Packed Bed Thermal Energy Storage Research Articles

A Comprehensive Parametric CFD Investigation on Packed Bed Thermal Energy Storage System with Encapsulated Solid–Solid Phase Change Materials in Discharging Mode

A Comprehensive Parametric CFD Investigation on Packed Bed Thermal Energy Storage System with Encapsulated Solid–Solid Phase Change Materials in Discharging Mode

Performance Analysis on Combined Energy Supply System Based on Carnot Battery with Packed-Bed Thermal Energy Storage

Pumped-thermal electricity storage (PTES) is a promising energy storage technology with high-efficiency, energy density, and versatility of installation conditions. In this study, a 20 kW/5 h phase change packed-bed thermal energy storage experimental system is established and employed to validate the accuracy of thermal energy storage (TES) component within the broader PTES system. Moreover, a novel combined system based on latent TES is proposed, incorporating Joule-Brayton and organic Rankine cycle-based subsystems for supplying cold, heat, electricity, and hydrogen. Operational strategies are also explored to optimize the multifunctional capabilities of the system. The thermal energy density of the system, when phase change materials (PCMs) are used instead of sensible heat storage materials, can be improved from 167.85 kWh/m3 to 272.58 kWh/m3. Proton exchange membrane electrolyzer cycle (PEMEC) is coupled into the Carnot battery system, and a comprehensive analysis of the system's performance is conducted. With the charging time of 5 h, the energy performance of the multi-generation system (EPMG) can be reached up to 143% and 146% in combined cooling, heating, and power (CCHP) and multi-generation energy system (MGES) modes, respectively. The MGES mode is made 3.44% more exergy efficient than the CCHP mode as a result of the ingenious coupling of the hydrogen production process with the power generation process and heating/cooling processes. The system in one charging/discharging process has the capability to generate 240.86 kg of hydrogen, 34.82 MWh of heat, 12.97 MWh of cold, and 40.90 MWh of electricity.

A novel PCM/expanded graphite composite sphere with high thermal conductivity and excellent shape stability used for a packed-bed thermal energy system

In this research, a novel phase change material (NPCM) sphere was developed and its application in a packed-bed thermal energy storage (PBTES) system during thermal energy storage was studied. Paraffin wax (PW) with a melting point of 40 °C was selected as phase change material (PCM), expanded graphite (EG) as thermal conductivity enhancement material, and epoxy resin (ER) as a surface coating. The results show that the three-dimensional heat conduction network constructed by EG foam improves the thermal conductivity of PW/EG. The thermal conductivity of NPCM is anisotropic. The thermal conductivities perpendicular and parallel to the EG compression direction are 9.03 (W/m·K) and 5.58 W/(m·K). NPCM has excellent shape stability with a leakage rate of only 2.95 %. Then, a PBTE system was built to record the temperature evolution of NPCM spheres at various inlet temperatures and volume flow rates during thermal energy storage, and thermodynamic analysis was performed. The results are as follows. (1) The temperature of the NPCM sphere near the inlet rises more rapidly and the melting time of PCM is shorter. (2) Increasing the inlet temperature improves the heat transfer and shortens the melting time of PCM while increasing the temperature inhomogeneity of the NPCM spheres. Increasing the inlet temperature increases the energy storage capacity. However, higher inlet temperature leads to lower energy efficiency and exergy efficiency. The energy efficiency and exergy efficiency are 49.66 % and 67.64 % for the inlet temperature of 60 °C, respectively. When the inlet temperature increases from 60 °C to 80 °C, the energy efficiency and exergy efficiency decrease by 16.13 % and 16.22 %, respectively. (3) Higher inlet volume flow rate also promotes heat transfer and reduces the melting time of the PCM, but has little effect on the temperature inhomogeneity of the NPCM spheres. Increasing the inlet volume flow rate does not increase the energy storage capacity. Similarly, increasing the inlet volume flow rate also results in a decrease in energy efficiency and exergy efficiency. At the inlet volume flow rate of 19.28 m3/h, the energy efficiency and exergy efficiency are 41.65 % and 56.67 %, respectively. When the inlet volume flow rate increases from 19.28 m3/h to 25.16 m3/h, the energy efficiency reduces by 7.80 % while the exergy efficiency reduces by 7.41 %. This research provides a foundation for the application of the NPCM sphere.

