Three-dimensional Phenomena Research Articles

Advanced CFD simulation of two-phase anion exchange membrane water electrolysis

Anion exchange membrane (AEM) water electrolysis is a promising and inexpensive solution for hydrogen production and environmental problems. Owing to its low technical proficiency, AEM electrolysis necessitates high fidelity to improve its durability, reliability, and efficiency. Therefore, a CFD-based model for AEM electrolysis was developed to analyze the three-dimensional and two-phase phenomena inside the cell. The temperature, pressure, and gas generation profiles inside the cell were studied by combining electrochemical models with mass, momentum, and heat transfer models. Parameters were estimated using the experimental data from a high-accuracy model. The results showed that the applied voltage, which determined the exothermic/endothermic mode, significantly influenced the water electrolysis performance. Specifically, in the exothermic mode, with voltages exceeding the thermo-neutral voltage (1.48 V), the amount of hydrogen generated (15.53, 25.05, and 28.82 mol/m3 at 1.6, 1.8, and 2.0 V, respectively) was higher than that in the endothermic mode (4.78 mol/m3 at 1.45 V). However, the increased gas generation caused a rapid increase in the temperature and pressure drop inside the cell, which adversely affected durability. The model developed in this study can be used in experiments of various scales to optimize serpentine designs and commercial AEM electrolysis stack developments.

Evaluating Force-based Haptics for Immersive Tangible Interactions with Surface Visualizations.

Haptic feedback provides an essential sensory stimulus crucial for interaction and analyzing three-dimensional spatio-temporal phenomena on surface visualizations. Given its ability to provide enhanced spatial perception and scene maneuverability, virtual reality (VR) catalyzes haptic interactions on surface visualizations. Various interaction modes, encompassing both mid-air and on-surface interactions-with or without the application of assisting force stimuli-have been explored using haptic force feedback devices. In this paper, we evaluate the use of on-surface and assisted on-surface haptic modes of interaction compared to a no-haptic interaction mode. A force-based haptic stylus is used for all three modalities; the on-surface mode uses collision based forces, whereas the assisted on-surface mode is accompanied by an additional snapping force. We conducted a within-subjects user study involving fundamental interaction tasks performed on surface visualizations. Keeping a consistent visual design across all three modes, our study incorporates tasks that require the localization of the highest, lowest, and random points on surfaces; and tasks that focus on brushing curves on surfaces with varying complexity and occlusion levels. Our findings show that participants took almost the same time to brush curves using all the interaction modes. They could draw smoother curves using the on-surface interaction modes compared to the no-haptic mode. However, the assisted on-surface mode provided better accuracy than the on-surface mode. The on-surface mode was slower in point localization, but the accuracy depended on the visual cues and occlusions associated with the tasks. Finally, we discuss participant feedback on using haptic force feedback as a tangible input modality and share takeaways to aid the design of haptics-based tangible interactions for surface visualizations.

An Experimental Investigation Of Local Thermo-Fluidic Heat Transfer In A U-Shaped Mini-Channel Sink

This study investigates experimentally a heated U-shaped mini-channel heat sink using Infrared Thermography and Particle Image Velocimetry for a water coolant flow of Reynolds numbers of 280, 650, and 1350 (based on the hydraulic channel diameter). The choice of this cell geometry is based on its role as a simplified unit of a serpentine heat exchanger, which is proved to be one of the most promising for cooling processes. The use of the infrared camera allows the detection of temperature fields on top of the external surface of the cell. Therefore, aiming to derive the temperature distribution on the channel roof, a dedicated transfer function is implemented. Moreover, we employed the lumped capacitance model for thermal analysis on both infrared measurements and thermocouple data. The latter are recorded to capture the cooling process of the aluminium base and water temperature at the end of the outlet tube. As a result, thermal transient rate, cooling magnitude and equilibrium temperature are obtained. These parameters indicate that higher Reynolds numbers correspond to increased thermal transient rates, enhanced cooling effects, and lower equilibrium temperatures. A non-uniform distribution of heat transfer along the channel is reported, with the most efficient cooling area localized close to the first 90-degree corner. These findings are consistent with numerical simulations and previous experimental observations. PIV results reveal the presence of two fluid acceleration zones following both 90-degree corners, which contribute to improve the water cooling ability in their respective regions. Additionally, the formation of two recirculating bubbles is reported at the inner wall from corners vertices, whose intensity is dependent on Reynolds number, pushing the main flow towards the outer channel wall and reducing the local heat transfer. Turbulent kinetic energy distributions are also investigated, pointing out the presence of intense areas that better match with regions of minimum equilibrium temperature than maximum velocity zones. This suggests the presence of local turbulent unsteadiness and three-dimensional phenomena, which contributes significantly to cooling enhancement.

