In this article, we extend a previously developed globally optimal enumeration methodology for the synthesis of Heat Exchanger Networks to the simultaneous synthesis of the network and the basic design of Heat Exchangers. Our procedure guarantees global optimality, unlike previous approaches, such as Pinch Technology, metaheuristics, or mathematical programming that do not guarantee it and sometimes do not even guarantee local optimality. The procedure is not iterative, and does not present any convergence issues. To enumerate HEN structures, we use linear methods and for the HEX design we use Set Trimming followed by sorting. In addition, because some network structures are incompatible with single shell exchangers, we use multiple shell exchangers in series. The comparison of the results of the proposed approach with two solution alternatives from the literature in two different problems indicates that considerable cost reductions may be obtained.

In this work, the enumeration algorithms presented in parts I and II for the globally optimal synthesis of heat exchanger networks are extended to consider non-isothermal mixing. The previous models are modified by adding non-isothermal mixing constraints and new models are constructed to target the bounds of the energy consumption and the binding exchanger minimum approximation temperature. These new models are solved using algorithms that involve solving the solution of systems of equations instead of mathematical programming. We also present two alternatives for optimizing each enumerated structure, namely, the use of a global solver, or the use of a golden search with simple resolution of non-isothermal mixing model for fixed energy consumption. The non-isothermal mixing model is reformulated as a convex model, either solved using nonlinear programming or a programming-free methodology, i.e. solving Karush-Kuhn-Tucker equations. A global optimum search algorithm is developed and examples are tested comparing the proposed strategies.