Comparison of Single-Phase Mathematical Models for Solid-State Packed Beds for Thermal Energy Storage

This article presents an analytical solution for the evaluation of the thermal performance of packed bed sensible heat storage. The numerical model developed was tested for four different solid storage mediums. The thermal energy equation is solved numerically by deploying the finite difference method. The presented analytical solution is based on a novel mathematical approach. The numerical model was validated using the computer simulation package Comsol Multiphysics v5.3. Our numerical model results are in good agreement with the published experimental data, with an overall difference of ~10%. Hence, the numerical model is an efficient way of evaluating the thermal performance of packed bed thermal energy storage systems compared to other numerical strategies or computer simulation techniques. This proves that the novel analytical model has shown to be a reliable and broadly accurate approach to acquire the thermal performance of sensible heat storage.

Techno-Economic Analysis of Using Reversible Turbomachinery for Pumped Thermal Energy Storage Systems

Abstract The objective of this paper is to assess the techno-economic performance of different cycle configurations for pumped thermal energy storage (PTES), including the effects of charging electricity costs. Reversible turbomachinery was employed to reduce the capital cost of the system. Brayton cycles with different working fluids and a subcritical Rankine cycle operating with ammonia were compared. Both liquid and packed bed thermal storages were investigated. A new cost correlation for turbomachines, initially established for the turbines of organic Rankine cycles, was developed for compressors and reversible machines. This correlation is based on the number of stages and physical size of the machine, which were estimated considering thermodynamic as well as mechanical limitations. The results indicate that for a plant size of 50 MW and a discharge duration of 8 h, the Brayton system with liquid storage and helium as a working fluid has the lowest levelized cost of storage at 0.138 $/kWh, mainly due to the high thermal conductivity of the fluid. Packed bed thermal energy storage systems were found to be more expensive than liquid storage systems due to the large cost of the pressure vessels, with cost parity reached at a discharge duration of 4 h. However, at this duration, lithium-ion batteries are likely to be cheaper. The results suggest that the levelized cost of storage for the Rankine cycle-based system is slightly higher at 0.151 $/kWh.

Investigation and improvement of complex characteristics of packed bed thermal energy storage (PBTES) in adiabatic compressed air energy storage (A-CAES) systems

With the application of large-scale renewable energy, power grids have put forward explicit demands for energy storage. Among the various forms of energy storage systems, the adiabatic compressed air energy storage (A-CAES) system has received more attention due to its environmental friendliness and adaptability. As a key link in the regenerative A-CAES, thermal energy storage (TES) has an important impact on the efficiency of the system. Among various forms of TES, PBTES has better economy and adaptability. However, there is insufficient research on the impact of PBTES structure on A-CAES systems. Therefore, a dimensionless governing equation for the PBTES is proposed to study the depth effect of the PBTES structure. Through comparing with the pilot-scale and industrial-scale PBTES experimental data, the maximum error of the model is 2.3%, which proves that the model has good accuracy in the simulation of different scales of PBTES. The result of research shows that: the improved thickness of the structural layer is between 0.1 m and 0.15 m. The increase in the number of cycles of the A-CAES system results in a gradual increase in system efficiency. For the A-CAES system, the round-trip efficiency is improved by 4.1%, reaching 64%, with the improvement of the wall, volume ratio, and height-to-diameter ratio of PBTES.

