###### Abstract  
This paper presents an investigation on the optimum design for a plate-fin heat exchanger (PFHE) of a gas and supercritical carbon dioxide combined cycle which uses thermal oil as intermediate heat-transfer fluid. This may promote the heat transfer from low heat-flux exhaust to a high heat-flux supercritical carbon dioxide stream. The number of fin layers, plate width and geometrical parameters of fins on both sides of PFHE are selected as variables to be optimized by a non-dominated sorting genetic algorithm-II (NSGA-II), which is a multi-objective genetic algorithm. For the condition of heat transfer area and pressure drop on the exhaust side, which are the objective indexes, the result of NSGA-II is a Pareto frontier. The technique for order of preference by similarity to ideal solution (TOPSIS) approach is applied to choose the optimum solution from the Pareto frontier. Finally, further simulation is performed to analyze the effect of each parameter to objective indexes and confirm the rationality of optimization results. gas turbine; thermal oil loop; supercritical carbon dioxide; plate-fin heat exchanger; optimization +
Footnote †: journal: Applied Sciences  
supercritical CO\({}_{2}\) and water. [PERSON] et al. [5] investigated the heat transfer characteristics of a brazed plate heat exchanger for supercritical CO\({}_{2}\) and water. [PERSON] et al. [6] conducted a size optimization study for the heat exchanger which was applied in a marine supercritical CO\({}_{2}\) Brayton cycle. [PERSON] et al. [7] optimized microtube heat exchangers for supercritical CO\({}_{2}\) cooling. [PERSON] and [PERSON] [8] designed a compact heat exchanger for heat transfer between supercritical CO\({}_{2}\) and liquid sodium. A printed circuit heat exchanger (PCHE) was also suggested for the heat transfer of supercritical carbon dioxide. Although a PCHE had been designed for exhaust gas waste heat recovery [9], the pressure loss in the semi-channels of the PCHE was very large. Moreover, the use of heat transfer medium may promote the heat transfer from low heat-flux exhaust to high heat-flux s-CO\({}_{2}\) stream [10]. In this case, the design of a heat exchanger which shoulders the heat-transfer task seems particularly crucial, and plate-fin heat exchangers (PFHE) are a feasible solution because of their high thermal efficiency and large heat transfer area per unit volume [11]. Among these former heat exchangers, it seems that the plate-fin heat exchanger is a better solution for the gas turbine and supercritical carbon dioxide combined cycle with thermal oil loop. Several researchers have explored the optimization method for design parameters of plate-fin heat exchangers. [PERSON] et al. [12] used the heat transfer j correlations to design a compact plate-fin heat exchanger, and results showed that this model was viable for PFHE with offset trip fins and wavy fins. [PERSON] et al. [13] focused on the heat transfer characteristics of vertical upward flow in plate-fin heat exchangers. [PERSON] et al. [14] conducted an optimization for the fin types of multi-stream plate-fin heat exchangers. [PERSON] et al. [15] focused on the inlet configuration design to enhance the thermodynamic performance of plate-fin heat exchangers. [PERSON] et al. [16] carried out a numerical investigation on fin configurations of plate-fin heat exchangers. Moreover, researchers begin to employ artificial intelligence approaches to optimize the design parameters of plate-fin heat exchangers, such as neural networks [17]. [PERSON] et al. [18] used a genetic algorithm to optimize the PFHE layer stacking pattern with low thermal Hess in abnormal operating conditions. [PERSON] et al. [19] employed bees algorithm hybrid with particle swarm optimization to complete a thermal-economic design of plate fin heat exchangers. [PERSON] et al. [20] used a multi-objective genetic algorithm to obtain the geometric parameters of serrated fins in PFHE, considering heat transfer enhancement, decrease in flow resistance and maximum stress.