Validation of a three-dimensional two-phase code, CUPID, using a rod-bundle boiling test facility, SIRIUS-3D

In nuclear power plants, the occurrence of a three-dimensional mixing phenomenon in two-phase flow can help mitigate the peak cladding temperature of fuels in a core. Simulating this phenomenon necessitates subchannel-scale analysis. CUPID is a three-dimensional thermal hydraulic analysis code developed by KAERI. This paper presents the validation results of the code against rod bundle tests conducted using SIRIUS-3D, a 5 × 5 rod bundle test facility. One test utilized subchannel void sensors, while the other employed X-ray CT. To validate the SIRIUS-3D test data, subchannel-scale nodes were constructed for CUPID calculation. For improved convergence, the implicit friction calculation was conducted with a small CFL ratio. The drag coefficient interfacial friction model without the EVVD model yielded the best prediction. The void fraction was over-predicted at a low velocity of 0.1 m/s, which could be improved by reducing the interfacial friction.

Improvement of macroscopic turbulence model for subchannel analysis in the rod bundle array

The PRIUS program was established to generate an experimental database for the 6 × 4 and 12 × 6 rod bundle geometry. The database will be used to address the subchannel and CFD code analysis required for modeling and validation. This is necessary because Small Break Loss of Coolant Accident (SBLOCA) and Intermediate Break Loss of Coolant Accident (IBLOCA) present three-dimensional phenomena in the core due to the radial power profile, crossflow, and diffusion-dispersion. Therefore, specific experimental programs are required, especially during core reflooding, to investigate the large-scale three-dimensional effects. However, validating each sensitive model of the code separately in the presence of 3D effects is not possible due to the inability to implement instrumentation at high pressure and temperature steam-water flow conditions. The PRIUS test program uses a single-phase flow test to simulate a non-homogeneous velocity distribution and provide information on crossflow with radial mixing effects between subchannels. The CUPID code, which uses a macroscopic turbulence model, has been validated using the PRIUS-II experimental database. Existing macroscopic turbulence models were also validated for their prediction capabilities with different inlet flow conditions. However, the validation revealed significant errors in the shear region between subchannels. An improved macroscopic turbulence model showed promising results in predicting turbulence kinetic energy in porous media analysis.

Three-dimensional analysis reveals diverse heat wave types in Europe

Heat waves are among the most studied atmospheric hazards but commonly investigated near-surface temperature patterns provide only limited insight into their complex structure. Here we propose and evaluate a novel approach to the analysis of heat waves as three-dimensional (3D) phenomena, employing the ERA5 reanalysis in three European regions during 1979–2022. Four types of heat waves based on their vertical cross sections of temperature anomalies are introduced: near-surface, lower-tropospheric, higher-tropospheric, and omnipresent. The individual heat wave types differ in length, predominant occurrence within summer, and soil moisture preconditioning. While near-surface heat waves may persist for more than 2 weeks, those located mainly in higher troposphere are shortest (5 days at most). This demonstrates that warm advection must be accompanied by a downward propagation of positive temperature anomalies through air subsidence and diabatic heating to maintain long-lasting heat waves. We also show that soil-moisture preconditioning is crucial for near-surface heat waves only, thus pointing to different driving mechanisms for the individual 3D heat wave types.

An Effective Arbitrary Lagrangian-Eulerian-Lattice Boltzmann Flux Solver Integrated with the Mode Superposition Method for Flutter Prediction

An Effective Arbitrary Lagrangian-Eulerian-Lattice Boltzmann Flux Solver Integrated with the Mode Superposition Method for Flutter Prediction

Analytical reconstruction of axisymmetric curved shock wave/boundary layer interactions

