Introduction

Energy recovery systems, such as heat sinks, heat exchangers, and condensers, are very important in improving the overall process efficiency of different thermal energy systems. Among these devices, many operate under low to moderate Reynolds numbers, where thermal performance becomes limited due to weak mixing, boundary-layer growth, and reduction of temperature gradients. Several conventional performance enhancement techniques are incorporated, such as active mixing, surface treatments, inserts, etc. However, these strategies increase system complexity, pressure drop, or energy consumption, thereby offsetting the benefits.

In this context, simple geometric design innovations prove crucial in enhancing heat transfer using passive modes [1]. Helical geometries can be employed to improve fluid mixing and heat transfer owing to their curvature-driven secondary flow features (Dean vortices) [2]. Despite their simplicity and inherent compactness, certain aspects are less-explored, particularly how specific geometric modulations can be systematically mapped to different dominant thermal resistances across applications. Furthermore, these geometries offer potential as transferable, general-purpose design guidelines rather than case-specific enhancements, for various energy systems. The present work synthesizes and reinterprets isolated helical-geometry studies applied to three representative applications, a (i) heat sink, (ii) cross-flow heat exchanger, and (iii) conical coil condenser, to establish a unified design framework based on the spatial tuning of s curvature-induced feature. The aim of this work is to demonstrate a common passive geometric principle that can be achieved by adjusting geometric parameters, and leveraged across different energy systems to achieve scalable and mechanism-informed performance enhancement.

Methods

This study is based on validated CFD simulations, which are carried out for three distinct thermal systems employing helical geometries. In all cases, steady-state, laminar flow conditions are considered, which are representative of compact thermal energy systems. Working fluids and boundary conditions were selected to demonstrate application-relevant operating conditions relevant for each application. For heat sink configuration, helical fins were employed to enhance coolant-side heat removal, and relate flow intensification with thermal performance [3]. In a cross-flow heat exchanger, interaction between internal helical flow and external cross-flow was examined to evaluate heat transfer rate and efficiency [4]. For the condenser, both simple helical and conical helical coils of equal tube length were analysed to investigate the influence of cone angle on secondary flow development and heat extraction along the flow path. In all cases, the analysis mainly focuses on flow fields, temperature fields, and non-dimensional heat transfer metrics. Improvements in heat transfer were found to primarily be the effect of curvature-induced secondary flow intensification.

Results

All the systems showed a common underlying enhancement mechanism, governed by helical geometry, even though there are differences in applications. Centrifugal forces generated due to curvature lead to the formation of secondary flow structures, which result in the enhanced transverse mixing and disruption of thermal boundary layers. In the heat sink configuration, swirl-induced natural convection results in reduced surface temperature non-uniformity and enhanced fin efficiency by 10-15%. The cross-flow heat exchanger demonstrates improved Nu (1.4 to 2.5 times) and heat exchanger efficiency up to 90% due to flow intensification and tortuosity. In the condenser system, geometric modification through conical design led to progressive intensification of secondary flow, which compensates for decreasing temperature gradients, resulting in an overall heat extraction enhancement of ~14%. Cross-comparison of these applications shows that, although the dominant thermal limitations are different, as poor mixing in heat sinks, boundary-layer growth in heat exchangers, and temperature gradient decay in condensers, the helical design principle consistently mitigates these limitations through a common passive mechanism [5], and highlights the versatility of helical-geometry-based enhancements.

Conclusions

Implementation of helical configurations serve as an effective and broadly applicable design strategy for enhancing thermal energy recovery. By intensifying secondary flow, simple helical geometries are shown to improve heat transfer, in a passive manner, without increasing complexity and energy consumption. This analysis, covering a heat sink, cross-flow heat exchanger, and condenser, emphasizes the potential of geometry-driven design innovations in a unified, cross-application framework. The findings provide generalized and transferable design insights that can be used for the development of next-generation passive energy devices for compact industrial and environmental applications.

References

[1] M.A. Rahman, Review on heat transfer augmentation in helically coiled tube heat exchanger, International Journal of Thermofluids 24 (2024). https://doi.org/10.1016/j.ijft.2024.100937.

[2] J.O.D.B. Lira, H.G. Riella, N. Padoin, C. Soares, Fluid dynamics and mass transfer in curved reactors: A CFD study on Dean flow effects, J. Environ. Chem. Eng. 10 (2022). https://doi.org/10.1016/j.jece.2022.108304.

