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The leakage flow has a significant impact on the aerodynamic losses and efficiency of the compressor. This paper investigates the loss mechanism in the tip region based on a high-load cantilevered stator cascade. Firstly, a high-fidelity flow field structure was obtained based on the Enhanced Delay Detached Eddy Simulation (EDDES) method. Subsequently, the Liutex method was employed to study the vortex structures in the tip region. The results indicate the presence of a tip leakage vortex (TLV), passage vortex (PV), and induced vortex (IV) in the tip region. At i=4°,8°, the induced vortex interacts with the PV and low-energy fluid, forming a “three-shape” mixed vortex. Finally, a qualitative and quantitative analysis of the loss sources in the tip flow field was conducted based on the entropy generation rate, and the impact of the incidence on the losses was explored. The loss sources in the tip flow field included endwall loss, blade profile loss, wake loss, and secondary flow loss. At i=0°, the loss primarily originated from the endwall and blade profile, accounting for 40% and 39%, respectively. As the incidence increased, the absolute value of losses increased, and the proportion of loss caused by secondary flow significantly increased. At i=8°, the proportion of secondary flow loss reached 47%, indicating the most significant impact.

A marine condenser with exhausted steam as the working fluid is researched in this paper. Constructal designs of the condenser are numerically conducted based on single and multi-objective optimizations, respectively. In the single objective optimization, there is an optimal dimensionless tube diameter leading to the minimum total pumping power required by the condenser. After constructal optimization, the total pumping power is decreased by 42.3%. In addition, with the increase in mass flow rate of the steam and heat transfer area and the decrease in total heat transfer rate, the minimum total pumping power required by the condenser decreases. In the multi-objective optimization, the Pareto optimal set of the entropy generation rate and total pumping power is gained. The optimal results gained by three decision methods in the Pareto optimal set and single objective optimizations are compared by the deviation index. The optimal construct gained by the TOPSIS decision method corresponding to the smallest deviation index is recommended in the optimal design of the condenser. These research ideas can also be used to design other heat transfer devices.

A printed circuit cooler for S-CO 2 cycle is optimized by constructal design. First of all, a complex function composed of pumping power consumption and entropy generation rate is optimized. Volumes of cooler and heat transfer channel are fixed, which are used to achieve optimal heat transfer channel radius and minimal complex function. The optimized structural design of the cooler reduces overall pumping power consumption and complex function by 23.96% and 5.70%, respectively, and e entropy generation rate is increased by 12.55%. There is an optimal number of plate layers that can yield a bi-minimum complex function. Secondly, the NSGA-II is used for multi-objective optimization (MOO), dense distribution of optimal channel radius ( R Rh , opt ) is between 0.8 and 1.0 mm, whereas that of optimal plate layer number ( N c , opt ) is between 100 and 160. The smallest deviation index obtained by LINMAP or TOPSIS decision-making method is 0.088. In this case, R Rh , opt and N c , opt are 1.0 mm and 144, respectively. This result can be considered the best alternative for MOO design scheme of printed circuit cooler with the objectives of entropy generation rate and overall pumping power consumption. Theoretical guidance for structure designs of printed circuit coolers can be served from constructal optimization results obtained herein.

Based on the square heat-generation body (HGB) with “arrow-shaped” high-thermal-conductivity channel (HTCC) model established in the previous literature, we performed multi-objective optimization (MOO) with maximum temperature difference (MTD) minimization and entropy-generation rate (EGR) minimization as optimization objectives for its performance. Pareto frontiers with optimal set were obtained based on NSGA-II. TOPSIS, LINMAP, and Shannon entropy decision methods were used to select the optimal results in Pareto frontiers, and the deviation index was used to compare and analyze advantages and disadvantages of the optimal results for each decision method. At the same time, multi-objective constructal designs of the “arrow-shaped” HTCC were carried out through optimization of single degree of freedom (DOF), two DOF, and three DOF, respectively, and the thermal performance of the square heat-generation body under optimizations of different DOF were compared. The results show that constructal design with the MOO method can achieve the best compromise between the maximum thermal resistance and the irreversible loss of heat transfer of the square heat-generation body, thereby improving the comprehensive thermal performance of the square heat-generation body. The MOO results vary with different DOF, and optimization with increasing DOF can further improve the comprehensive thermal performance of square HGBs.

This paper aims to give a comprehensive energetic-exergetic performance analysis on the impacts of injecting-submillimeter of air bubbles into both sides of cold and hot water streams before the entrance port of a corrugated plate heat exchanger (C-PHE) having ten plates within counterflow configuration. Hence, optimize the energy and exergy effectiveness at different operating conditions for counter and parallel fluid flow configurations. Hot streams were studied in seven flow rates ranging from 280 L/h to 880 L/h with a regular step of 100 L/h, and constant hot water temperature and cold-water stream of 50 °C and 290 L/h, respectively. Hence, the air was discharged with four flow rates ranging between 150 and 840 L/h. The obtained results showed the vital role of the ABI technique in enhancing the NTU and effectiveness by 59% and 18.6%, respectively, for CWS. The entropy generation was reduced to 0.038 W/K and the augmentation entropy generation number to 0.087 at the low airflow rate for CWS, which are the main parameters for evaluating the EGM. These two parameters increase the Witte-Shamsundar-efficiency to a maximum value of 98.6% at the same operating conditions. Moreover, the exergy effectiveness was enhanced to a maximum value of 80.9% at a high ABI flow rate and low volumetric rate of the hot stream at CWS. The thermo-economic assessment has been carried out, which revelers the positive effects of ABI on the combined energetic and exergetic performance on both sides, i.e., hot and cold sides.

