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18 pages, 1001 KB

Open AccessArticle

Correlation-Based Single-Phase Heat Transfer Assessment of Binary HFE/Ethyl Acetate Mixtures in Minichannels

by Artur Piasecki and Magdalena Piasecka

Energies 2026, 19(10), 2291; https://doi.org/10.3390/en19102291 - 9 May 2026

Viewed by 176

Abstract

This work presents a correlation-based framework for comparative assessment of single-phase forced convection of binary hydrofluoroether/ethyl acetate (HFE/EA) mixtures in rectangular minichannels. Density, kinematic viscosity, and thermal conductivity were measured at 293.1, 313.1, and 328.1 K for selected compositions of HFE-7100/EA, HFE-7300/EA, and [...] Read more.

This work presents a correlation-based framework for comparative assessment of single-phase forced convection of binary hydrofluoroether/ethyl acetate (HFE/EA) mixtures in rectangular minichannels. Density, kinematic viscosity, and thermal conductivity were measured at 293.1, 313.1, and 328.1 K for selected compositions of HFE-7100/EA, HFE-7300/EA, and HFE-73DE/EA. Because several DSC-derived mixture-specific heat values were not sufficiently reliable for direct use, the mixture-specific heat capacity was estimated from literature-supported pure-component values using an ideal-mixture, mass-fraction-weighted approximation and used only for evaluation of the Prandtl number. Heat transfer was then assessed using the Sieder–Tate correlation for laminar thermally developing flow in two representative minichannel geometries. The highest predicted values for the HFE-7100/EA and HFE-7300/EA families were obtained for the most EA-rich retained compositions, whereas in the retained HFE-73DE/EA subset, the 50/50 mixture performed best because of its higher thermal conductivity. Validation against an experimental dataset for pure HFE-7100 in the short module showed systematic overprediction, with a mean relative difference of −13.44% and a MAPE of 15.6%. The calculated values should, therefore, be used for relative comparison rather than treated as unbiased absolute predictions. Full article

(This article belongs to the Special Issue Heat Transfer Analysis: Recent Challenges and Applications—2nd Edition)

19 pages, 7922 KB

Open AccessArticle

Comparison of Analytical and Numerical Methods for Predicting the Shell-Side Heat Transfer Coefficient in Heat Exchanger with Segmental Baffles

by Janusz T. Cieśliński, Jacek Barański, Kamil Stasiak, Krzysztof Tesch and Paweł Dąbrowski

Energies 2026, 19(9), 2114; https://doi.org/10.3390/en19092114 - 28 Apr 2026

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Abstract

This study reports the calculated values results of the shell-side heat transfer coefficient for a shell-and-tube heat exchanger with an inner shell diameter of 200 mm and a length of 518 mm, containing 85 tubes arranged in a staggered layout. Shell-side cross-flow was [...] Read more.

This study reports the calculated values results of the shell-side heat transfer coefficient for a shell-and-tube heat exchanger with an inner shell diameter of 200 mm and a length of 518 mm, containing 85 tubes arranged in a staggered layout. Shell-side cross-flow was generated by nine standard segmental baffles with a 25% baffle cut and a baffle pitch of 48 mm. In particular, the effect of 13 combinations of shell-to-baffle and baffle-to-tube gaps on the heat transfer coefficient was investigated. Moreover, the influence of sealing strips and tube bundle diameter on the heat transfer coefficient was also examined. The calculations were carried out using three different approaches, namely the Gaddis-Gnielinski method, the extended Bell-Delaware method, and Aspen EDR code. Numerical simulations for an idealized heat exchanger were also conducted using Ansys Fluent and OpenFOAM. As far as the authors are aware, this is the first study to compare two computational methods widely regarded as reference approaches for shell-and-tube heat exchangers, namely the Bell-Delaware and the Gaddis-Gnielinski approaches. The results obtained using the Aspen EDR code, a widely recognized software tool for modeling and design of heat exchangers, were evaluated against the forecast of the Bell-Delaware and Gaddis-Gnielinski approaches. Full article

