A Novel Heat Exchanger Design Method Using a Delayed Rejection Adaptive Metropolis Hasting Algorithm

Abstract In this study, a shell-and-tube heat exchanger (STHX) design based on seven continuous independent design variables is proposed. Delayed Rejection Adaptive Metropolis hasting (DRAM) was utilized as a powerful tool in the Markov chain Monte Carlo (MCMC) sampling method. This Reverse Sampling (RS) method was used to find the probability distribution of design variables of the shell and tube heat exchanger. Thanks to this probability distribution, an uncertainty analysis was also performed to find the quality of these variables. In addition, a decision-making strategy based on confidence intervals of design variables and on the Total Annual Cost (TAC) provides the final selection of design variables. Results indicated high accuracies for the estimation of design variables which leads to marginally improved performance compared to commonly used optimization methods. In order to verify the capability of the proposed method, a case of study is also presented, it shows that a significant cost reduction is feasible with respect to multi-objective and single-objective optimization methods. Furthermore, the selected variables have good quality (in terms of probability distribution) and a lower TAC was also achieved. Results show that the costs of the proposed design are lower than those obtained from optimization method reported in previous studies. The algorithm was also used to determine the impact of using probability values for the design variables rather than single values to obtain the best heat transfer area and pumping power. In particular, a reduction of the TAC up to 3.5% was achieved in the case considered.

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