  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.