(This article belongs to the Special Issue Heat Transfer Analysis: Recent Challenges and Applications—2nd Edition)

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27 pages, 6134 KB

Open AccessArticle

SHAP-Based Insights into Environmental and Economic Performance of a Shower Heat Exchanger Under Unbalanced Flow Conditions: A Feasibility Study

by Sabina Kordana-Obuch and Mariusz Starzec

Energies 2026, 19(8), 1845; https://doi.org/10.3390/en19081845 - 9 Apr 2026

Viewed by 461

Abstract

Heat recovery from greywater is one solution for improving the energy efficiency of buildings and reducing greenhouse gas emissions. Particular attention is paid to systems utilizing heat from shower water, which, due to its high temperature and regularity, represents a promising energy source. [...] Read more.

Heat recovery from greywater is one solution for improving the energy efficiency of buildings and reducing greenhouse gas emissions. Particular attention is paid to systems utilizing heat from shower water, which, due to its high temperature and regularity, represents a promising energy source. However, the interplay of parameters determining the financial and environmental effectiveness of such a solution has not yet been fully explored. Therefore, the aim of this paper was to identify key variables influencing the feasibility of using a shower heat exchanger operating under unbalanced flow conditions and to assess the consistency between financial and environmental effects. The analyzed net present values ranged from −€1381 to €52,168. Greenhouse gas emission reduction values ranged between 61 kgCO₂e and 37,207 kgCO₂e. The analysis was conducted using predictive modeling and the SHAP (SHapley Additive exPlanations) method, which allows for the interpretation of the impact of individual variables on the forecasted net present value and potential greenhouse gas emission reduction. A global analysis was carried out to determine the relative importance of variables, as well as a local analysis for selected cases. The results showed that operational variables related to shower use, particularly shower length and mixed water flow rate, significantly influenced the prediction results of both models. In the case of emission reduction, greenhouse gas emission intensity and its change over time also had a significant impact, whilst the financial effects were determined by the energy price from the perspective of the subsequent years of the system’s operation. Full article

(This article belongs to the Special Issue Heat Transfer Analysis: Recent Challenges and Applications—2nd Edition)

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20 pages, 5719 KB

Open AccessArticle

Heat Transfer and Thermo-Mechanical Analysis of Plastic-Strain Evolution in Laser-Welded Thin-Walled Laminated Cooling Plates with Non-Uniform Stiffness

by Chengkun Li, Yujia Cai, Han Wang, Zhihang Zhang, Fang Han, Xiaoqing Zhu, Chengcheng Wang and Zhibo Dong

Energies 2026, 19(6), 1536; https://doi.org/10.3390/en19061536 - 20 Mar 2026

Viewed by 321

Abstract

Thin-walled laminated cooling plates integrate internal channels and pin-fin cores, producing reduced and spatially non-uniform stiffness that changes welding restraint and distortion. This study investigates stiffness-controlled plastic-strain evolution in laser butt welding of GH3230 laminated plates, with geometrically identical solid plates as reference. [...] Read more.

Thin-walled laminated cooling plates integrate internal channels and pin-fin cores, producing reduced and spatially non-uniform stiffness that changes welding restraint and distortion. This study investigates stiffness-controlled plastic-strain evolution in laser butt welding of GH3230 laminated plates, with geometrically identical solid plates as reference. A coupled heat-transfer and thermo-mechanical finite element model was developed in MSC Marc using a composite Gaussian surface–volumetric moving heat source and temperature-dependent properties. The thermal solution was validated against near-weld thermal cycles and fusion geometry; mechanical predictions were evaluated by CMM distortion and residual-stress measurements. Both structures show comparable residual-stress magnitudes and spatial trends, indicating that residual stress is governed mainly by the local weld thermal gradient. In contrast, the laminated plate exhibits larger angular/bending distortion. Simulations show that, although the plastic-strain pattern is similar, the laminated plate develops higher peak plastic strain confined to a narrower band near the weld, with the transverse plastic strain dominating. Plastic strain–temperature paths reveal continued transverse plastic-strain accumulation during cooling with limited recovery, consistent with restraint redistribution induced by stiffness non-uniformity. An equivalent restraint–stiffness spring model explains this “narrower-but-stronger” plastic zone and links stiffness to yielding and residual plastic-strain magnitude, supporting distortion prediction and stiffness-informed control of welded laminated cooling plates. Full article

