Entransy dissipation-based constraint for optimization of heat exchanger networks in thermal systems

• Lagrange multiplier method is a good option in thermal system optimization.
• Entransy balance equation acts as a constraint without intermediate temperatures.
• Entransy dissipation-based method greatly simplifies the optimization.
• Entransy method is superior to traditional and entropy methods in some cases.

The Lagrange multiplier method is introduced for the global optimization of HENs (heat exchanger networks) with fixed layouts to give the optimal configuration of thermal systems that cannot be determined by other methods, such as HEN synthesis or linear programming method. A four-loop HEN with five heat exchangers and heat exchangers in thermodynamic systems are optimized as two examples from different perspectives. The first perspective is based on energy conservation where the energy and heat transfer equations act as the constraints in the Lagrange function. The second perspective is the heat transfer irreversibility where the entransy dissipation-based equation acts as the constraint. The entransy dissipation-based constraint eliminates the number of unknown intermediate fluid temperatures in the HENs and the corresponding number of constraints for HENs in thermal systems, which greatly simplifies the solution of optimization equations. Although the entropy generation-based equation can also act as a constraint, the intermediate fluid temperatures in the HENs cannot be eliminated because the entropy generation is a function of the absolute fluid temperature. As a result, the number of constraints is the same as when using energy conservation, so the optimization procedure for multi-component thermal systems cannot be simplified.