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

This work deals with an inverse two-dimensional nonlinear heat conduction problem to determine the top and lateral surface transfer coefficients. For this, the $\text{textsc}B$ayesian framework with the $\text{textsc}M$arkov Chain $\text{textsc}M$onte $\text{textsc}C$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.