(This article belongs to the Special Issue Heat Transfer Analysis: Recent Challenges and Applications—2nd Edition)

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22 pages, 2759 KB

Open AccessArticle

Evaluation of the Intensity of Heat and Mass Transfer Processes in Cavitation Environments

by Anatoliy Pavlenko

Energies 2026, 19(5), 1120; https://doi.org/10.3390/en19051120 - 24 Feb 2026

Viewed by 537

Abstract

This study investigates the impact of cavitation phenomena on heat and mass transfer in working fluids. To quantify the intensity of transport processes within cavitation bubble clusters, a numerical analysis of bubble dynamics was carried out with explicit consideration of fluid compressibility. The [...] Read more.

This study investigates the impact of cavitation phenomena on heat and mass transfer in working fluids. To quantify the intensity of transport processes within cavitation bubble clusters, a numerical analysis of bubble dynamics was carried out with explicit consideration of fluid compressibility. The results demonstrate that physicochemical transformations induced by cavitation are governed not only by shock waves and pressure pulses generated during bubble collapse, but also by extreme thermal effects arising within collapsing cavitation clouds. Under conditions of maximum bubble compression, the vapor inside the bubbles and the surrounding liquid may undergo a transition to a supercritical state. The developed model elucidates the structure of microflows in the interbubble region and provides a quantitative evaluation of local velocity, pressure, and heat flux fields. The systematic assessment of cavitation-enhanced heat and mass transfer offers valuable insights for the advancement of conventional heat and mass transfer technologies and the design of innovative devices in mechanical and chemical engineering. Full article

(This article belongs to the Special Issue Heat Transfer Analysis: Recent Challenges and Applications—2nd Edition)

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31 pages, 12934 KB

Open AccessArticle

Numerical Analysis of the Flow Downstream of the Exhaust Nozzle of a Miniature Turbojet Engine During Co-Combustion of Kerosene and Hydrogen

by Łukasz Brodzik, Bartosz Ciupek, Grigore Cican, Łukasz Semkło and Dominik Schroeder

Energies 2026, 19(4), 938; https://doi.org/10.3390/en19040938 - 11 Feb 2026

Viewed by 435

Abstract

Research related to the use of hydrogen is crucial because it can be a significant factor in reducing exhaust emissions into the environment. This work represents the second stage of research related to the analysis of exhaust gases from a miniature GTM 400 [...] Read more.

Research related to the use of hydrogen is crucial because it can be a significant factor in reducing exhaust emissions into the environment. This work represents the second stage of research related to the analysis of exhaust gases from a miniature GTM 400 MOD turbojet engine. Based on the parameters obtained in the experiment, a numerical study of the flow downstream of the exhaust nozzle was performed in ANSYS software (version R1, 2025). The main goal of the calculations was to obtain the temperature distribution and compare the values at checkpoints where actual measurements were taken. The study was conducted in two stages. In the first stage, the engine operated conventionally, burning kerosene. In the second stage, co-combustion of kerosene and hydrogen occurred in the engine. The numerical analysis enabled the visualization of the flow phenomenon for these stages within the considered rotational speeds. The analysis examined flow in domains where the gap was included and excluded. This gap was created by the different diameters of the container opening and the engine nozzle outlet. The study showed that ignoring the gap allows for temperatures closer to the experimental values. Results deemed satisfactory were less likely to be found in vortex areas, but more likely in areas closer to the container walls and the engine exhaust stream itself. The results of the conducted tests showed that the Root Mean Square Error RMSE was within the range of 9.5–22.8% relative to the average temperature values obtained from experimental measurements. The highest turbulence intensity occurred for hydrogen co-combustion at a higher rotational speed, reaching 284% for Variant 2 and 300% for Variant 1. The largest standard deviation for both fuel types at a distance of 0.083 m from the container wall was 68.5 K for variant 2 and 76 K for variant 1. At a distance of 0.166 m from the container wall, the deviation was 76 K for variant 2 and 83.8 K for variant 1. Full article

