Surface transfer coefficients estimation for heat conduction problem using the Bayesian framework

TL;DR

This paper presents a Bayesian approach with MCMC to estimate surface transfer coefficients in a heat conduction problem, using a simplified model to reduce computational load and ensure accurate probabilistic parameter estimation.

Contribution

It introduces a lumped one-dimensional model within a Bayesian framework for efficient inverse heat transfer coefficient estimation, validated through experimental data.

Findings

Accurate posterior distributions of transfer coefficients were obtained.

The lumped model provided reliable results with reduced computational effort.

Experimental validation confirmed the model's effectiveness.

Abstract

This work deals with an inverse two-dimensional nonlinear heat conduction problem to determine the top and lateral surface transfer coefficients. For this, the \textsc{B}ayesian framework with the \textsc{M}arkov Chain \textsc{M}onte \textsc{C}arlo algorithm is used to determine the posterior distribution of unknown parameters. To handle the computational burden, a lumped one-dimensional model is proposed. The lumped model approximations are considered within the parameter estimation procedure thanks to the Approximation Error Model. The experiments are carried out for several configurations of chamber ventilator speed. Experimental observations are obtained through a complete measurement uncertainty propagation. By solving the inverse problem, accurate probability distributions are determined. Additional investigations are performed to demonstrate the reliability of the lumped model, in terms of accuracy and computational gains.