[3] V.K. Jha, S.K. Bhaumik, Enhanced heat dissipation in helically finned heat sink through swirl effects in free convection, Int. J. Heat Mass Transf. 138 (2019) 889–902. https://doi.org/10.1016/j.ijheatmasstransfer.2019.04.099.

[4] V.K. Jha, S.K. Bhaumik, Enhanced cooling in compact helical tube cross-flow heat exchanger through higher area density and flow tortuosity, Int. J. Heat Mass Transf. 150 (2020) 119270. https://doi.org/10.1016/j.ijheatmasstransfer.2019.119270.

[5] V.K. Jha, K. Banerjee, S.K. Bhaumik, Enhanced thermal stability of novel helical-finned jacketed stirred tank heater, Appl. Therm. Eng. 184 (2021). https://doi.org/10.1016/j.applthermaleng.2020.116250.

Efficient thermal management has become increasingly important as modern electronic devices continue to shrink in size while operating at higher power densities, leading to elevated heat fluxes and localized overheating. Polymer composites offer an attractive platform for thermal management due to their low density, processability, and cost-effectiveness; however, their inherently low thermal conductivity limits their performance. Incorporation of graphene- and graphite-based fillers has emerged as a promising strategy to enhance heat dissipation; however, achieving high thermal conductivity in polymer composites remains challenging due to interfacial thermal resistance, filler agglomeration, and degradation of graphene’s lattice during chemical modification. Consequently, optimizing both polymer–filler interfacial interactions and the preservation of intrinsic phonon transport pathways is essential. In this work, the influence of graphene functionalization strategies and synthesis routes on thermal transport was systematically investigated in polyetherimide (PEI) composites. Several graphene-based fillers, including pristine graphene nanoplatelets (GnPs) and thermally expanded graphite (EG), were examined to elucidate how chemical modification and structural integrity govern heat conduction in polymer matrices. Edge-oxidized graphene (EGO) was prepared using a controlled edge-selective oxidation approach that preserved the sp²-bonded basal plane while introducing oxygen-containing functional groups primarily at the sheet edges. This selective functionalization enhanced polymer–filler interfacial bonding without significantly disrupting phonon transport, resulting in an 18% increase in thermal conductivity at 10 wt% filler loading compared to pristine GnP/PEI composites. In contrast, basal-plane-oxidized graphene (BGO), produced using the Hummers method, introduced oxygen functionalities directly onto the basal plane, leading to increased defect density and lattice distortion. These structural disruptions significantly impeded phonon propagation, causing a 57% reduction in thermal conductivity relative to pristine graphene-filled composites. Raman mapping, X-ray photoelectron spectroscopy (XPS), and Fourier transform infrared spectroscopy (FTIR) confirmed preferential edge functionalization in EGO and extensive basal-plane disorder in BGO, underscoring the importance of oxidation site control. To further enhance long-range phonon transport, EG was incorporated into PEI via a solvent-casting technique. EG, obtained by thermal expansion of graphite intercalation compounds, forms a three-dimensional interconnected network of continuous graphene sheets with minimal interlayer contact resistance. Preservation of the worm-like porous EG structure during solvent casting enabled the formation of an interpenetrating polymer–graphite network conducive to efficient phonon transport. As a result, thermal conductivity increased nearly linearly with EG loading, reaching 7.3 W/(mK) at 10 wt%, a substantial enhancement compared to pristine PEI (≈0.23 W/(mK)). The effect of intercalation chemistry on EG microstructure and performance was further evaluated using two expansion routes: H₂SO₄/H₂O₂ and H₂SO₄/NaClO₃. EG synthesized via the H₂O₂ route exhibited superior structural integrity, predominantly edge-localized oxidation, and enhanced graphitic continuity, resulting in thermal conductivities as high as 9.5 W/(mK) at 10 wt%. In contrast, EG produced using NaClO₃ showed greater basal-plane damage and reduced network continuity, yielding a lower thermal conductivity of 5.3 W/(mK). Raman ID/IG ratios, XPS oxygen speciation, and X-ray diffraction analysis corroborated these structural differences. Overall, this study demonstrates that controlling oxidation location, minimizing basal-plane damage, and preserving long-range graphitic networks are critical for achieving high thermal conductivity in polymer–graphene composites, providing key design principles for scalable thermal interface materials and advanced heat-spreading technologies.