(This article belongs to the Special Issue Heat Transfer Analysis: Recent Challenges and Applications—2nd Edition)

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20 pages, 2381 KB

Open AccessArticle

Experimental Verification of a Method for Improving the Efficiency of an Evaporative Tower Using IEC

by Bartosz Jagieła and Magdalena Jaremkiewicz

Energies 2026, 19(2), 554; https://doi.org/10.3390/en19020554 - 22 Jan 2026

Viewed by 344

Abstract

This paper analyses the impact of inlet air precooling on the efficiency and electricity consumption of an open-type evaporative cooling tower. An Indirect Evaporative Cooler (IEC) was used to reduce the inlet air temperature, and its influence on system efficiency was experimentally evaluated. [...] Read more.

This paper analyses the impact of inlet air precooling on the efficiency and electricity consumption of an open-type evaporative cooling tower. An Indirect Evaporative Cooler (IEC) was used to reduce the inlet air temperature, and its influence on system efficiency was experimentally evaluated. Although IEC units and the Maisotsenko cycle are increasingly discussed in the literature, no research to date has considered their effect on evaporative tower efficiency under actual operating conditions. For this purpose, a test stand was constructed comprising an open cooling tower and an IEC unit. The system operated automatically for 2952 h, corresponding to a full cooling season in Poland. Two sets of data collected during cooling tower operation were analysed: without precooling (Stage I) and with precooling using IEC (Stage II). Measurements were recorded every 10 s. Additionally, tests were conducted at elevated thermal loads and peak ambient temperatures. The comparative analysis concluded that air precooling using IEC reduced the cooling tower’s electricity consumption by approximately 15% and increased the SCOP of the cooling tower by 30%. This demonstrates the significant potential of the proposed solution. Full article

(This article belongs to the Special Issue Heat Transfer Analysis: Recent Challenges and Applications—2nd Edition)

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14 pages, 2827 KB

Open AccessArticle

Analysis of Heat Transfer Characteristics in a Latent Heat Storage Module Using Circular-Finned Tubes

by Ji-Woon Ko, Tae Hwan Song, Jong-Hoon Lee, Jong Hyeon Peck and Seung Jin Oh

Energies 2025, 18(23), 6325; https://doi.org/10.3390/en18236325 - 1 Dec 2025

Cited by 1 | Viewed by 749

Abstract

Latent heat thermal energy storage (LHTES) using inorganic salt hydrates is a promising technology for buffering renewable energy fluctuations; however, phase-dependent heat transfer remains insufficiently understood for design optimization. In this study, a shell-and-tube storage module with a circular-finned tube was constructed and [...] Read more.

Latent heat thermal energy storage (LHTES) using inorganic salt hydrates is a promising technology for buffering renewable energy fluctuations; however, phase-dependent heat transfer remains insufficiently understood for design optimization. In this study, a shell-and-tube storage module with a circular-finned tube was constructed and filled with 13.17 kg of barium hydroxide octahydrate (BHO). Discharge tests were conducted with heat transfer fluid (HTF) inlet temperatures ranging from 20 °C to 50 °C and flow rates of 10–25 L/min, while charging was performed at 90 °C. The overall heat transfer coefficient (

U_{o}

) was derived using the logarithmic mean temperature difference method, the inside coefficient (h_i) was calculated by the Petukhov correlation, and the outside coefficient (h_o) was obtained via thermal-resistance network. Results show that the average discharge energy was approximately 1.027 kWh (except 0.859 kWh at 50 °C inlet), with a mean utilization efficiency of 79.25%. The

U_{o}

was consistently highest in the liquid phase, followed by the latent and solid phases, with ranges of 0.257–0.863, 0.025–0.072, and 0.015–0.044 kW/m²·°C, respectively. Sensitivity analysis revealed that the HTF flow rate strongly influenced U_o across all phases, whereas inlet temperature played only a minor role. The outside coefficient

h_{o}

was 0.033–0.162 kW/m²·°C in the latent regime and 0.018–0.064 kW/m²·°C in the solid regime, with a notable peak around Reynolds number 1.3 × 10⁴ in the latent phase. These findings provide detailed phase-resolved