Experimental and numerical study of cylindrical encapsulated phase change material in packed bed thermal energy storage with expansion and shrinkage effects

Packed bed latent heat thermal energy storage (PBTES) is a promising technology for storing thermal energy with a relatively compact size and smaller temperature variation during phase change. In this study, a lab-scale low-cost PBTES with cylindrical shape encapsulation of phase change material (PCM) is designed and fabricated for evaluating the charging-alone and discharging-alone thermal performance for medium-temperature range (200–350 °C) latent heat storage applications. Air is used as a heat transfer fluid (HTF), and solar salt is employed as a PCM. A new numerical model incorporating shrinkage and expansion of PCM during phase change is developed by considering the packed bed as the porous medium and the melt fraction-based density variation of PCM to model the transport and solid-liquid phase change phenomena in the PBTES. The numerical model is validated with the in-house experimental results. The maximum thermal charging efficiency is found to be 67.1 % for the mass flow rate of 4.3 g/s and a maximum charging inlet air temperature of 360.9 °C. The maximum discharging efficiency of 86.1 % is obtained for the mass flow rate of 4.3 g/s and discharging inlet air temperature of 35 °C. It is found that the expansion and shrinkage effects are prominent during the phase change of PCM during the charging and discharging operations of the PBTES.

Exergy efficiency and thermocline degradation of a packed bed thermal energy storage in partial cycle operation: An experimental study

To enable the exploitation of the industry sectors’ huge waste heat potential this study investigates the utilization of packed bed thermal energy storage systems for the waste heat recovery in the iron and steel industry. The main goal is to assess the partial cycle operation of a packed bed thermal energy storage with industrial exhaust gas that is contaminated with high amounts of metal powder. A continuously rising accumulation of powder particles inside the packed bed requires the storage to be charged from the bottom in order to facilitate the removal of powder hold-up. Therefore, investigations focus on the dependency of the thermal performance of the storage on the flow direction of heat transfer fluid during charging/discharging. Exergy efficiency and thermocline degradation are evaluated as key performance indicators for different flow directions of the heat transfer fluid using a lab-scale test rig. Results show that, compared to charging from the top, a slightly faster thermocline degradation occurs for a storage that is charged from the bottom. Still, energy and exergy efficiencies in partial cycle operation are well above 85% and 80% respectively regardless of the heat transfer fluid flow direction. The thermal power rate during discharging is stable between 74% and 93% with respect to the maximum input rate for both charging the storage from the top and from the bottom. All in all, packed bed thermal energy storage systems are found to be suitable for waste heat recovery in industrial processes. Only a marginal deterioration of the thermal performance of the storage has to be expected if the storage is required to be charged from the bottom.

Performance investigation on the cascaded packed bed thermal energy storage system with encapsulated nano-enhanced phase change materials for high-temperature applications

Latent heat thermal energy storage (LHTES) systems based on phase change materials (PCMs) offer a reliable way to address the intermittency of renewable energy sources. The low thermal conductivity of PCMs, however, limits the practical use of LHTES systems. This work aims to investigate the effect of mixing graphene (Gr) and copper (Cu) nanoparticles at volume fractions varying from 0 % to 5 % with a PCM on the single charging/discharging performance of a cascaded packed bed LHTES system. The effect of the charge inlet temperature on the cyclic performance is also investigated by considering three cascaded configurations with encapsulated copper-nanoparticle-enhanced PCMs (Cu-NEPCMs) and six inlet temperatures ranging from 390 °C to 440 °C. A concentric-dispersion numerical model is developed to evaluate thermal performance. Synthetic PCMs with melting temperatures in the range of 320°C–380 °C are adopted as the heat storage medium, and molten salt is used as the heat transfer fluid. As the volume fraction of the Cu and Gr nanoparticles increases from 0 % to 5 %, the cascaded Cu-NEPCM and Gr-NEPCM storage systems exhibit decreases in the melting time by 14.4 % and 5.6 % and in the solidification time by 13.9 % and 6.5 %, respectively. As the inlet temperature increases from 390 °C to 440 °C, the optimal cascaded packed bed configuration among the three shows enhancements in the total energy storage in the bed, energy recovered by the salt from the bed, capacity ratio, and total utilization ratio by 82.2 %, 85.6 %, 20.3 %, and 50.5 %, respectively. This work provides insights into the design and operation of LHTES systems with enhanced performance.

