MCMC and approximation error model for the simultaneous estimation of heat flux and heat transfer coefficient using heat transfer experiments

Abstract

This work deals with the simultaneous estimation of the heat flux and the heat transfer coefficient from a mild steel fin losing heat to the ambient by natural convection. Steady state heat transfer experiments are performed on a mild steel fin of dimension 150x250x6 (all dimensions are in mm) placed on to an aluminum base plate of dimension 150x250x8 (all dimensions are in mm). The experimental set up is placed inside a large enclosure to avoid natural disturbances. Nine calibrated K-type thermocouples are used to measure the temperatures of the fin and the base plate. The forward solution of a three dimensional conjugate heat transfer fin model is solved using commercially available ANSYS software in order to obtain the temperature distribution of the fin. An inverse problem is proposed for the estimation of unknown parameters within the Bayesian framework of statistics. Furthermore, a model reduction in the form of Approximation Error Model (AEM) is considered for the inverse conjugate natural convection heat transfer problem. Such an approach not only mitigates the complexity of the inverse problem but also compensates the model reduction with all necessary statistical parameters. Additionally, the sample space within the Bayesian framework is explored with the help of Markov Chain Monte Carlo Method (MCMC) along with the Metropolis-Hastings algorithm. The results of the inverse estimation using Approximation Error Model based on the experimental temperature prove to be a promising alternative in inverse conjugate heat transfer problems. � 2018 International Heat Transfer Conference. All rights reserved.