U_{o}

and

h_{o}

data for inorganic salt hydrate storage and highlight design insights such as the diminishing returns of flow rate increase beyond a threshold, offering valuable guidelines for sizing and operation of LHTES in Power-to-Heat applications. Full article

(This article belongs to the Special Issue Heat Transfer Analysis: Recent Challenges and Applications—2nd Edition)

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30 pages, 16086 KB

Open AccessFeature PaperArticle

Conjugate Study on Thermal–Hydraulic Performance of Topology-Optimized Lattice-Filled Cooling Channel for Thermal Management of Solid-Oxide Fuel Cells

by Kirttayoth Yeranee, Yuli Cheng and Yu Rao

Energies 2025, 18(22), 6001; https://doi.org/10.3390/en18226001 - 15 Nov 2025

Cited by 2 | Viewed by 1057

Abstract

Integrated additional cooling channels offer precise thermal management for solid-oxide fuel cells (SOFCs), mitigating temperature gradients. This research studies the thermal–hydraulic performance of cooling channels integrated between SOFC interconnectors, including a Diamond-type triply periodic minimal surface (TPMS), a conventional topology-optimized structure, and a [...] Read more.

Integrated additional cooling channels offer precise thermal management for solid-oxide fuel cells (SOFCs), mitigating temperature gradients. This research studies the thermal–hydraulic performance of cooling channels integrated between SOFC interconnectors, including a Diamond-type triply periodic minimal surface (TPMS), a conventional topology-optimized structure, and a topology-optimized lattice-filled structure. A conjugate heat transfer analysis is employed to investigate the influences of flow rate within the range of Reynolds numbers from 300 to 5000, and the effects of coolant type, including air and liquid metals, as well as the impacts of structural material. The results demonstrate that the topology-optimized lattice-filled structure, generating high turbulence mixing, achieves superior temperature uniformity, especially at high flow rates, despite having higher thermal resistance and pressure loss than the conventional topology-optimized design. The coolant types show the largest influence on thermal–hydraulic performance, and the use of liquid gallium in the conventional optimized design obtains the best temperature uniformity, yielding differences between the maximum and minimum temperatures of less than 5 K. Moreover, the higher-thermal-conductivity material improves temperature uniformity, even at low flow rates. Overall, the optimized-baffle designs in the conventional topology-optimized model, utilizing high-conductivity coolant and structural materials, could be the most suitable for thermal management of the SOFC. Full article

(This article belongs to the Special Issue Heat Transfer Analysis: Recent Challenges and Applications—2nd Edition)

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Review

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54 pages, 3405 KB

Open AccessReview

Pathways for Greenhouse Thermal Management’s Contribution to Net-Zero Food Production

by Samson Sogbaike, Celestina Ezenwajiaku, Amir Badiee, Chris Bingham and Aliyu M. Aliyu

Energies 2026, 19(8), 1975; https://doi.org/10.3390/en19081975 - 19 Apr 2026

Viewed by 426

Abstract

Decarbonising greenhouse food production requires improvements in thermal management, energy efficiency, and system integration. Greenhouse energy demand is shaped by coupled heat and mass transfer processes, particularly envelope performance, ventilation, and latent heat associated with humidity control. This article synthesises recent advances in [...] Read more.

