed. The standard deviation in the estimation process is referred to as the uncertainty associated with the estimated parameters. © 2018, Indian Academy of Sciences.Item Inverse approach using bio-inspired algorithm within Bayesian framework for the estimation of heat transfer coefficients during solidification of casting(American Society of Mechanical Engineers (ASME), 2020) Vishweshwara, P.S.; Gnanasekaran, N.; Arun, M.In any parameter estimation problem, it is desirable to obtain more information in one single experiment. However, it is difficult to achieve multiple objectives in one single experiment. The work presented in this paper is the simultaneous estimation of heat transfer coefficient parameters, latent heat, and modeling error during the solidification of Al-4.5 wt %Cu alloy with the aid of Bayesian framework as an objective function that harmoniously matches the mathematical model and measurements. A 1D transient solidification problem is considered to be the mathematical model/forward model and numerically solved to obtain temperature distribution for the known boundary and initial conditions. Genetic algorithm (GA) and particle swarm optimization (PSO) are used as an inverse approach and the estimation of unknown parameters is accomplished for both pure and noisy temperature data. The use of Bayesian framework for the estimation of unknown parameters not only provides the information about the uncertainties associated with the estimates but also there is an inherent regularization term in which the inverse problem boils down to well-posed problem thereby plethora of information is extracted with less number of measurements. Finally, the results of this work open up new prospects for the solidification problem so as to obtain a feasible solution with the present approach. © © 2020 by ASME