Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Estimation of boundary heat flux in Micro-Channels Via Bayesian Inference By The Transitional Markov Chain Monte Carlo Algorithm
Submission Author:
Lucas Asth , RJ
Co-Authors:
Lucas Asth, Luiz A. S. Abreu, Diego Knupp, Leonardo Stutz, Eduardo Cunha Classe
Presenter: Eduardo Cunha Classe
doi://10.26678/ABCM.COBEM2023.COB2023-1816
Abstract
The estimation of heat fluxes at the boundary of micro-channels has great interest in many engineering applications as in micro-electromechanical systems or in thermal control of microelectronics. However, in cases where direct temperature measurements cannot be taken, this information can still be obtained through the application of an inverse problems approach. Inverse problems related to micro-scale heat transfer and microfluidics have become more widely studied in recent decades due to advances in technology. This work deals with a Bayesian inverse problem of boundary heat flux profile in a micro-channel under slip-flow conditions using the Transitional Markov Chain Monte Carlo method. The boundary heat flux profile is estimated based on non-intrusive temperature measurements supposedly taken with a thermographic camera. The direct problem was solved using the finite element method implemented by the NDSolve function, which is an intrinsic function of Mathematica Software. The Transitional Markov Chain Monte Carlo Method algorithm was used to solve the inverse problem due to its advantages over the classic Markov Chain Monte Carlo Method. Bayesian methods have become increasingly popular in inverse analysis due to their ability to incorporate prior information and quantify uncertainties. The Transitional Markov Chain Monte Carlo Method is a more recent Bayesian algorithm that has several advantages. It is a tune-free algorithm, meaning it does not require the specification of a proposal probability density function, and it can estimate the model evidence and make model comparisons without extra computation costs. The proposed methodology was analyzed by simulated temperature measurements with different boundary heat flux function shapes, revealing the capability of the approach, even in discontinuous functions. The proposed methodology provides a way to obtain statistical uncertainties based on temperature measurements, making it a valuable tool in the design and optimization of micro-channel heat transfer systems.
Keywords
Bayesian inference, Heat transfer, Inverse problems, Microchannel, Transitional Markov Chain Monte Carlo
