Design Optimization of Double-Pipe Heat Exchangers Using a Discretized Model

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.