Uncertainty Quantification in Steady-State Heat Transfer: A Comprehensive Analysis of DRAM and MCMC Methods with Applications to Thermal Systems

This research addresses the limitations of traditional deterministic methods in capturing uncertainties in heat transfer systems, particularly in parameter estimation and uncertainty quantification. We aim to evaluate and compare Delayed Rejection Adaptive Metropolis (DRAM) and Markov Chain Monte Carlo (MCMC) methods for uncertainty quantification in steady-state heat transfer, using experimental data from a copper rod with 15 temperature measurements. The study estimates heat flux and convective heat transfer coefficient parameters, comparing results with Ordinary Least Squares (OLS) estimation. Results show DRAM produces tighter parameter distributions (0.2312) compared to MCMC (0.2641), while both methods yield similar mean estimates and demonstrate strong negative correlation between parameters. A comparison with OLS shows close agreement across all three methods, concluding that DRAM provides slightly superior performance in parameter estimation accuracy while all methods effectively capture parameter uncertainties in steady-state heat transfer analysis.