Heat Transfer Fluid Inlet Research Articles

Experimental study on the thermal response of a metal foam dual phase change unit thermal storage tank

Adding fins or metal foam to phase change units can effectively enhance the heat storage efficiency of thermal energy storage (TES) tanks, thereby improving the reliability of TES tanks in coordinating renewable energy supply and demand. In this study, an experimental TES tank platform was designed and constructed to investigate how the addition of straight fins, metal foam, and straight fin/metal foam composite materials to paraffin affects the temperature response during the heat storage process. High-temperature water was selected as the heat transfer fluid (HTF) and injected from the top into the TES tank at the same paraffin fill level, and T-type thermocouples were arranged along the central axis of the phase change unit. TES tanks filled with either pure paraffin or composite phase change materials were tested by varying the HTF inlet temperature and velocity, and temperature response data were captured and recorded using a KEYSIGHT DAQ970A data logger. The results indicated that increasing the HTF inlet temperature significantly enhanced the heat storage rate while increasing the HTF inlet velocity had varying effects on different phase change units. A comprehensive analysis suggested that an inlet velocity of 1.3 m3/h (from a range of 0.8–1.8 m3/h) was reasonable. The addition of enhancement measures improved the temperature drift phenomena and effectively increased the temperature response rates and distribution uniformity. Moreover, the straight fin/metal foam composite material exhibited the best performance.

A novel flat coil tube heat exchanger for metal hydride hydrogen storage reactors

Metal hydride (MH) based hydrogen storage is one of the potential methods for achieving higher volumetric storage densities. However, its poor thermal conductivity limits heat transfer during exothermic hydriding and endothermic dehydriding processes. Hence, heat transfer augmentation is essential in MH reactors to speed up the charging and discharging of hydrogen. The present study proposes a novel flat coil tube heat exchanger with a spiral fin for heat transfer augmentation. It offered superior performance than conventional single and double helical tube heat exchangers, taking 35.3 and 16.7% less time for 90% storage time. Further, optimization of design parameters (pitch and fin thickness) is carried out considering several key parameters such as weight ratio (WR), gravimetric exergy output rate (GEOR), and energy efficiency (EE). A pitch of 30 mm with a fin thickness of 0.25 mm is optimum according to a novel performance index. The influence of the operating parameters (H2 supply pressure and heat transfer fluid inlet temperature) on the absorption performance is investigated for the optimized design. Finally, a single desorption case is presented at 1 bar and 333 K to gain insights about desorption behavior.

CFD Analysis of a Latent Thermal Storage System (PCM) for Integration with an Air-Water Heat Pump

Heat pumps driven by sustainable electricity sources have been identified as a technology that can contribute to reduce carbon dioxide emissions. Furthermore, a heat pump can also provide energy savings when combined with a thermal energy storage system. Heat pumps can optimize their efficiency by accumulating thermal energy during periods of lower electricity demand, resulting in shorter operational durations and decreased overall energy consumption. In this work, the combination of a latent heat storage system with an air-water heat pump has been numerically analysed and experimentally tested. A phase change material (PCM) heat exchanger with an immersed plate was designed using a 3D CFD model (COMSOL Multiphysics®). The heat exchanger configuration with six steel plates immersed in the phase change material tank was proposed to enhance heat transfer in the storage system. The developed model is validated against experimental data from a real case study, demonstrating a maximum error of approximately 3% during the discharging phase. Additionally, the study explores the effects of different inlet heat transfer fluid temperatures and flow rates on the PCM solidification time.

Parametric Analysis of a Latent Heat Storage System for Predicting the Charging and Discharging Time

Latent Heat Storages (LHS) are essential for harnessing renewable energy by storing surplus energy for later use. This research aims to enhance the predictability of charging and discharging times in LHS systems, a crucial step for effective energy management and optimizing renewable energy utilization. A comprehensive parametric analysis was conducted using computational fluid dynamics (CFD) to develop correlation equations for forecasting these times under diverse geometric and operational settings. Parameters considered includes the heat transfer fluid (HTF) inlet temperature, phase change material (PCM) thickness-to-length ratio, Reynold’s number, and HTF inlet location. The enthalpy-porosity method and Boussinesq model were employed in numerical simulations to account for natural convection during charging. The influence of the mushy-zone constant on the PCM’s temperature profile was investigated and found to be significant. The bottom HTF injection was found to reduce the charging times, while extending discharging durations. The thickness-to-length ratio of the PCM emerged as the most influential factor, with Reynold’s number exerting the least influence in the cycle. Analysis showed that increasing PCM thickness-to-length ratio consistently led to longer charging time. Four correlations were developed with an impressive average multiple R of 0.999463, signifying high predictability for charging and discharging times.