Design optimization of an innovative layered radial-flow high-temperature packed bed thermal energy storage

The present work introduces an innovative layered radial flow packed-bed thermal energy storage able to provide enhanced thermal and hydrostatic performance, limiting their inherent trade-off. The performance of the proposed packed-bed thermal energy storage concept is modelled, in both thermal and hydrodynamic aspects, via a 1D-two phases numerical approach. Representative storage sizes for industrial applications and laboratory prototype are considered to highlight the potential for scaling and the representativeness of prototyping. Configurations with two and three coaxial layers are also analyzed. The investigation includes a multi-objective optimization of the thermal energy storage design considering a set of main design variables and a set of sensitivity analyses aimed at highlighting the influence of major operational parameters. The results show that the proposed storage geometry can provide simultaneous optimization of both thermal and hydrodynamic performance. The proposed storage unit could attain pressure drop reductions higher than 70 % with respect to uniform radial flow packed bed storage (and higher than 85 % with respect to axial flow units) at the expense of a useful duration reduction lower than 5 %. Industrial scale storage would benefit from low aspect ratios and arrangement with modular units, ensuring enhanced system flexibility and reduced parasitic consumptions thanks to lower pressure losses meanwhile guaranteeing extensive useful durations in both charge and discharge operation. Downscaled prototypes can provide a good representation of the thermal and hydrodynamic behavior of the proposed thermal energy storage solution and a relevant base for validation. This work paves the way for future prototyping and validation of the proposed layered radial flow packed-bed thermal energy storage concept.

Optimization of PCM layer height of cascaded two-layered packed-bed thermal energy storage tank with capsules of varying diameters based on genetic algorithm

The packed-bed thermal energy storage (PBTES) technology exhibits significant potential for utilization in various energy sectors, including concentrating solar power, city heating systems and power peaking. This paper uses a genetic algorithm (GA) to optimize the phase change material (PCM) layer height arrangement of cascaded two-layered PBTES with capsules of varying diameters to enhance thermal performance during charging. The optimization process considers the oscillatory distribution of radial porosity, and the objective function utilized for assessing the thermal performance of the system is thermal energy storage (TES) rate density. The TES rate density for over 2000 different layer height arrangements was calculated. The findings indicate that the PCM layer height significantly influences the thermal performance of the tank in each layer. The charging performance is optimal when the layer height ratio of high and low melting point PCM is 12.05 % and 87.95 %, respectively, which is the optimal model. In comparison to the original model with equal bed height, the optimal model demonstrates a reduction in charging time of 28 %, increases the TES rate density by 17.68 %, and the greatest improvement in charging efficiency reached 31.28 %. And reduces the unit TES cost by 13 %. This study shows that GA is an effective tool for optimizing the structural arrangement of PBTES.

Experimental study on storage performance of packed bed solar thermal energy storage system using steel slag

Renewable energy sources are challenging due to their intermittent and unstable power output. However, Thermal Energy Storage (TES) systems offer an effective solution to address this issue. Among the available heat storage options, the air-packed bed is widely preferred in heat storage due to its cost-effectiveness and stability. This study investigates the feasibility of utilizing steel slag, a by-product of the steel industry, as the heat storage material in an air-packed bed. The research examines the flow characteristic, thermal performance, and heat storage properties of Packed Bed Thermal Energy Storage (PBTES) systems. Additionally, the study explores the impact of different heat storage temperatures and inlet air flows on the performance of PBTES and finds that Steel slag exhibits promising potential for broad applications in solid thermal storage. Finally, a Morris sensitivity analysis based on Latin Hypercube Sampling (LHS) is conducted. The findings demonstrate that the specific heat and density of air significantly influence the calculation of heat storage. Therefore, to achieve high accuracy in the analysis, it is crucial to consider the variations of these two parameters with temperature and pressure.

