In this article, we present for the first time, a globally optimal design procedure of gasketed-plate heat exchangers using a new proposed technique: Set Trimming. Set Trimming is a recently developed optimization technique based on the sequential application of inequality constraints to gradually reduce the search space. This method eliminates several drawbacks that affect other optimization techniques: (i) it guarantees global optimality; (ii) it does not depend on good initial estimates; (iii) it guarantees convergence; and (iv) it does not require any tuning of algorithm parameters. The formulation of the optimization problem corresponds to the minimization of the heat exchanger area or the total annualized cost subjected to pressure drop bounds, flow velocity bounds, and required area constraint. Another contribution of this work is a new analysis of the Set Trimming method by finding the fastest algorithmic alternative through methodical application of each constraint. To validate the conjecture that our Set Trimming method is computationally faster for the design of plate heat exchangers, we compare its performance with results obtained using mixed-integer nonlinear programming (MINLP), mixed-integer linear programming (MILP), particle swarm optimization (PSO), genetic algorithms (GA), and simulated annealing (SA), which showed increased performance by orders of magnitude. These results suggest that Set Trimming can be a useful resource for the solution of design problems when the degrees of freedom are represented by integer variables.

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The design optimization of heat exchangers is a topic extensively investigated in the literature. The majority of the papers that addressed this problem employed closed-form analytical solutions to describe the behavior of the equipment, such as the logarithmic mean temperature difference (LMTD) and effectiveness (ε-NTU) methods. These analytical solutions are based on the hypothesis of uniform values of the physical properties and heat transfer coefficients. This assumption may imply considerable errors in several situations. Aiming at eliminating these limitations, we present a novel integer linear model for the optimal design of hairpin double-pipe heat exchangers. Our novel method discretizes the temperature field inside the exchangers and, together with appropriate rigorous reformulations, renders a linear model. Numerical results illustrate the performance of the proposed approach, showing that the analytical solutions can significantly undersize or oversize the heat exchanger.

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