In practical aerodynamic scenarios, interactions between curved shock waves and boundary layers with composite shock curvatures in both streamwise and spanwise directions are encountered more frequently than those induced by planar oblique shocks. To gain a more systematic understanding of this phenomenon in physics, internal and external axisymmetric curved shock wave/boundary layer interactions (AC-SBLI) are being studied analytically by establishing the underlying relations within the flow structures. Specifically, based on reconstructing the dominant structures of AC-SBLI as a semi-analytical model, this study focuses on the impacts of shock spanwise curvatures on separation and the mechanism of their action. It reveals that spanwise curvatures affect the separation in both internal and external AC-SBLI, but each exhibits a different influence pattern, emphasizing apparent axisymmetric characteristic. The spanwise curvatures exert influence indirectly by altering the compression ratio and directly by affecting the distribution of streamwise shock intensities. These findings propose a new approach to estimating the flow structures in AC-SBLI, where analyzing the spanwise curvatures will assist with comprehending other more intricate three-dimensional separation phenomena.

On the Darcy–Forchheimer flow of carbon nanotubes nanofluid across a stretching surface for the impact of heat source/sink and Ohmic heating

This research leads to carrying out the productivity and the efficiency of the carbon nanotubes (CNTs) that have extensive applications in solar collectors. Due to the superior thermal as well as electrical properties, the use of CNTs has an important contribution to the nanotechnology revolution. Therefore, owing to the aforementioned vital points, this investigation intended to put forth the thermophysical properties of both single and multi-walled CNT nanofluids past a stretching surface. Additionally, an electrically conducting nanofluid flow phenomenon enriches due to the inclusion of dissipation (Ohmic heating) and external heat source/sink. The dimensional form of the three-dimensional fluid flow phenomena is transformed to a non-dimensional form with the use of similarity transformation and further numerical procedure is implemented to solve the nonlinear governing equations. The substantial significance of the characterizing parameters is presented briefly via figures and the comparative analysis with the earlier investigation is deployed through the table. However, the main findings of this study are as follows: A significant attenuation in the shear rate is marked for the enhanced inertial drag but it augments for the augmented values of the magnetization; further, particle concentrations of both the CNTs favor accelerating the fluid momentum as well as temperature distribution.

An exploratory review of the fintech influence field

Fintech as a three-dimensional phenomenon reflects the rapidly changing technological, financial and business environment. The bibliometric analysis of scientific articles allowed us to identify the main themes and create a map of the field of fintech influences. Systematization of scientific articles revealed the influence of economic development and socio-demographic inequality on fintech development. Government regulatory policies can accelerate the digitisation of financial services and financial inclusion and help the fintech sector face geopolitical challenges. Fintech’s impact was divided into three areas: financial stability and sustainable development, the business ecosystem and human behaviour. The research we summarised allowed us to identify the mechanisms through which fintech influences various fields. A complex approach to the influence of fintech enables us to understand the phenomenon and make better decisions.

New higher-order accurate super-compact scheme for three-dimensional natural convection and entropy generation

Exploring natural convection in three dimensions through numerical analysis has become essential for gaining a deeper understanding of this process compared to studying it in just two dimensions. This paper presents an enhanced analysis of three-dimensional (3D) natural convection phenomena within an air-filled cubical cavity, with a primary focus on heat transfer characteristics. The distinguishing feature of this research lies in the pioneering application of the newly developed higher-order accurate super-compact finite difference scheme to study 3D natural convection and entropy generation. This numerical method is renowned for its fourth-order spatial accuracy and second-order temporal accuracy. The super-compact scheme employs 19 grid points at the current time level (nth time level) while utilizing just seven grid points from the subsequent time level [(n+1)th time level. The flow is considered to be 3D, time-varying, laminar, and incompressible. First, the newly developed numerical code has undergone validation through quantitative and qualitative comparisons with existing results. Then, we analyze the flow phenomena and heat transfer dynamics within the cavity for various Rayleigh numbers (102≤Ra≤105) with a fixed Prandtl number (Pr = 0.71) by using this scheme. Various parameters such as local Nusselt numbers, averaged Nusselt numbers, local entropy, Bejan number, streamlines, and isotherm dispersion are studied in this work. It is found that as the Rayleigh number (Ra) increases, the Bejan number (Be) decreases, while the total entropy increases. When the Ra is less than or equal to 104, the Be remains above 0.5, indicating that irreversibility primarily arises from heat transfer. However, as we transition to Ra=105, the Be falls below 0.5, signaling that irreversibility is now predominantly driven by viscous effects. To the best of our knowledge, this research marks a pioneering effort by introducing the application of the higher order super-compact (HOSC) scheme for the examination of heat transfer within a 3D cubic cavity, thus endowing our work with a truly novel and pioneering character. It is worth mentioning that, before this study, there has been no precedent in the exploration of heat transfer using the super-compact scheme, thus endowing our work with a truly novel and pioneering character.

