A Bayesian Inference Approach for Inverse Transient Heat Transfer Problem

Inverse transient heat transfer problems are important in many applications including process control, metallurgy, aerospace, and nuclear engineering. However, the existing techniques cannot solve inverse heat transfer problems when the unknown parameters vary with space and time. In this study, a Bayesian inference approach is developed to solve such inverse heat transfer problems. The posterior probability density function (PPDF) of unknown parameters is computed from temperature measurements in a circular steam header. The Markov chain Monte Carlo method (MCMC) is used to estimate the statistics of unknown parameters, while the Metropolis-Hastings (MH) algorithm is used to generate random samples for the posterior state space. The inverse solution is obtained by computing the expectation of the PPDF. The simulation results indicate that the estimates using MCMC-MH samples are accurate; the Bayesian approach can capture the probability distribution of the unknown local convective heat transfer coefficients and steam temperature. The stochastic Bayesian inference approach can be applied to efficiently estimate unknown boundary conditions at inaccessible locations.