Estimative of the inlet temperature profile in ducts via Markov Chain Monte Carlo Method

Abstract

This work deals with the employment of a Bayesian methodology in order to solve an inverse problem in forced convective heat transfer in steady state laminar flow between parallel plates. The direct problem involves calculating temperatures along the duct, once boundary conditions are specified. The direct problem was numerically solved in a computational platform, Mathematica, with the finite element method, by applying the built-in tool, NDSolve. The inverse problem consists of estimating the inlet temperature profile from non-intrusive temperature measurements, supposedly taken by using infrared thermography. The Bayesian approach taken to estimate the inverse problem solution, uses a Markov Chain Monte Carlo method. The accuracy of the present solution approach was examined by using simulated measurements, containing random noises.