Implementation of the preCICE coupling interface for AC2/ATHLET

Abstract The design of new nuclear reactor types as well as the analysis of certain phenomena in existing reactors require to consider different physical models and three-dimensional phenomena like the effect of turbulence in fluids and three-dimensional (3D) heat conduction in complex structures. One-dimensional (1D) lumped parameter system codes used to simulate transients in nuclear reactors lack high-resolution models. Special codes like computational fluid dynamics (CFD) or computational structural mechanics codes (CSM) can simulate those, but they require significantly more computational resources. Therefore, different coupling methods have been developed to limit the use of computationally expensive codes to those parts of a plant where they are really needed and couple them with systems codes, which simulate the rest. The library preCICE enables simultaneous coupling of multiple simulation programs, e.g., the 3D CFD code OpenFOAM and the 3D CSM code CalculiX. preCICE coupling interfaces were developed for the system code ATHLET. We focused on fluid-fluid couplings and conjugate heat-transfer couplings. Coupled simulations were performed for an experiment at the test facility TALL for the transition from forced to natural circulation coupling ATHLET with OpenFOAM, and a generic building condenser geometry coupling the three codes ATHLET, CalculiX, and OpenFOAM. The correct integral transfer of the quantities at the coupling interfaces was verified. However, it was found that coupled quantities at the interfaces need to be converted from 0D to 2D and backwards considering the underlying physics, which goes beyond the pure numerical considerations of the preCICE library.

Ejecta behavior during plume-surface interactions under rarefied atmospheric conditions

Plume-surface interactions (PSI) occur during the take-off and landing of interplanetary vehicles, leading to particle ejection and the formation of craters. This can be detrimental to the vehicle and any structures or infrastructure near the landing site. A major challenge in developing a comprehensive understanding of this three-dimensional phenomenon is the need to characterize the ejecta and cratering dynamics simultaneously. Here, experiments are conducted in a vacuum chamber at different nozzle heights and ambient pressure conditions using high-speed stereo-photogrammetry and planar particle tracking velocimetry to quantify the cratering and ejecta dynamics. Predictably, it was observed that the trajectory of ejecta with a large Stokes number was mostly unaffected by the nozzle flow after leaving the crater. Under rarefied conditions, the ejecta kinematics (velocity, ejection angle, range, and height) were significantly different compared to continuum conditions. Finally, the findings demonstrate a dependency between ejecta kinematics and crater topology for the current test cases, providing critical insights into particle ejection’s initial characteristics.

Tetraedrijske homonuklearne tetramerne vrste

Tetrahedral homonuclear tetrameric species are neutral or ionic tetrahedra of chemical elements, true molecular tetrahedra in strict geometrical sense. The aim of this work was to find all true elemental tetrahedra experimentally determined as stable and capable of being transferred from one medium/condition to another, to rationalize their structures and properties, and seek their technological significance. A database of elemental tetrahedra was built based on reliable literature, and a dataset of molecular descriptors was generated. Correlation analysis, hierarchical cluster analysis, principal component analysis, and some regression analysis were carried out. Twelve chemical elements from Groups 13 – 15 have tetrahedral species: anions E<sub>4</sub><sup>8–</sup> (Al, Ga, In, Tl), anions E<sub>4</sub><sup>4–</sup> (Si, Ge, Sn, Pb), neutral molecules E<sub>4</sub> (P, As, Sb), and cations E<sub>4</sub><sup>+</sup> (P, As, Sb, Bi). These species appear in 39 forms, such as gas phase, solid Zintl phases, thin films, Zintl phase ammoniates, and cage compounds, among others. Zintl phases and forms of P<sub>4</sub> and Sb<sub>4</sub> are important for synthesis of new materials, chemical reactions, and other applications. Data compression has shown that the true tetrahedral species are a three-dimensional phenomenon, and that true tetrahedra can be distinguished from fictive tetrahedra. Grouping of the tetrahedra according to their periodic groups, charges, frequency, and diversity class values, tetrahedral size, and metallic character, were observed. Empirical rules for species size and principal components were established for true tetrahedra. Most descriptors are parabolic functions of the class variable. True tetrahedral species partly remain a puzzle and should be further investigated.