The global automotive and logistics sectors currently face an escalating environmental crisis driven by the prolific discharge of particulate matter and greenhouse gases from conventional diesel-powered internal combustion engines. While the industry has pivoted toward renewable alternatives such as biodiesel and bioethanol, these oxygenated fuels often present inherent limitations regarding oxidative stability, lower energy density, and phase separation when utilized in ternary blends. To address these physicochemical deficiencies, this study investigates the synthesis and application of a novel ternary blend consisting of conventional diesel, biodiesel, and bioethanol (70:20:10) (DBE), augmented with coconut shell-derived nanobiochar (CNS) as a high-surface-area heterogeneous catalyst. The research specifically explores the impact of varying CNS nanobiochar concentrations—0, 20, 30, and 40 ppm—on the holistic fuel profile to determine an optimal formulation for modern compression ignition systems. The experimental methodology involved a rigorous series of laboratory analyses conducted in strict accordance with ASTM standards, including ASTM D445 for kinematic viscosity and ASTM D93 for flash point. Critical physicochemical parameters, including density, fire point, corrosiveness, and calorific value, were evaluated using specialized analytical instrumentation. The results revealed that while density and corrosiveness remained relatively stable across the various dosages, viscosity and thermal stability metrics exhibited significant sensitivity to nanobiochar loading. Notably, the 20 ppm CNS concentration emerged as the most effective variant, demonstrating the lowest kinematic viscosity at 5.6 mm2/s and superior safety characteristics with a flash point of 58°C, alongside a calorific value of 29.18 MJ/kg. In engine performance evaluations, the 20 ppm DBE-CNS blend significantly enhanced Brake Thermal Efficiency (BTE) and optimized Specific Fuel Consumption (SFC) compared to the unblended diesel baseline. The catalytic effect of the nanobiochar facilitated a micro-explosion phenomenon during combustion, leading to cleaner burning and a measurable reduction in hazardous pollutants, including carbon monoxide (CO), nitrogen oxides (NOx), and carbon dioxide (CO2). The study concludes that micro-dosages of coconut shell nanobiochar serve as a viable mechanism for upgrading renewable fuel blends, though further research is recommended to explore long-term effects on fuel injector durability and tribological wear.

Introduction

The rapid growth of electricity demand in Indonesia has led to the extensive operation of gas engine power plants (PLTMG) due to their flexibility and relatively high efficiency. Nevertheless, a significant fraction of the fuel energy, typically around 25–30%, is rejected to the environment as exhaust gas waste heat. The exhaust gas temperature of gas engines commonly ranges from 350 to 450°C, indicating a considerable potential for waste heat recovery (WHR). Organic Rankine Cycle (ORC) technology has been widely recognized as an effective solution for converting low- to medium-temperature waste heat into useful electrical power.

Previous studies have demonstrated the feasibility of ORC integration with internal combustion engines. However, most investigations focus on generic operating conditions or rely on simplified thermodynamic models. Moreover, studies that simultaneously integrate energy, exergy, and environmental (3E) analyses using real operational data remain limited, particularly for gas engine power plants. Therefore, this study aims to evaluate the energetic, exergetic, and environmental performance of an ORC system integrated with an existing PLTMG using a comprehensive thermodynamic simulation framework.

Materials and Methods

A thermodynamic model of the ORC system was developed using Aspen HYSYS, which enables accurate representation of multiphase flows and heat exchanger behavior. Real operational data from a gas engine power plant were used as boundary conditions, including exhaust gas temperature and mass flow rate. The ORC configuration consists of an evaporator, turbine, condenser, and pump operating under steady-state conditions.

Six working fluids were investigated: R600 (butane), R600a (isobutane), R601 (pentane), R601a (isopentane), R134a, and R744 (CO₂). All simulations were conducted at a constant working fluid mass flow rate of 10 kg/s. The system performance was evaluated using energy and exergy analyses based on the First and Second Laws of Thermodynamics. Environmental performance was assessed by estimating fuel savings and the corresponding reduction in CO₂ emissions resulting from the additional power generated by the ORC system.

Results and Discussion

The simulation results indicate that the selection of working fluid has a pronounced impact on ORC performance. The turbine power output varies significantly among the investigated fluids, ranging from 139.5 kW for R744 (CO₂) to 1331 kW for R601 (pentane). Hydrocarbon-based working fluids generally exhibit superior performance due to better thermodynamic matching with the exhaust gas heat source.

