Inverse Techniques for the Estimation of Multiple Parameters Using Steady State Heat Transfer Experiments

Abstract

The aim of the present research work is to estimate the unknown parameters by using the information obtained from in-house steady state heat transfer experiments and to employ stochastic inverse techniques. With the advent of latest technologies in the field of advance computing, conjugate heat transfer problems that are highly complex can easily be solved to obtain temperature distributions. In the present work, suitable mathematical models are proposed as forward models for a class of conjugate heat transfer problem. The first problem solved was a conjugate heat transfer from a mild steel fin. The numerical model is developed using ANSYS FLUENT with an extended model which facilitates natural convection heat transfer. Based on the experimental temperatures and with accompanying mathematical model, heat flux is estimated using Genetic Algorithm as inverse method. To accelerate the inverse estimation, Genetic algorithm is assisted with the Levenberg- Marquardt method for the estimation of the heat flux, thus making the whole process as hybrid estimation. In the second problem, 3-D conjugate fin model is proposed for the estimation of heat flux and heat transfer coefficient using Artificial Neural Network (ANN) method. The novelty of the work is to inject the experimental temperature methodologically in to the forward model which is trained by Neural network thereby the forward model is driven by experimental data and to accomplish the task of parameter estimation, ANN is used as inverse method that leads to a non-iterative solution. The concept of a priori information is then introduced for the simultaneous estimation of heat flux and heat transfer coefficient using experimental data. This was accomplished using Bayesian framework along with Markov Chain Monte Carlo (MCMC) method to condition the posterior probability density function. A powerful Metropolis-Hastings algorithm is exploited in order to attain stable Markov chains during the process of inverse estimation. Finally, this was followed by estimation of heat generation and heat transfer coefficient from a Teflon cylinder within the Bayesian framework.