Development of methodological recommendations for teaching physics based on the development of spatial imagination

Relevance. In modern education, much attention is paid to the development of critical thinking and cognitive skills of students, including the ability to spatial reasoning. This is important for the successful mastery of subjects, especially physics, where understanding of three-dimensional objects and phenomena is of key importance.Purpose. The purpose of this study is to create a methodology for teaching physics with an emphasis on the development of students� spatial imaginations. To test the effectiveness of the developed methodology, an experiment was conducted to assess the level of spatial imagination development of the participating students and to compare the results before and after the application of the methodology.Methodology. One of the key methods developed by the study is the use of visualizations and three-dimensional models in the learning process.Results. The main results of this study are related to the development of methodological recommendations for teaching physics based on the active development of students� spatial imaginations. This allows students to better understand abstract physical concepts, such as the structure of an atom or vector operations, through visual images. The study also identified effective techniques for developing students� spatial abilities. These include the inclusion of three-dimensional puzzle elements in assignments or solving problems involving the construction of spatial models, which helps students to better understand the geometric relationships and interactions of bodies in space. In addition, the importance of using interactive teaching methods, such as conducting virtual experiments or discussing three-dimensional simulations, was identified as contributing to a deeper understanding of the material.Conclusions. The practical significance of this study is to provide a specific methodology for physics teachers, which will optimize the learning process, increase students� understanding of the theory and develop their spatial imagination more effectively.

Calorimetric studies of yttrium doped non-conventional phase-change materials for improved performance

Though phase-change materials (PCMs) are regarded as constituent part of next-generation phase-change memory and other unfolding optoelectronic applications, the kinetics study of glass transition and crystallization, significant property in switching remains obscure in high-temperature region. Hence, this paper reports the investigation of glass transition and crystallization kinetics of Te(1-x) (GeSe0.5)Yx (TGSY) chalcogenide glass using differential scanning calorimetry (DSC) at heating rates 5, 10, 15, 20 °C/min. The effect of increasing Y quantity has been described by connecting structural relaxation kinematics during glass transition phenomena and devitrification while crystallization in chalcogenide glasses with their varied physicochemical characteristics. The inclusion of Y causes a discernible rise in the crystallization rate. The system is compatible with a strong glass-forming liquid, according to the Te(1-x) (GeSe0.5) Yx material fragility index. According to the average values of the kinetic exponent factors, there is heterogeneous nucleation for the investigated composition, which is subsequently followed by a two- or three-dimensional crystal growth phenomenon. Different glass stability criteria have been discussed based on the relationship between the characteristic temperatures. The CZW and CLX criteria were found to be inappropriate for discussing glass stability (GS) for the studied compositions based on the heating rate and composition dependencies of all criteria. The CYL criteria of Yuan et al. is the finest and it demonstrates the optimal ability for evaluating the GS, according to the data that was extracted from several GS criteria and their relative change parameters. By adding Y, thermal stability parameter and enthalpy emitted during the transition of glass and crystalline phases have been found to have an inverse relationship. All studied properties can conclude the application of studied material in phase-change material devices.

On computational simulations of dynamic stall and its three-dimensional nature

In this paper, we investigate the three-dimensional nature of dynamic stall. Conducting the investigation, the flow around a harmonically pitching National Advisory Committee for Aeronautics (NACA) 0012 airfoil is numerically simulated using Unsteady-Reynolds-Averaged Navier–Stokes (URANS) and multiple detached eddy simulation (DES) solvers: the Delayed-DES (DDES) and the Improved-DDES (IDDES). Two- and three-dimensional simulations are performed for each solver, and the results are compared against experimental measurements in the literature. The results showed that three-dimensional simulations surpass two-dimensional ones in capturing the stages of dynamic stall and predicting the lift coefficient values, with a distinguished performance of the DES solvers over the URANS ones. For instance, the IDDES simulations, as an inherently three-dimensional solver, predicted the necessary cascaded amalgamation process of vortices to form the adequate strength of the dynamic stall vortex. This vortex size and timing provided accurate and sufficient suction that resulted in identical matching of the numerical and experimental lift coefficients at the peak value. Hence, the hypothesis that dynamic stall has a three-dimensional nature is supported by the superiority of the three-dimensional simulation in all aspects. In conclusion, it is found that dynamic stall is intrinsically a three-dimensional phenomenon.