An experimental investigation on the heat transfer characteristics of cascaded thermal storage units based on multichannel flat tubes

A latent heat storage unit made of a two-stage phase change material (PCM) can decrease the mismatch between supply and demand of energy. The cascaded phase change thermal storage stores and utilizes energy hierarchically. A two-stage cascaded thermal storage unit based on multichannel flat tubes and compact fins is developed in this study. The device uses water as the heat transfer fluid (HTF). Melting/solidification time, charging/discharging power, thermal efficiency, and exergy efficiency are evaluated for different HTF inlet temperatures and PCM volume flow rates. At the charging conditions of 70 °C and 1.5 L/min, the melting time for paraffin and lauric acid are 21and 20 min, respectively. The thermal efficiencies of the first and second stages of the thermal storage unit are 70.62 % and 70.40 %, respectively, and the exergy efficiencies are 81.25 % and 81.19 %. Given the small pressure loss of the pump and the high heat transfer performance of the heat storage system, using 70 °C and 1.5 L/min as experimental conditions for HTF is the key to obtaining short PCM melting times and high power.

Experimental study of a latent heat thermal energy storage system using erythritol for medium temperature applications

Using solar energy and waste heat for medium-temperature thermal applications depends on efficient and economical heat storage development. Developing a compact thermal energy storage system is essential to use excess thermal energy from a source in a process or to shift the utilisation time of solar thermal energy or recovered waste heat. Phase change materials are commonly used for energy storage applications globally. In this work, a latent heat thermal energy storage (LHTES) system with 2.37 kg of Erythritol as the phase change material (PCM) has been studied. A shell and tube heat storage system is selected due to its effectiveness in heat transfer. Synthetic silicone oil Hi-Tech Therm-60 was used as heat transfer fluid. Thermal stability tests in a differential scanning calorimeter (DSC) for a small sample mass and a specifically designed experiment for a larger sample mass were performed to assess the stability of the PCM. The time-dependent temperature distribution inside the storage system and the effect of heat transfer fluid (HTF) inlet temperature on the charging behaviour were studied during the charging process. Charging time and melt fraction have been calculated. No significant change in melting temperature and a 10% reduction in latent heat of PCM was observed in the thermal stability test for a small sample mass in DSC. The charging time of the storage device was observed to be 91–97 min and 195 min for 140 °C and 130 °C HTF inlet temperatures, respectively. The total stored energy in the system was 922 kJ with a Stefan number of 0.59. Temperature variation during the charging process inside the storage also suggests a buoyancy effect, leading to increased natural convection during the melting process.

Modelling a latent heat thermal storage demonstrator and identification of the model key-parameters

Latent Heat Thermal Energy Storage (LHTES) has a great potential to reduce CO2 emissions in urban areas, when associated to a district heating network. It facilitates the flexibility of the network by decoupling the production and consumption. Thus, consumption peaks that are often managed with fossil fuels will be managed by unloading the storages of the network. LHTES based on tube and shell is the most widely studied technology, as it combines low cost, high maturity, and high compactness factor. This paper presents a numerical model to simulate the thermohydraulic behaviour of a shell-and-tube LHTES, based on a 1D approach for the heat transfer fluid (HTF) and a 1.5D approach for the Phase Change Material (PCM). The objective is to develop a model representing a whole system, faster than a Computational Fluid Dynamic approach while keeping a sufficient degree of accuracy. The paper focuses on the presentation of the model and its validation against experimental data from a real-scale 180 kWh demonstrator, currently in operation in the substation of the urban heating network of Grenoble, France. The validation against three different charges is presented, two charges at a constant flow rate (0.6 and 1.6 kg/s-1) and one at constant power (60 kW). The model gives results with an accuracy superior to 95 % and >80 % of the points are between the experimental uncertainty curves. It has also been found that the model loses its accuracy when the inlet HTF temperature abruptly decreases and the top collector does not behave as a stratified tank anymore (the relative error on total energy accumulated reaches 35 %). In the second part of the paper, a sensitivity study to the main parameters of the model shows that the model is sensible to the discretization of the collectors, the precision of the Nusselt correlation for convective transfers in the tubes, and the fusion temperature of the PCM. These parameters can induce up to respectively 22 % (0D model for the collectors' volume), 4.5 % to 9 % (considering the annular space as a flat plane or a cylindrical tube) and 3 % to 6 % (error of 0.5 to 1 °C in the PCM fusion temperature) error.

