## 1 Introduction  
Air-to-air heat exchangers with cross-corrugated triangular ducts are widely used in many applications, such as electronic cooling, aerospace, air conditioning and refrigeration, petroleum refineries, automobiles, and chemical industries. Figure 1 shows the schematic of the air-to-air heat exchanger with cross-corrugated triangular ducts, where the two unmixed cross flows exchange heat through the corrugated plate. Flat plates are corrugated to form a series of parallel equilateral triangular ducts. Sheets of the same corrugated plates are then stacked together to form a 90\({}^{\circ}\) orientation angle, which guarantees the same flow pattern for the fluid on both side. Compared with air-to-air heat exchangers with other channel ducts, the air-to-air heat exchangers with cross-corrugated triangular ducts have some advantages like higher heat exchange capacity, higher mechanical strength and more compact size [1]. In recent years, the heat exchangers with cross-corrugate triangular ducts have attracted attention owing to their advantages. Many researchers have investigated the characteristics of heat transfer and flow of the cross-corrugated heat exchangers to enhance the heat transfer and decrease the pressure loss [2; 3; 4; 5; 6; 7]. Some researchers studied the effect of geometric parameters on the thermohydraulic characteristics of the cross-corrugated heat exchangers. [PERSON] et al. [8] experimentally investigated the effect of the corrugation inclination angle on the thermohydraulic performance of plates from \(0^{\circ}\) to \(90^{\circ}\). The results showed that the heat transfer and pressure drop increased with an increase of corrugation inclination angle. [PERSON] et al. [9] experimentally investigated the effect of the geometric parameters like the inclination angle, the wavelength, the amplitude and the shape of corrugation on thermohydraulic performance of the corrugated heat exchangers. Their results showed that the geometries were of significant influence on the heat transfer and pressure drop. [PERSON] et al. [10] conducted a series of experiments to study the effect of chevron angle on heat transfer performance in plate heat exchangers using ZnO/water nanofluid. [PERSON] et al. [11] numerically investigated the inclination angle on the performance of the corrugated heat exchanger. [PERSON] and [PERSON] [12] studied the effect of Apex angle and aspect ratio on heat transfer, pressure drop and thermohydraulic performance of periodic cross-corrugated channels using Computational Fluid Dynamics (CFD). They showed that Apex angle strongly influenced the heat transfer and pressure drop in triangular cross-section corrugated channels. The aspect ratio had a relatively greater impact on flow friction loss, compared to its effect on the heat transfer. These experimental and numerical studies identified that the geometric parameters have a significant effect on the thermohydraulic characteristics of the exchanger. Geometric optimization is one effective way of enhancing the heat transfer and decreasing the pressure drop. The entropy generation minimization (EGM), proposed by [PERSON] [13], is a very useful technology to optimize the thermal process, thermal system and thermal equipment. The EGM is based on the theory that a thermodynamically optimized system is the least irreversible, or minimum entropy generation in the system. [PERSON] and [PERSON] [14] used the EGM to optimize the cross-flow heat exchanger. They found that the minimum entropy generation number depended on flow path length, dimensionless mass velocity, and dimensionless heat transfer. [PERSON] et al. [15] minimized the entropy generation number of tube-tube heat exchanger to develop analytical expressions for optimal value of tube diameter, Dean number and Reynolds number. [PERSON] et al. [16] studied thermal-hydraulic and entropy generation for turbulent flow inside a corrugated channel. [PERSON] and [PERSON] [17] investigated the entropy generation of cylindrical heat pipe using nanofluid.