Decarbonising greenhouse food production requires improvements in thermal management, energy efficiency, and system integration. Greenhouse energy demand is shaped by coupled heat and mass transfer processes, particularly envelope performance, ventilation, and latent heat associated with humidity control. This article synthesises recent advances in greenhouse microclimate control with emphasis on heat transfer, low-carbon heating and cooling, thermal storage, renewable and waste heat integration, and advanced modelling and control approaches. The review shows that humidity control and latent load management are primary drivers of winter energy use, as moisture removal through ventilation and dehumidification directly increases the sensible heating required to maintain indoor temperature setpoints. When assessed using realistic psychrometric relationships, ventilation and dehumidification can dominate peak heating demand and seasonal consumption. The performance of heat pumps, storage systems, semi-closed greenhouse concepts, and renewable heat pathways depends on how thermal loads are defined, how system boundaries are set, and how technologies are integrated in operation. Digital twins, predictive control, and hybrid physics-data models are increasingly used to manage variability in weather, energy prices, and infrastructure constraints. Greenhouse decarbonisation cannot be treated as a simple substitution of energy sources. System performance depends on coordinated design and operation, including heat recovery, moisture removal, and integration of supply technologies. Semi-closed and heat recovery-based configurations can reduce the ventilation–heating penalty and lower primary energy demand compared with vent-to-dry approaches. Long-term market projections suggest that the commercial greenhouse sector could expand substantially by 2050 under plausible growth scenarios, reflecting increased capital investment rather than a proportional rise in global food output. Net-zero greenhouse production is achievable through combined improvements in thermal management, electrification, and renewable energy integration. However, large-scale deployment depends on consistent modelling assumptions, credible economic assessment, and alignment with heat and CO₂ supply infrastructure. The transition is therefore shaped by system integration and planning as much as by individual technologies. Full article

(This article belongs to the Special Issue Heat Transfer Analysis: Recent Challenges and Applications—2nd Edition)

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19 pages, 1091 KB

Open AccessReview

Applications of Methods of Solving Inverse Heat Conduction Problems for Energy-Intensive Industrial Processes and Energy Conversion—Current State of the Art and Recent Challenges

by Magda Joachimiak and Damian Joachimiak

Energies 2026, 19(5), 1291; https://doi.org/10.3390/en19051291 - 4 Mar 2026

Viewed by 820

Abstract

This paper presents methods and applications of inverse heat conduction problems (IHCPs) that are ill-posed in the Hadamard sense. The IHCP solution allows for the determination of boundary conditions in the form of heat flux or temperature in places where measurement is impossible [...] Read more.

This paper presents methods and applications of inverse heat conduction problems (IHCPs) that are ill-posed in the Hadamard sense. The IHCP solution allows for the determination of boundary conditions in the form of heat flux or temperature in places where measurement is impossible or difficult to perform. The applications of IHCP solutions to energy-intensive industrial processes, such as heat treatment and thermochemical treatment, are described. Examples are given of determining boundary conditions on the inner surface of the wall of a power boiler and piston machine, as well as on the surface of a gas turbine blade. It is noted that the application of IHCP solutions to the above-mentioned issues often requires simplification of the computational model, in particular, the method of stabilising the inverse problem (IP). For this purpose, quasi-regularisation of IP and machine learning are currently used. Methods with stabilising properties and neural networks were identified as a challenging and interesting direction for the development of IHCP solutions. Full article

(This article belongs to the Special Issue Heat Transfer Analysis: Recent Challenges and Applications—2nd Edition)

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Other

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33 pages, 810 KB

Open AccessPerspective

The Port-Hamiltonian Formulation of Thermodynamics—A New Perspective

by Janusz Badur and Piotr Józef Ziółkowski

Energies 2026, 19(2), 324; https://doi.org/10.3390/en19020324 - 8 Jan 2026

Viewed by 864

Abstract

This paper proposes a change in the traditional epistemological paradigm and a look at classical thermodynamics from the point of view of control theory, with the aim of discovering energy state variables. The paper proposes a transition from “causality” to “purposefulness” in nature, [...] Read more.

This paper proposes a change in the traditional epistemological paradigm and a look at classical thermodynamics from the point of view of control theory, with the aim of discovering energy state variables. The paper proposes a transition from “causality” to “purposefulness” in nature, which is called port-Hamiltonian thermodynamics. It is unclear whether classical thermodynamics can be incorporated into the formalism of port-Hamiltonian field theory, and it is likely that thermodynamics will need to be expanded or even completely reformulated. The main goal is to satisfy the First and Second Laws of Thermodynamics a priori. Full article

(This article belongs to the Special Issue Heat Transfer Analysis: Recent Challenges and Applications—2nd Edition)

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