Linear method for the design of shell and tube heat exchangers including fouling modeling

•A fouling model is inserted into the design optimization of heat exchangers.•The mathematical problem consists in a mixed-integer linear programming (MILP).•The results indicate a better performance when compared to conventional approaches. Typical heat exchanger design procedures are based on the use of fixed values of fouling factors, mostly based on estimates coming from practice. However, fouling depends on thermofluidynamic conditions (e.g. flow velocity) which values are consequence of the selection of design variables (e.g. baffle spacing). Therefore, the inclusion of fouling models into an optimal design procedure may yield better solutions. In this article, we extend a recent globally optimal linear formulation for the design of shell and tube heat exchangers (Gonçalves et al., 2017). Our extension leads to a linear model and consists on adding velocity dependent fouling factors. A comparison with design examples based on fixed fouling factors indicates that the linear problem can identify better design solutions, without involving any external convergence loop.