The highest thermal efficiency of the ORC system is achieved using R601, reaching 21.89%, followed by R601a with 19.29%. In contrast, R134a and R744 demonstrate relatively low thermal efficiencies of 6.56% and 3.30%, respectively. From an exergetic perspective, R600 (butane) provides the highest exergy efficiency at 17.36%, indicating lower irreversibilities during energy conversion processes.

In terms of environmental performance, the integration of the ORC system results in a substantial reduction in fuel consumption and associated CO₂ emissions. The maximum CO₂ reduction is obtained with R601, reaching approximately 0.19 kg CO₂ per Nm³ of natural gas, while R744 exhibits the lowest reduction at around 0.02 kg CO₂ per Nm³. These findings confirm that higher turbine power output directly translates into greater fuel savings and emission reductions.

The novelty of this study lies in the application of a comprehensive 3E analysis using Aspen HYSYS combined with real operational data from a gas engine power plant in Indonesia, as well as the systematic comparison of hydrocarbon and CO₂-based working fluids under identical operating conditions.

Conclusions

This study demonstrates that ORC-based waste heat recovery is a technically feasible and effective approach for enhancing the performance of gas engine power plants. The results show that ORC integration can generate additional net power ranging from approximately 140 kW to 1331 kW, depending on the selected working fluid. Among the investigated fluids, R601 (pentane) provides the best overall performance in terms of thermal efficiency and CO₂ emission reduction, while R600 (butane) achieves the highest exergy efficiency. Although CO₂ (R744) offers advantages in terms of safety and environmental compatibility, its thermodynamic performance is comparatively lower under the investigated conditions. Overall, the findings highlight the critical role of working fluid selection and demonstrate the effectiveness of a 3E-based evaluation framework for ORC applications in gas engine power plants.

References

1. Bari, S., & Hossain, S. N. (2013). Waste heat recovery from the exhaust of a diesel engine using Organic Rankine Cycle. Applied Thermal Engineering, 61, 355–363.
2. Nadaf, S. A., & Gangavati, P. B. (2014). A review on waste heat recovery and utilization from diesel engines. Renewable and Sustainable Energy Reviews, 29, 1–12.
3. Quoilin, S., Van Den Broek, M., Declaye, S., Dewallef, P., & Lemort, V. (2013). Techno-economic survey of Organic Rankine Cycle (ORC) systems. Renewable and Sustainable Energy Reviews, 22, 168–186.
4. Guo, Y., Wang, J., & Dai, Y. (2011). Thermodynamic analysis of a supercritical CO₂ Rankine cycle for low-grade heat recovery. Energy, 36, 327–335.

Introduction: For the process fluid from the distillation column, a temperature reduction is needed, and originally an air-cooled heat exchanger has been used. In order to increase the energy efficiency, a plate heat exchanger is designed, manufactured, and put into operation as a substitute in this position. Several attempts to obtain the best applicable materials and welding technology for the plates have been made. The best solution has lasted eight years. In order to optimize performance and service life, two heat exchangers of the same construction and materials but with different joining methods of the plates are compared.

Method: Material for the construction of the air-cooled heat exchanger is X6CrNiTi18-10 (EN 10088-2). The initial plate heat exchanger is made of X2CrNiMo17-12-2 (EN 10088-2) and has a service life of five years. Its substitute is made from super austenitic stainless steel Avecta SMO 254 X1NiCrMoCuN20-18-7 (EN 10088-4), but it fails within a year due to defects in the large area of laser-welded seams. Detailed consideration of all operating conditions is performed, as well as corrosion evaluation. Comparison is made between the two applicable types of plate’s welding processes—Tungsten Inert Gas (TIG) and Laser welding. The resulting structure and manufacturing technology are investigated. Possible post-weld treatment is proposed in order to reduce the remaining residual stresses. Consideration is made for heat utilization, and subsequently, a new material is proposed: NiCr23Mo16Cu (Hastelloy^® C-2000^®). After detecting leaking, the defective plates' edges are examined with visual and penetrant testing. Positive material identification is carried out. Microhardness of the base metal and welding zone is performed, together with microstructure analysis.

