Método Transicional de Monte Carlo via Cadeias de Markov em transferência de calor: contribuições para eficiência energética e diagnósticos de melanoma cutâneo

Abstract

The present work explores the applicability of the Transitional Markov Chain Monte Carlo (TMCMC) Bayesian method to three problems in heat transfer. This method employs Bayes' theorem to enable a smooth transition between prior and posterior probability distributions, allowing the estimation of narrower or multimodal posteriors from weakly informative priors. Additionally, the method facilitates model analysis and selection as a byproduct. The first approach addresses a classical heat transfer problem with applications in various contemporary issues, employing the TMCMC Bayesian method alongside the classical Markov Chain Monte Carlo (MCMC) method using the Metropolis-Hastings (MH) algorithm. These methods estimate the inlet temperature profile in a parallel-plate duct based on downstream temperature measurements, with the second method verification the results obtained by TMCMC. In the second problem, the TMCMC method is used to estimate the timevarying thermal contact conductance between plates, aiming to identify failures resulting from undesired force variations in the system. Thin plates are considered, and the Lumped Capacitance Method is applied. Furthermore, a model selection analysis is performed to determine the failure profile. Finally, the last problem focuses on detecting cutaneous melanoma through dynamic thermography measurements on the skin surface using the TMCMC method. Additionally, simpler models for skin tissue diagnosis are analyzed and selected as part of the study.