Thermodynamic performance of cascaded latent heat storage systems for building heating

Decarbonization of building space heating is essential for China to meet its carbon neutrality goal by 2060. Cascaded latent heat storage (CLHS) coupled with electric heating is a promising technology to promote renewable energy consumption, reduce carbon emissions, and save on heating bills. However, few studies have focused on the thorough investigation of the superiority of the CLHS system over a non-cascaded system. This study investigated the effects of heat transfer fluid (HTF) flow rates, HTF inlet temperatures, and number of stages on the thermodynamic performance of non-cascaded and CLHS systems based on energy and entransy analysis. Results showed that, compared with the non-cascaded system, the charged thermal energy and discharged thermal energy of the two-stage CLHS system increased by 26.5%–44.6% and 19.8%–74.5%, respectively, and the entransy increase of cold HTF increased by 20.0%–75.7%; while, in heating systems, it is not guaranteed that thermodynamic performance improves by using more stages in the CLHS system.

Experimental investigation of thermal characteristics of phase change material in finned heat exchangers

A significant challenge to the widespread use of practical latent heat energy storage systems based on phase change materials is the inherent low thermal conductivity of these materials. Inserting fins is considered one of the effective methods of heat transfer enhancement. In the present paper, an experimental investigation of the melting process of PCM in finned and unfinned heat exchangers is conducted. The experimental setup was constructed, and the measurement system was used to monitor the transient progress of the melting process. The heat exchanger comprises annular horizontal concentric double pipes, where the inner tube is heated by flowing water as heat transfer fluid (HTF), and the outer shell is thermally insulated. Four configurations of fins of the same fin/PCM volume ratio are attached to the inner tube. These configurations are longitudinal fin (LF), circular fin (CF), longitudinal perforated fin (LPF), and circular perforated fin (CPF). The effect of inlet HTF temperatures of 60, 70, and 80 °C is tested. The experimental findings indicate that the thermal performance of finned heat exchangers exceeds that of unfinned heat exchangers. Also, the perforated finned heat exchangers showed a higher thermal feature than the unperforated ones. In addition, the CPF achieved the lowest melting time and the highest melting rate, followed by LPF, CF, and LF. The maximum reductions of melting time are 71.1 %, 70.6 %, and 70.2 % due to using CPF HE instead of UF HE for inlet HTF temperatures of 60, 70, and 80 °C, respectively.

Charging performance of structured packed-bed latent thermal energy storage unit with phase change material capsules

A mathematical model of the charging process for a structured packed-bed latent thermal energy storage unit with phase change material capsules is established. The thermal-hydrodynamic characteristics of the unit are investigated. The impacts of the heat transfer fluid inlet velocity, heat transfer fluid inlet temperature, initial temperature of the latent thermal energy storage unit, and diameters of the phase change material capsules are analyzed. The charging performance of a scaled-up latent thermal energy storage unit is studied. The numerical results indicate that the structured packing configuration of the structured packed-bed latent thermal energy storage unit influences the periodic flow characteristics of the latent thermal energy storage unit. The melting behaviors in each phase change material capsule are synchronous due to the excellent heat transfer capacity of the latent thermal energy storage unit. With the increasing initial temperature of the latent thermal energy storage unit, the duration of the charging process varies little, but the total heat storage capacity of the unit decreases. The decreasing diameter of the phase change material capsule significantly shortens the charging process of the latent thermal energy storage unit. The total heat storage capacities of the latent thermal energy storage unit with different phase change material capsule diameters are nearly the same. The heat storage capacity of the phase change material unit can be easily scaled up by adding more phase change material capsules and extending the phase change material capsule zone. The scale-up of the structured packed-bed latent thermal energy storage unit does not affect the charging time of the latent thermal energy storage unit.