Results: The heat exchanger is operating on gasoline/crude oil with process inlet T^о = 135 – 152 ^оС and process outlet T^о = 78 – 95 ^оС. For the crude oil, we have an ambient inlet temperature and an outlet of around 100 ^оС. pH is 6 +/-0.5, with an operating pressure of gasoline 5,4 bar and crude oil 12,5 bar. The overhead vapors of gasoline are directed to the plate heat exchanger. A comparison is done for two different welding methods/regimes for samples of the plates in order to simulate and detect the initial conditions that led to the defects. Both have used PA positions, autogenous weld without edge preparation for a thickness of 1.2 mm. TIG welding was performed at 50 A and 10 V, with a tungsten electrode diameter of 1.6 mm. Laser parameters were as follows: power 1800 W, speed of application 25 mm/s, distance to workpiece 120 mm, with Ar 100% gas at a flow rate of 4 l/min. For the TIG welding, the achieved values of microhardness in the welded zone are 200 - 220 HV1, and in the heat-affected zone, they were 191-208 HV1. Laser welding measurements yield, correspondingly, 230 - 246 HV1 and 174 - 193 HV1. For the laser method, the received hardness values are above the permissible limit and over 1.4 times higher than those shown by the base metal. It is vital to perform treatment after welding, which shows that in the welding zone the hardness value falls to 190-192 HV1.

Conclusion: The aim of the investigation is to define and propose the best mechanically reliable heat exchanger option for a critical refinery position. Resulting is that either additional filler material has to be specified for the welding or mandatory treatment for stress relief has to be applied in order to retain the corrosion resistance and operational life of the equipment.

Funding: The author acknowledges support from project BG16RFPR002-1.014-0005.

Introduction: The dual-pressure evaporation Organic Rankine Cycle (ORC) consists of two evaporation and compression processes, which yield a better temperature match during evaporation and lower exergy loss than a single-pressure evaporation ORC, resulting in the highest exergy efficiency and maximum net power output.

Methodology: In this study, an assessment process is designed and simulated by AspenPlus (V12) on the dual-pressure evaporation ORC to determine the maximum and assessed net power output, overall exergy efficiency, and thermo-economic parameters, including the Specific Purchased Equipment Cost (SPEC), Net Earning (NE), and Payback Period (PBP). Therefore, we evaluate to make a comparison between R245fa as an old but high-performance refrigerant working fluid with R1336mzz(Z) as a substitute and environmentally friendly refrigerant working fluid with low Global Warming Potential (GWP), Ozon Depletion Potential (ODP), and very low lifetime in the atmosphere in pure and different mole fraction of zeotropic mixtures based on effect of different geothermal water temperatures as a heat source (100, 125, 150, 175, and 200 °C).

Results: The results reveal that, based on the design and simulation of a new assessment process for the dual-pressure evaporation ORC under subcritical conditions at 0.05 bar below the critical pressure of the working fluids, geothermal water temperature is considered a fundamental key parameter in this assessment process. We increased the geothermal water temperatures and discuss the results from two perspectives: thermodynamic and thermo-economic. Regarding the thermodynamic results, the maximum net power output and overall exergy efficiency increase significantly due to the increased heat duty in the evaporators and a better temperature match between pure and zeotropic working fluid mixtures and geothermal water during both high- and low-pressure evaporation. In this case, among pure working fluids, the maximum net power output for R1336mzz(Z) showed 12.05%, 15.55%, 21.09%, 8.84%, and 5.12% improvements compared with R245fa at 100, 125, 150 °C, 175 °C, and 200 °C, respectively, because of higher evaporator heat duty and higher thermal conductivity. Furthermore, for all mole fractions of binary zeotropic mixtures of working fluids, based on this newly designed assessment process, the R1336mzz(Z)/R245fa (0.8/0.2) reveals a maximum improvement of 23.86%, corresponding to 2049 kW, which is the highest maximum net power output among all pure and zeotropic mixtures at a geothermal water temperature of 150 °C. Also, these results are reflected in the overall exergy efficiency of pure R1336mzz(Z) at all five geothermal water temperatures, with 5.01%, 6.22%, 10.11%, 4.03%, and 3.74%, improvements. R1336mzz(Z)/R245fa (0.8/0.2) illustrates a 17.99% improvement at 150 °C and reaches 88.95% as the highest exergy efficiency compared with all pure and zeotropic mixtures. These results are due to the lower irreversibility arising from lower viscosity and a higher reduced temperature of the geothermal water output. According to the thermo-economic results, the SPEC, as an indication of economic efficiency for pure working fluids, shows a reduction of 18.05-24.08% for R1336mzz(Z) across all geothermal water temperatures compared with R245fa due to its higher maximum net power output. For all mole fractions of binary zeotropic mixtures of working fluids, R1336mzz(Z)/R245fa (0.8/0.2) shows a 26.43% reduction in SPEC at 150 °C compared with all pure and zeotropic mixtures. To support this, the higher heat duty during evaporation processes indicates a greater required heat exchanger area. On the other hand, the lower high and low pressures in the compression processes of R1336mzz(Z) have a positive effect on SPEC. However, among the other thermo-economic results, the NE for R1336mzz(Z) is slightly higher than that for R245fa, owing to the higher maximum net power output, and this increase in NE has a positive effect on PBP. Based on the designed assessment process, PBP was reduced to its minimum value, reaching 13.21 years, for R1336mzz(Z)/R245fa (0.8/0.2). Finally, in terms of environmental analysis results, R1336mzz(Z)/R245fa (0.8/0.2) was selected at a geothermal water temperature of 150 °C, with a GWP of 207.6, compared with R245fa with 1030 GWP.