A graphics-accelerated deep neural network approach for turbomachinery flows based on large eddy simulation

In turbomachinery, strongly unsteady rotor–stator interaction triggers complex three-dimensional turbulent flow phenomena such as flow separation and vortex dynamics. Large eddy simulation (LES) is an advanced numerical method that has recently been used to resolve large-scale turbulent motions and model subgrid-scale turbulence in turbomachinery. To largely reduce the computing cost of LES for turbomachinery flow, a graphics processing unit (GPU)-accelerated deep neural network-based flow field prediction approach is explored, which combines convolutional neural network autoencoder (CNN-AE) with long short-term memory (LSTM). CNN-AE extracts spatial features of turbomachinery flow by mapping high-dimensional flow fields into low-dimensional space, while LSTM is used to predict the temporal evolution of fluid dynamics. Automatic mixed precision (AMP) is employed to achieve rapid neural network training using Nvidia GTX 1080 Ti GPU, which shows a significant speedup compared with that without AMP. We evaluated the proposed CNN-AE-LSTM (CAL) method against gated recurrent units (GRU) and simple recurrent network (SRN) on two types of turbomachinery, i.e., centrifugal and axial flow pumps. The results show that the proposed CAL shows better capability of capturing the vortex structure details of turbomachinery. When predicting the temporal vorticity field, the mean square error of CAL results is 0.105%–0.124% for centrifugal pumps and 0.071%–0.072% for axial flow pumps. Meanwhile, the structural similarity index measure of the CAL results is 92.51%–92.77% for centrifugal pumps and 93.81%–94.61% for axial flow pumps. The proposed CAL is noticeably better than GRU and SRN in terms of both mean square error and structural similarity index measure.

Multiscale Thermal-Hydraulic Analysis of the ATHENA Core Simulator

In the framework of the ALFRED research and development program, the ATHENA facility will be constructed for thermal-hydraulic analysis of full-scale ALFRED components and systems. The source system of the facility is the core simulator, which aims to be representative of an ALFRED average fuel assembly. Computational fluid dynamics (CFD) codes are gaining attention for the analysis of complex systems in pool-type reactors since they are able to reproduce three-dimensional phenomena. In this paper, a multiscale approach based on porous media is proposed to reduce the computational cost of the core simulator CFD model. The multiscale approach starts with the detailed simulation of the infinite lattice domain of the fuel assembly to characterize the porous media hydraulic behavior. Then the porous media are applied in the system model. Three different approaches are investigated: (1) adopting a single porous media for the entire fuel assembly, (2) representing the bundle with two porous domains, and (3) adopting the so-called hybrid medium. The results have been compared with the reference detailed CFD simulation for performance evaluation. The first step of the analysis is the application of the multiscale approach on the CIRCE fuel pin simulator to carry out a turbulence model validation against experimental data and a comparison of the three approaches with a proven CFD model. Then the approach is applied on the ATHENA core simulator exploiting the CIRCE results. The results obtained with the porous media models are compared with a detailed CFD simulation of the core simulator to evaluate the performance of the three approaches. Eventually, the best solution is applied on a model of the entire ATHENA core simulator integrated with the feeding region. The model is tested also in transient conditions. The numerical experiment demonstrates the effectiveness of the multiscale approach in reducing the computational cost while maintaining high accuracy in representing the quantities of interest.

Dual-fluid topology optimization of printed-circuit heat exchanger with low-pumping-power design

This study proposes a novel design for a printed-circuit heat exchanger (PCHE) using a dual-fluid topology optimization method. To account for the three-dimensional (3D) heat transfer phenomena using the two-dimensional (2D) computational domains, three distinct physical domains are defined: two design domains with density fields of hot and cold fluids, and a thermal conduction domain placed between both fluid fields. To account for the local heat transfer variation within a design domain, the local heat transfer coefficient is expressed using the density fields for the hot- and cold-fluid domains. Here, the design geometry had pillar-shaped fixed density values considering the metal 3D printing. Each flow region had a constant flow rate as the boundary condition with the constraint of the maximum pressure drop between the inlet and outlet. The total amount of the heat transferred between the hot and cold domains was maximized as an objective function. For the validation, the thermal performance of the topology-optimized PCHE was compared to that of a conventional PCHE. The topology-optimized PCHE showed a 66% higher heat transfer rate compared to the conventional PCHE under identical pumping-power conditions.