Configurational explorations and optimizations of a phase change material based thermal energy storage with tube bundle

Compared to the extensive attentions paid to latent heat thermal energy storage (LHTES) with single tube in shell, the configurations of multiple serpentine tubes as bundles are less explored. Maldistributions of heat transfer and temperature along the heat transfer fluid (HTF) tube and charging process are barely discussed and improved. In this study, a numerical model is developed and validated. Targeting to charging process, effects of configurational parameters are revealed in detail with a focus on the maldistributions. Results show that a smaller tube pitch and a larger tube branch number benefit the charging time and charging power, while the dominant influence factor could switch from Reynolds number to heat transfer area. Moreover, the phase change material (PCM) temperature maldistribution exists for more than 50% of the charging time. Moreover, a chart with five classified zones to evaluate the charging time is proposed. Cases with unevenly allocated HTF tubes are further investigated. It is found that as the HTF inlet mass flow rate is 0.167 kg/s, the melting time of the two-region case and three-region case could be reduced by 11.1% and 14.1%, respectively. There exists a pseudo-minimum charging time when the HTF inlet mass flow rate is 1.667 kg/s.

Thermal performance investigation of finned latent heat storage of shell‐and‐tube, shell‐and‐nozzle, and shell‐and‐reducer models

AbstractThree models of latent heat storage with circular fins were studied numerically and experimentally in this paper. The models were shell‐and‐tube, shell‐and‐nozzle, and shell‐and‐reducer. These models were investigated for two different inlets of heat transfer fluid (HTF), from the bottom and top of the models, so the number of studied cases was six. The results of the comparison between the cases showed that the different HTF inlet with a fixed mass flow rate greatly affects the completion time of the melting process; the bottom inlet of HTF accelerates the melting compared to the top inlet because it enhances the role of natural convection. Compared with shell‐and‐tube with bottom HTF inlet, the shell‐and‐nozzle with bottom inlet reduces the melting time by 11.2%, while the shell‐and‐reducer with bottom inlet delays the melting by 24%. The results of the top HTF inlet cases showed that shell‐and‐nozzle delays the melting by 16% compared with shell‐and‐tube, while the melting is not completed in shell‐and‐reducer. Shell‐and‐nozzle with a bottom HTF inlet shows the shortest melting time and the best thermal performance among all the other cases due to the geometric design of the model. On comparing the numerical and experimental results, good agreement was found between them.

Design and thermodynamic analysis of an innovative parabolic trough photovoltaic/thermal system with film-based beam splitter

This study aims to find a feasible photovoltaic/thermal (PV/T) utilization method based on film-based beam splitting technology. In contrast with previous studies, the main novelty of this paper is proposing the design of an innovative PV/T system using both parabolic trough concentrator (PTC) and film-based beam splitter (FBS). The design approach of the PV/T system is presented. A new FBS used for this PV/T system is designed by using the Needle method, and its average reflectivity and transmissivity are 27.2% and 72.8%. By using Ray Tracing and Computational Fluid Dynamics (CFD) simulation methods, the performance evaluation of the PV/T system is conducted. The evaluation results reveal that when the East-West sun tracking error is 0.2°, the optical efficiencies of the photovoltaic module and the solar thermal collector tube (TCT) can be kept at 95% and 93.9%. Moreover, when the heat transfer fluid (HTF) in the TCT is selected to be the ethylene glycol, the operation analysis results demonstrate that the photoelectric efficiency of the photovoltaic module is 25.4% and the thermal efficiency of the PV/T system is 17.24%. The thermal performance of the system can be improved when the HTF flow velocity is increased properly or when the inlet HTF temperature is decreased. The technical feasibility of the proposed PV/T system can be revealed from the analysis results of this study.

Optimization design and performance investigation on the cascaded packed-bed thermal energy storage system with spherical capsules