Conclusion: Overall, according to the designed and simulated assessment process for the dual-pressure evaporation ORC, the substantial improvement in overall exergy efficiency for R1336mzz(Z)/R245fa (0.8/0.2) indicates lower irreversibility during evaporation and a smaller temperature reduction of the geothermal water output. Likewise, the lowest SPEC and PBP of R1336mzz(Z)/R245fa (0.8/0.2), as the optimal composition compared with all pure and zeotropic mixtures, are attributed to its higher maximum net power output resulting from higher thermal conductivity and lower viscosity. Therefore, the newly designed and simulated assessment process identified R1336mzz(Z)/R245fa (0.8/0.2) as the best binary zeotropic mixture to substitute R245fa.

The low-carbon transition in the EU is structured around a legally binding path to climate neutrality by 2050, with deep emission cuts and a full transformation of the energy and industrial system by 2030–2040. The member states of the European Union are deeply engaged in the energy transition, evidencing a consolidated commitment to advancing sustainability objectives and reducing carbon emissions. Public authorities across the Union have undertaken substantial efforts by designing and operationalizing comprehensive regulatory frameworks that stimulate and, where appropriate, mandate responsible behavior on the part of both firms and final consumers. These frameworks are oriented towards accelerating the diffusion of renewable energy sources, improving energy efficiency across sectors, and fostering innovation in low‑carbon and clean technologies. At the same time, the regulatory architecture reinforces initiatives that promote corporate social responsibility and raise consumer awareness, seeking to ensure that economic growth trajectories are compatible with environmental protection and long-term climate objectives.

In this context, the present study aims to investigate the interdependencies between a series of socio-economic and environmental factors that influence the level of CO2 emissions in the member states of the European Union, paying special attention to the often pronounced differences between the EU15 and the EU27 countries. By using a combination of statistical methods and machine learning techniques, the analysis explores the link between carbon dioxide emissions and relevant indicators, such as foreign direct investment, energy consumption, the degree of urbanization and the level of literacy. The objective is to generate empirical evidence and analytical insights to support the formulation of concrete strategies at the public policy level. The results obtained aim to provide decision-makers with information on the most effective levers for reducing emissions in both the EU15 and the EU27 countries, thus contributing to the achievement of the wider objectives of the European Union in terms of environmental sustainability and climate neutrality.

Exergy analysis provides a thermodynamically rigorous measure of energy quality by explicitly accounting for irreversibilities, entropy generation, and the true useful work potential of energy conversion systems. Although widely used for performance assessment of renewable energy technologies, exergy evaluation is typically conducted through system-specific thermodynamic modeling or detailed numerical simulations. Such approaches, while accurate, are computationally intensive and often tailored to individual configurations, limiting scalability and rapid optimization across diverse renewable platforms. In contrast, machine learning methods have been increasingly adopted for renewable energy forecasting and performance prediction; however, most existing studies focus primarily on energy efficiency and rely on purely data-driven architectures that lack thermodynamic consistency and physical interpretability. This work presents a physics-guided machine learning framework for predicting exergy efficiency across solar thermal, wind, and biomass-based systems. A feedforward neural network architecture comprising three hidden layers with ReLU activation functions is trained on a curated dataset assembled from published case studies and publicly available performance data. Input variables include key operational and thermodynamic parameters relevant to each system type, enabling cross-technology applicability within a unified modeling structure. To ensure physical consistency, constraints derived from the first and second laws of thermodynamics are incorporated directly into the loss function as penalty terms. These regularization components enforce non-negative entropy generation and maintain consistency between exergy destruction, input exergy, and exergy efficiency definitions during training. Model performance is evaluated using five-fold cross-validation and standard regression metrics, including root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²). The proposed framework achieves an average R² of 0.93 and an MAE of 0.037 in exergy efficiency prediction. Compared with a conventional neural network baseline, the physics-guided model demonstrates improved predictive stability and a lower incidence of physically inconsistent outputs, particularly under off-design operating conditions. Unlike prior system-specific exergy prediction approaches, this study proposes a unified physics-guided framework applicable across multiple renewable technologies. The findings indicate that embedding thermodynamic constraints within the learning process enhances robustness and interpretability while preserving computational efficiency, providing a scalable alternative to purely simulation-based exergy assessment for renewable energy optimization and sustainability analysis.