Numerical and experimental analysis of instability in high temperature packed-bed rock thermal energy storage systems

Due to heat losses of preferential areas of packed-bed energy storage systems, transverse temperature variations may occur during the charging, discharging and standby processes. Furthermore, the heat losses of preferential areas of the storage tank cause a lower pressure drop in these areas resulting in an increased mass flow rate and further cooling, and thereby an enhanced transverse temperature variation, in a positive feedback loop – a phenomenon called instability. The transverse temperature variations may deteriorate the performance and thereby the economic feasibility of packed-bed energy storage systems. In this paper, numerical and experimental investigations of an air-based packed-bed rock thermal energy storage system for large-scale high temperature applications are presented. The objective of the study is to predict the instability and to analyze the effect of different standby durations and storage size on the instability of the air-based packed-bed system. Transient axisymmetric computational fluid dynamics models were developed for the standby and discharging processes of the packed-bed thermal energy storage systems. In addition, experimental investigations were carried out at a test facility located at Stiesdal Storage, Denmark, using magnetite rocks as heat storage material and air as heat transfer fluid. The results suggest that the numerical predictions are in good agreement with the test data. The instability phenomenon is found to increase with the standby duration, resulting in a maximum difference of 161 K between the maximum rock temperature and the outlet air temperature for a standby period of 10 h followed by a discharging process. Moreover, the results indicate that the maximum difference between the rock temperature and outlet temperature is 73 K and 56 K for a reduced-scale and a full-scale system (no standby period), respectively.

An effective thermal conductivity correlation for three high-temperature chloride salts melting in a spherical thermal storage capsule

ABSTRACT Chloride salts are viable phase change materials (PCMs) for packed-bed thermal energy storage for third-generation concentrating solar power (CSP) systems. In the study, a two-dimensional, axisymmetric and transient model is developed to simulate the constrained melting process of three chloride salts (NaCl-CaCl2, LiCl and MgCl2) in a spherical capsule while considering the natural convection of the salt. The simulation results lead to the proposal of an effective thermal conductivity correlation for the liquid part of these three PCMs’ melting process in a sphere, represented as λ eff/λ l = 0.38Ra 0.26(δ/R i)0.25. Additionally, a simplified conduction-controlled numerical model has been developed for predicting the melting process of chloride salts in a spherical capsule with improved accuracy and efficiency. The proposed correlation improves the conduction-controlled model’s accuracy in predicting the melting process compared to other correlations previously reported in literature. The proposed correlation comprehensively reflects the conduction and natural convection of the chloride salts during the constrained melting process in a sphere.

Effect of orientation and nanoparticle addition of a encapsulated phase change material on heat transfer in a packed bed thermal energy storage system – A numerical analysis

Thermal energy storage technology research is growing globally due to the increased awareness of the clean energy demand and limitations of fossil fuel commodities. The packed bed latent heat thermal energy storage (PBLHTES) system is one among it promising a greater number of applications like solar water heating, industrial waste heat recovery process, thermal power generations, thermal comfort of buildings etc., Due to the high latent heat capacities, available in wide temperature ranges and minimal volume change, solid-to-liquid phase change materials (PCMs) are more attractive than any other latent heat materials to use in the PBLHTES system. Although, the low conductivity of PCM restricts the heat transfer while the charging and discharging periods. Therefore, it is necessary to incorporate thermal enhancement techniques in a PBLHTES system to improve the melting rate of the PCM. In this work, it is attempted to carry the 2-D numerical analysis of PBLHTES system provided with encapsulated PCM staggered in the flow direction of heat transfer fluid. The numerical results are validated with the experimental work. The effect of the inclination of PCM capsules with the flow direction (0°, 2.5°, 5°, 7.5°, and 10°), the addition of Multi-walled carbon nanotubes (MWCNT) nanoparticles (0 %, 1 %, 2 %, 3 %, 4 %, and 5 %) on energy absorbed by the PCM are studied. Also, the contours of temperature distribution and liquid fraction of the PCM with time are presented. The results revealed that the temperature distribution of HTF rises when PCM spheres orientated to the HTF shifted from 0 to 2.5° later it reduces. Though HTF temperature rises, the PCM temperature, liquid Fraction and energy absorbed decline when the capsules inclined to the flow direction. This is mainly due to the reason that the HTF moves outwards from the flow direction and towards the edges of the container, which makes the HTF carry a more amount of heat without sharing with the PCM capsules. Therefore, these arrangements will be helpful to switch over the ideal high-temperature HTF at the outlet without charging the TES system and vice versa. An improvement of 13.16 % melting rate is observed from 0 to 3 % of a nanoparticle addition and only 4 % enhancement is noted from 3 to 5 % MWCNT deposition. The effect of nanoparticles on energy absorbed by the PCM is nearly constant after 3 % of Multi-walled carbon nanotubes (MWCNT) addition. Therefore, this is the optimum MWCNT volume concentration to be added. The maximum energy absorbed with 3 % MWCNT for 60 min of time is 98.7 kJ and 97 kJ which are 3.5 % and 3.65 % more than the pure PCM for the standard case (0°) and 2.5° angle of attack of EPCMs with the flow direction.