Most of the previous researches on the cascaded packed-bed latent heat storage (CPTES) system are the thermal performance optimization based on numerical calculation. Experimental studies are few and mainly focus on single design parameter at low-temperature conditions. Lack of the detailed temperature - flow field experimental data and optimization scheme for the CPTES system. In this paper, an optimized two-layered filling structure of packed-bed heat storage system (OT-PTES) was proposed, which considers melting temperature of phase change material (PCM), capsule diameter, and filling volume ratio. The heat transfer process of PCM capsule and heat transfer fluid (HTF) during charging/discharging process were studied in detail by experiments. Under consistent working conditions, the average charging/discharging rate, total heat capacity, overall efficiency, and exergy efficiency was evaluated. And the influences of HTF inlet flow and the volume filling ratio of two-layered on thermal performance were analyzed. Finally, the concentric diffusion model was used to simulate the system to further optimize its hierarchical structure. The results are concluded as follows: (1) The temperature difference between PCM capsule and HTF at the interface changes continuously, and there is also an obvious temperature gradient in the radial direction of HTF, which improves the heat transfer efficiency. (2) Through experiments, the packed-bed with single large/small size PCM capsules are compared with the OT-PTES system. The overall efficiency of the latter is 74.2%, increased by 3.38% and 8.28%, and the exergy efficiency is 62.7%, increased by 7.5% and 52%. It is proved that the OT-PTES system has better charging/discharging performance. (3) When the volume filling rate = 1/2, the system has the best thermal performance (75.04%) and exergy efficiency (67.1%). (4) The numerical simulation results show that the overall performance of the packed-bed is optimal when the capsule size composition is 20–30 mm and the temperature difference of PCMs melting point is 60 ℃. In summary, OT-PTES is an optimized system with better heat storage performance. This study can provide experimental data support for the optimal design of the PLTES system and useful guidance for industrial applications.

Improving the melting performance of phase change material (PCM) in a latent heat thermal energy storage unit via a non-uniform arrangement of longitudinal fin

The application of latent heat thermal energy storage (LHTES) technology in solar energy utilization is greatly restricted by the low thermal conductivity of phase change material (PCM). This paper proposed a non-uniform arrangement of a longitudinal fin in a typical LHTES unit to improve the melting performance of PCM. Water is used as the heat transfer fluid (HTF) and paraffin (RT35) is selected as the PCM. A three-dimensional computational model is built to simulate the melting process of PCM, and its result is verified by experimental data. Firstly, the melting performance of PCM in the LHTES unit with four kinds of fin arrangements is comparatively studied, and its heat transfer mechanism is characterized via the maximum velocity of liquid PCM. In addition, the influences of HTF inlet temperature and flow rate, as well as heat transfer tube material on the complete melting time of three typical fin arrangements are also investigated. The results implied that the complete melting time of the non-uniform arrangement of the longitudinal fin reduces by 30.91% relative to the conventional longitudinal fin (Case 2). The results also revealed that the melting rate of PCM is related not only to the intensity of natural convection but also to the distribution of natural convection in the whole melting process.

Numerical investigation of a thermal energy storage system based on the serpentine tube reactor

Thermochemical heat storage (TCHS) technology is widely concerned for its high energy storage density (ESD) and long-term storage of energy in the form of chemical energy for long-term thermal storage applications. TCHS with hydrated salt as the thermochemical material (TCM) has low regeneration temperature, clean reaction products, and appropriate heat release temperature, which is suitable for the application of medium and low temperature applications. A 3D numerical model is developed to simulate and understand the hydration (heat discharging) process of the serpentine tube reactor filled with hydrate of K2CO3. The coupled multiphysics includes fluid flow, heat and mass transfer, and chemical reaction process. Variations of hydration characteristics, such as temperature and conversion, are discussed in detail. The heat discharging processes at different vapor pressure (1200 Pa–1600 Pa) and different inlet flow rates (0.5–5 m/s) of heat transfer fluid (HTF) are investigated. It is found that higher vapor pressure can significantly increase output temperature, and a higher HTF inlet flow rate can improve overall heat exchange performance. By increasing the vapor pressure from 1200 Pa to 1600 Pa, the maximum outlet temperature lift could be significantly increased by 7.9 %. However, pipe shape has little effect on enhancing the performance of the reactor.

Investigation on the Melting Performance of a Phase Change Material Based on a Shell-and-Tube Thermal Energy Storage Unit with a Rectangular Fin Configuration

A case study on the melting performance of a shell-and-tube phase change material (PCM) thermal energy storage unit with a novel rectangular fin configuration is conducted in this paper. Paraffin wax and circulated water are employed as the PCM and heat transfer fluid (HTF), respectively. It can be observed that the melting performance could be significantly improved by using rectangular fins. Melting photographs demonstrate that the melting of the PCM is firstly dominated by heat conduction; then, the melting rate is improved further due to natural convection. Moreover, the results illustrate that the influence of the inlet HTF temperature on the melting performance is significantly greater than that of the inlet HTF flow rate. The liquid fraction of paraffin wax in the PCM unit with a higher inlet HTF temperature is always higher than that with a lower inlet HTF temperature at the same time. The total charging time is reduced by 62.38% and the average charging rate is increased by 165.51% when the inlet HTF temperature is increased from 57 °C to 68 °C. As a result, a higher value of the inlet HTF temperature and a lower value of the HTF flow rate are able to improve the energy efficiency of the PCM unit with a rectangular fin configuration.