We investigated the dependence of the maximum figure of merit of SiGe alloy on the material parameter B. We used Si_xGe_1-x samples with N- and P-type conductivity and different component compositions. For comparison, we calculated (ZT)_max ̶ B dependences for SiGe, as well as for materials containing them according to the data available in the literature. For both types Si_xGe_1-x the dependence (ZT)_max ̶ B forms a regular network together with the data for thermoelectrics containing SiGe and separately for Si or Ge. It is similar to the dependence (ZT)_max – B* (generalized parameter) of thermoelectric materials. The temperature dependence of the electronic quality factor is also considered, which provides information on the presence of additional effects. For p- and n-Si_xGe_1-x, these dependencies initially indicate the presence of additional scattering, and then band convergence and the bipolar effect are added.

Introduction

In this work, we used the dependence of the maximum figure of merit (ZT=σS²T/k; σ—specific electrical conductivity; S—Seebeck coefficient; T—absolute temperature; and k—total thermal conductivity) of SiGe alloy on the material parameter B=B_ET/k_L (B_E= σS²/B_S is electronic quality factor, B_S ≅ is the scaled power factor, S_r≅1.16∙10⁴ is the reduced Seebeck coefficient), and k_L is the lattice component of thermal conductivity. We used Si_xGe_1-x samples with p- and n-type conductivity and different component compositions. For comparison, we calculated (ZT)_max ̶ B dependences for SiGe, as well as for materials containing them according to the data available in the literature [1,2].

Method

We used Si_xGe_1-x samples with different component compositions (x = 0.7, 0.72, 0.76, 0.8, and 0.83). Boron was used as a dopant to obtain p-type conductivity, and phosphorus was used for n-type conductivity. The initial charge carrier concentration was 3.2∙10²⁶ m⁻³. It was determined by measuring the Hall constant at room temperature. The studies were conducted at temperatures of 30–1150 °C: the upper limit was limited by the melting point of the alloy. The measurement error for S was ~3%, and for resistivity ρ (=σ⁻¹), ~5%. Thermal conductivity was also measured with an error of no more than ~7%. The methodology for sample preparation is described in previous works [3,4].

Results

In addition to our samples, parameter B was also calculated for Ge_0.9Bi_0.1Te, nano-SiGe, Si+2%P, Si_0.88P_0.02, Si₈₀Ge₂₀+2%P, Si_0.58Ge_0.42, GeTe+1%Sb, GeTe+3%Sb, nanocrystalline Si, Ge_0.98In_0.02Te, SiGe+3%SrTiO₃, (Si_0.8Ge_0.2)_0.98P_0.02(SiC)_0.03, Cu₂₆Cr₂Ge₆S₃₂, (Si_0.8Ge_0.2)_0.98P_0.02(SiC)_0.015, Cu₂₆CrWGe₆S₃₂, (MnSi_1.7/Ge)₆, SiGe+5%Mg₂Si, GeTe, Ge_0.98Ta_0.02Te, Ge_0.92Ta_0.02Sb_0.06Te, SiGe, Si₉₅Ge₅P₂, Bi_0.06In_0.01Cd_0.02Te, Ge_0.888Sb_0.1In_0.012Te, Si_0.99P_0.01, GeTe+0.1%C₆₀, Ge_0.89Sb_0.1In_0.01Te, GeTe+5%Bi, Ge_0.995W_0.005Te, Ge_0.893Sb_0.1In_0.007Te, Ge_0.93In_0.01Bi_0.06Te, Ge_0.91Sb_0.09Te, Ge_0.92Sb_0.08Te, GeTe+0.2%C₆₀, nanostructured Si₈₀Ge₂₀, WSi₂+Si_xGe_1-x, and others.

