Applying Bayesian Markov chain Monte Carlo (MCMC) modeling to predict the melting behavior of phase change materials. (January 2022) - Goodarzi, Marjan; Elkotb, Mohamed Abdelghany; Alanazi, Abdullah K.; Abo-Dief, Hala M.; Mansir, Ibrahim B.; Tirth, Vineet; Gamaoun, Fehmi
Abstract: A key practical application of PCM-based spherical containers is in packed bed thermal energy storage (TES) devices utilized for air conditioning in large buildings. Proposing high-precision models for the melting characteristics in spherical containers can provide deep insights into the design of TES systems. Herein, a methodology based on Bayesian inference was adopted to provide reliable models that predict the melting rate ( f ) and surface-averaged Nusselt number ( Nu ) as two significant factors in PCM melting process in spherical heat storage units. Five proposed models for f and Nu prediction were applied to available datasets. The input of Bayesian-based predictive models included three important dimensionless parameters of the melting problem, namely Ste, Gr, and Fo. Ste (Stefan number) describes the driving force of melting, Gr (Grashof number) reflects the natural convection intensity, and Fo (Fourier number) represents the dimensionless time. For accurate inference of model parameters using the Bayesian Markov chain Monte Carlo (MCMC) technique, an analysis was performed by coding in the WinBUGS language. Several statistical performance criteria (R 2, RMSE, and MSE) were utilized to evaluate the efficiency of Bayesian-based predictive models. The results showed that model #4 recorded R 2  = 0.980 in the prediction of melting rate. Furthermore, model #5 with R 2  = 0.966, had the best performance in predicting the values of surface-averaged Nusselt number. The models recommended in this research yield superior results compared to the previous study, which suggested R 2  = 0.975 and R 2  = 0. 925 for f and Nu, respectively.