LSTM-BP neural network analysis on solid-liquid phase change in a multi-channel thermal storage tank

Latent heat thermal storage (LHTS) system is a crucial technology for achieving carbon neutrality and alleviating energy stress. Although metal foam can ameliorate the thermal storage rate of the LHTS system, the impact of the inlet velocity and temperature of heat transfer fluid (HTF) on the phase transition of phase change material (PCM) needs to be properly designed to achieve optimal performance. A novel multi-channel LHTS tank with metal foam is designed. A three-dimensional numerical model is established to describe the transient melting process in the LHTS tank. Besides, a new LSTM-BP neural network is developed, in which the HTF inlet velocity, temperature and time are employed as input data. Simulated results are consistent with the previous measurement data, verifying the correctness of the numerical methods. Results suggest that the whole melting time of the PCM is diminishing with increasing HTF velocity (or temperature). The machine learning prediction results show minor differences with the simulation results. The developed machine learning model provides new adaptive approaches for thermal storage design and operation.

Charging and discharging processes of low capacity nano-PCM based cool thermal energy storage system: An experimental study

The present study aims to investigate the performance of the low-capacity energy storage tank in different heat transfer fluid (HTF) conditions (at various flow rates) filled with spherical capsules containing nano-enhanced phase change material (nano-PCM). The nano-PCM is prepared by dispersing functionalized graphene nanoplatelets (f-GNP) with deionized (DI) water. The influence of HTF inlet temperature and volumetric flow rates on the total charging and discharging time of an energy storage tank filled with 35 spherical capsules are analyzed. The maximum reduction in total charging and discharging time of 18.26% and 22.81% is recorded for different HTF conditions. The amount of latent heat energy stored is nearly 5.5 times higher than the sensible heat stored at the HTF temperature of −4 °C. The cumulative energy recovery of 2637 kJ is recorded during the discharging process, which is 85.89% of the actual energy stored (3070 kJ) in the storage tank. In addition, the dispersion of f-GNP reduces the specific energy consumption (SEC) by around 28% for the nano-PCM at −4 °C HTF temperature. It is found that the required output temperature and average melting rate can be achieved in practical applications through the control of the flow rate of HTF and its inlet temperature.

Experimental analysis to improve charge/discharge of thermal energy storage in phase change materials using helical coil and porous metal foam

The use of phase change materials (PCM) for latent heat thermal energy storage (LHTES) is a common method of storing thermal energy in buildings. Because the thermal conductivity of the PCMs is low, so the rate of their energy charge/discharge would be confined. To overcome this issue, a new design is proposed using helical coil to maximize the contact surface between the heat transfer fluid (HTF) and the PCM. Both sides of the helical coil are filled with PCM, while in the inner region, copper metal foams (porosity of 0.9 and density of 12 PPI) are utilized for heat transfer rate enhancement. Effects of various parameters, including the inlet HTF flow rate, its temperature, and use of porous media on thermal energy storage performance in charge and discharge processes are analyzed experimentally. Six thermocouples are placed inside the PCM in different regions and melting and solidification processes are recorded using a thermal imaging camera. Results are presented in terms of temperature variation in different regions, temperature contours, mean temperature response, Stefan number, the charge/discharge time, and the extracted power of discharge. The results reveal that using porous media can remarkably reduce the charge/discharge time up to 57 %, which is depended on the inlet working fluid temperature. The charging time reduction is higher when the inlet HTF temperature increases. When the flow rate of HTF is increased, the charging time can be slightly shortened, while this effect becomes dominant when using porous media. Use of porous media could also accelerate the discharge time, while a faster discharge rate was observed for lower HTF flow rates during discharging the stored energy. Also, a lower initial temperature of the inlet HTF provides faster depletion rate.