Multi-factor analysis and optimization design of a cascaded packed-bed thermal storage system coupled with adiabatic compressed air energy storage

In an adiabatic compressed air energy storage (A-CAES), one of the key components is the heat storage system, in which the packed bed filled with encapsulated phase-change capsules has been widely investigated because of its excellent thermal performance. In this paper, a packed-bed thermal energy storage model with three layers of phase change materials (PCM) is proposed in the context of an A-CAES. Four factors primarily affecting the thermal performance of the packed bed thermal storage system, namely the mass flow rate of heat transfer fluid (HTF), the inlet temperature of HTF, the cascade situation of PCM, and the arrangement of particle sizes, are critically analyzed by conducing the orthogonal experiments. On this basis, the machine learning method is applied to predict and optimize the thermal performance of the packed bed aiming to find the optimal results. The comparison of results between the optimized and original models expressively shows a reduction of 8.46% in PCM mass, an increase of 92.18%/116.82% in the overall heat storage/release quantity, and an increase of 19.23% in the overall efficiency. This work outlooks a guideline for the potential application of packed bed in A-CAES.

Modeling and analysis of PCM‐encapsulated solar thermal energy storage system for space heating

AbstractIn this study, a phase change material (PCM)‐encapsulated packed‐bed thermal energy storage (PB‐TES) system is intended for Day‐round space heating in the winter. Solar concentric collectors act for day‐time heating and TES charging, while the stored energy can be used at night and intermediate time for space heating. A region‐wise techno‐economic analysis of PCM candidates is made to compare the costs and sizes of solar collectors and PB‐TES. A spherical capsule filled with sodium nitrite (NaNO2) and sodium nitrate (NaNO3) is numerically investigated during the PCM charging at constant thermal input. After complete liquefication, the charging time for NaNO2 and NaNO3 capsules is 3280 and 4300 s, respectively, holding the maximum stored energy of 733.4 KJ/kg at 285°C and 687.27 kJ/kg at 310.12°C, respectively. In addition, the stored exergy is obtained 238.78 and 234.74 kJ/kg for NaNO2 and NaNO3, respectively; however, the average exergetic effectiveness for NaNO2 and NaNO3 are 0.54 and 0.46. Despite the lower energy storage capacity (kJ/kg) of NaNO3, the PB‐TES volume is less with NaNO3 than with NaNO2 due to higher density. However, the average cost ($/tonne) of NaNO3 PCM is 50% higher than NaNO2. Subsequently, the thermal efficiency of the proposed system is estimated at 27.68% and 26.94% during day and night‐time operations.