In this research, for the first time, the impact of wavy orientations on the entropy generation and exergy destruction of the wavy microchannel working with various types of aqueous nanofluid is addressed. To this end, two Left–Right and Up–Down wavy microchannels were developed, and the laminar flows of silver, aluminum oxide, and hybrid silver-aluminum oxide nanofluids, each with concentrations of 1%, 2%, and 3%, were numerically simulated using the multi-phase mixture model. The simulation was carried out at constant pumping powers of 0.05 W, 0.15 W, 0.25 W, and 0.35 W, and the inlet temperature of 300 K. The results demonstrated that the total exergy destruction for the Left–Right wavy microchannel is on average 20% lower than the Up-Down one. In both of the microchannels, using nanofluid decreases the destructed exergy, with the largest irreversibility reduction related to the silver nanofluid case. Also, utilizing nanofluids increases the effectiveness number, while raising the pumping power declines it. Moreover, the values of the effectiveness number are higher for the Up-Down wavy microchannel compared to those of the Left–Right one. Finally, for 3% silver nanofluid at pumping power of 0.05 W in the Left–Right wavy microchannel, the highest value of second law efficiency is obtained, while it is lowest for the water at pumping power of 0.35W in the Up–Down wavy microchannel.

To explore the influence of guide vanes on the energy loss of hydraulic turbines, a pump characterized by a simple structure and convenient operation was selected as the research subject. Entropy generation theory was utilized to analyze entropy generation losses at different flow rates, with a particular emphasis on the mechanisms in the impeller and draft tube. The findings indicate that turbulent entropy production dominates energy dissipation. Under the best efficiency point (BEP), the total entropy generation loss of Z0 = 11 turbine was 7.18% and 5.76% lower than that of Z0 = 7 and Z0 = 9, respectively. The proportion of entropy generation loss in the impeller was highest under low-flow and optimal operating conditions, while the proportion of entropy generation loss in the draft tube was highest under high-flow conditions. In guide-vane-free turbines, the impeller’s high turbulent entropy generation rate was attributed to vortices and backflow caused by significant velocity gradients. For guide-vane-equipped turbines, high turbulent entropy generation rates arose from rotor–stator interactions and flow separation at blade inlets. Under high-flow-rate conditions, the entropy generation loss in the draft tube was significantly larger than that in other flow components, primarily due to vortices generated by excessive velocity circulation at the impeller outlet near the upstream draft tube flow passages, leading to high turbulent entropy generation rates.

Exergy analysis evaluates the efficiency of system components by quantifying the rate of entropy generation. In general, the exergy destruction rate or irreversibility rate was directly obtained through the exergy balance equation. However, this method cannot determine the origin of the component’s entropy generation rate, which is a very important factor in system design and improvement. In this study, a thorough energy, exergy, and thermoeconomic analysis of a proton-exchange membrane fuel cell (PEMFC) was performed, providing the heat transfer rate, entropy generation rate, and cost loss rate of each component. The irreversibility rate of each component was obtained by the Gouy–Stodola theorem. Detailed and extensive exergy and thermoeconomic analyses of the PEMFC system determined that water cooling units experience the greatest heat transfer among the components in the studied PEMFC system, resulting in the greatest irreversibility and, thus, the greatest monetary flow loss.

The exothermic reactor for ammonia synthesis is a primary device determining the performance of the energy storage system. The Braun-type ammonia synthesis reactor is used as the exothermic reactor to improve the heat release rate. Due to the entirely different usage scenarios and design objectives, its parameters need to be redesigned and optimized. Based on finite-time thermodynamics, a one-dimensional model is established to analyze the effects of inlet gas molar flow rate, hydrogen–nitrogen ratio, reactor length and inlet temperature on the total entropy generation rate and the total exothermic rate of the reactor. It’s found that the total exothermic rate mainly depends on the inlet molar flow rate. Furthermore, considering the minimum total entropy generation rate and maximum total exothermic rate, the NSGA-II algorithm is applied to optimize seven reactor parameters including the inlet molar flow rate, lengths and temperatures of the three reactors. Lastly, the optimized reactor is obtained from the Pareto front using three fuzzy decision methods and deviation index. Compared with the reference reactor, the total exothermic rate of the optimized reactor is improved by 12.6% while the total entropy generation rate is reduced by 3.4%. The results in this paper can provide some guidance for the optimal design and application of exothermic reactors in practical engineering.

Abstract This study focuses on fractional-order derivatives for the unsteady flow of magnetohydrodynamic (MHD) methanol-iron oxide (CH3OH-Fe3O4) nanofluid over a permeable vertical plate. The utilization of fractional-order derivatives provides a mathematical representation of the flow model. The concluding model, consisting of a system of fractional-order transient partial differential equations, has been solved using the finite difference method, and graphical illustrations demonstrate the effects of key parameters on the flow field. Velocity and temperature profiles provide insights into nanofluid behavior. Additionally, essential quantities such as skin friction coefficient, Nusselt number, Bejan number, and entropy generation rate have been depicted graphically. Comparison with previous studies authenticates the accuracy of the anticipated model, contributing to new intuitions into MHD nanofluid flow over a permeable vertical plate. It is worth noting that the current model, incorporating fractional-order derivatives, contributes to understanding the physical characteristics of MHD CH3OH-Fe3O4 nanofluid flow over a permeable vertical plate, research that has not been extensively explored before. Graphical Abstract Graphical Abstract