  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.