Packed bed thermal energy storage for waste heat recovery in the iron and steel industry: A cold model study on powder hold-up and pressure drop

Waste heat recovery in the energy intensive industry is one of the most important measures for the mitigation of climate change. The present study examines the integration of a packed bed thermal energy storage for waste heat recovery in the iron and steel industry. Along with the highly fluctuating availability of excess heat the main difficulty of waste heat recovery in industrial processes is the high amount of powder that is transported by the hot exhaust gases. Therefore, the experimental investigations in this study focus on the powder hold-up and pressure drop in a packed bed thermal energy storage that is operated with a gas-powder two phase exhaust gas as heat transfer fluid. The ultimate goal is, to assess its suitability and robustness under such challenging operational conditions. The results indicate, that 98% of the powder that is introduced into the system with the heat transfer fluid during charging accumulates in the packed bed. Remarkably, most of the powder hold-up in the packed bed is concentrated near the surface at which the heat transfer fluid enters the packed bed. When reversing the flow direction of the heat transfer fluid to discharge the storage with a clean single phase gas, this gas is not contaminated with the powder that has been accumulated in previous charging periods. The entirety of these findings reinforces the suitability of packed bed thermal energy storage systems for waste heat recovery in the energy intensive industry.

A comparison of packed-bed flow topologies for high-temperature thermal energy storage under constrained conditions

Packed-bed thermal energy storage (PBTES) systems are cost-effective when natural rocks and industrial by-products are used as filler materials. In addition, its combination with gaseous heat transfer fluids (HTF) might increase operating temperatures. Nevertheless, the state-of-the-art design of PBTES containers has several drawbacks related to thermal losses and thermocline control in the flow direction. The present article develops a comparative study of four PBTES flow topologies: a conventional vertical cylinder, a truncated cone shape with two flow directions, and the novel radial-flow packed-bed concept. Considering the operational constraints of a high-temperature Concentrated Solar Power (CSP) plant using atmospheric air as HTF, the cyclic behavior of the system is modeled to determine the thermal and exergy performance. Although radial-flow PBTES is a potential candidate for reducing overall thermal losses by 63% against conventional approaches, the spread of the thermocline through the radial direction causes the reduction of the utilization factor, delivering the required thermal power for a limited time. Also, conventional designs are 54% cheaper in terms of costs per stored energy. A parametric analysis of the design and operational conditions suggests that increasing the cut-off charging and discharging temperatures maximizes the utilization factor, but designing for minimum costs and exergy losses increases the round-trip efficiency, limiting the charge–discharge operation. This work contributes as a guideline to size and select operating conditions of different PBTES topologies according to first and second-law approaches.

Entropy generation minimization of hybrid nanofluid mixed convection flow in lid-driven square enclosure with heat-generating porous layer on inner walls

PurposeThis study aims to numerically scrutinize the entropy generation minimization and mixed convective heat transfer of multi-walled carbon nanotubes–Fe3O4/water hybrid nanofluid flow in a lid-driven square enclosure with heat generation in the presence of a porous layer on inner surfaces, considering local thermal non-equilibrium (LTNE) approach and the non-Darcy flow model.Design/methodology/approachThe dimensionless governing equations for hybrid nanofluid and solid phases are solved by applying the finite volume method and semi-implicit method for pressure-linked equations algorithm.FindingsThe roles of the internal heat generation in the porous layer, LTNE model and nanoparticles volume fraction on mixed convection phenomenon and entropy generation are introduced for lid-driven cavity hybrid nanofluid flow. Based on the investigation of entropy generation and heat transfer, the minimum total entropy generation and average Nusselt numbers are found at 1 ≤ Ri ≤ 10 where the effect of the forced and free convection flow directions being opposite each other is very significant. When considering various nanoparticle volume fractions, it becomes evident that the minimum entropy generation occurs in the case of φ = 0.1%. The outcomes of LTNE number reveal the operating parameters in which thermal equilibrium occurs between hybrid nanofluid and solid phases.Originality/valueThe analysis of entropy generation under various shear and buoyancy forces plays a significant role in the suitable thermal design and optimization of mixed convective heat transfer applications. This research significantly contributes to the optimization of design and the advancement of innovative solutions across diverse engineering disciplines, such as packed-bed thermal energy storage and thermal insulation.