For both types of Si_xGe_1-x, the dependence (ZT)_max ̶ B forms a regular network together with the data for thermoelectrics containing SiGe and separately for Si or Ge. This dependence is similar to the dependence (ZT)_max – B* (generalized parameter [5]) of thermoelectric materials.

We note that the issue of maximizing the figure of merit for Si_xGe_1-x was also considered by us in previous work [6]. There, the following empirical formulas were obtained: (ZT)_max≅3.2B+0.05, (ZT)_max≅0.39x+0.28 and lg(ZT)_max≅-0.4lgσ'+6.2, where σ' is the universal electrical conductivity (σ'=(q/k_B)²σ/B_E=(q/k_B)²B_S/S²). The dependence (ZT)_max – B differs from the dependence obtained in this work, since only our samples were considered there.

Conclusion

We investigated the dependence of the maximum figure of merit of SiGe alloy on the material parameter B. We used Si_xGe_1-x samples with p- and n-type conductivity and different component compositions. For comparison, we calculated (ZT)_max ̶ B dependences for SiGe, as well as for materials containing them according to the data available in the literature. For both types of Si_xGe_1-x, the dependence (ZT)_max ̶ B forms a regular network together with the data for thermoelectrics containing SiGe and separately for Si or Ge. For p- and n-Si_xGe_1-x, the temperature dependences of the electron quality factor initially indicate the presence of additional scattering, and then band convergence and the bipolar effect are added.

References

1. Wang J., YinY., Che Ch., Cui M. Energies, 2025, 18, 2122.
2. Sun F.-H., Li H., Tan J. et al. Materiomics, 2024, 218-233.
3. Bokuchava G., Barbakadze K, Nakhutsrishvili I. Material Sci. & Engin., 2023, 7, 54-57.
4. Bokuchava G., Barbakadze K., Nakhutsrishvili I. Bull. Georg. Acad. Sci., 2023, 17, 33-37.
5. Liu W., Han Z., Ji J. et al. Materials Today Phys., 2022, 31, 100989.
6. Nakhutsrishvili I., Adamia , Kakhniashvili G. Materials Sci. Res. and Rev., 2023, 6, 918-922.

The European Union Emissions Trading System (EU ETS) serves as the primary market-based mechanism for driving the continent toward carbon neutrality. However, the market for EU Allowance (EUA) prices is characterized by significant historical volatility driven by regulatory shifts, geopolitical shocks, and complex energy dynamics. This inherent instability poses substantial challenges for industrial operators managing compliance costs and for regulators ensuring market credibility. This research addresses these challenges by developing a robust quantitative framework for the short-term forecasting of EUA prices to support effective risk management.

The study utilizes a comprehensive 10-year dataset of daily closing prices spanning from September 2015 to September 2025. To capture the "Energy Complex" influencing carbon demand, the analysis incorporates key energy drivers, including Natural Gas (TTF benchmark), Coal (Rotterdam API2), and Brent Crude Oil. To ensure econometric rigor, an Augmented Dickey-Fuller (ADF) test was applied to all variables, confirming that the raw price series were non-stationary. To address this, the study applied first-order differencing to achieve stationarity, focusing on daily returns rather than price levels. While cointegration and Vector Error Correction Models (VECM) were considered, a differenced Multivariate Vector Autoregression (VAR) and a Lasso Regression model were prioritized to better capture short-term dynamic interdependencies and mitigate the risks of model overfitting in high-dimensional datasets.

The evaluation protocol employs a one-day-ahead forecasting horizon based on a strict chronological out-of-sample backtesting procedure. The data is divided into an 80% training set (September 201 –2023) and a 20% test set (2024–September 2025). To reflect real-world trading conditions, the models were evaluated using an expanding window approach, ensuring that all available historical information was utilized for each prediction. The models are compared against a "Naive" Baseline, which assumes the price for T+1 is equal to the price at T, a rigorous benchmark in efficient financial markets.

The findings demonstrate that both the VAR and Lasso models significantly outperform the naive baseline in terms of Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE), confirming that the carbon market contains valuable predictive signals rather than following a random walk. Notably, the Lasso model’s feature selection capabilities identify natural gas as the most influential driver of carbon price formation, validating the critical role of fuel-switching dynamics in the European power sector. By providing a replicable methodology for isolating volatility drivers, this research offers essential tools for capital allocation and policy monitoring.