Enhancement of the Thermal Energy Storage Using Heat-Pipe-Assisted Phase Change Material

: Usage of phase change materials’ (PCMs) latent heat has been investigated as a promising method for thermal energy storage applications. However, one of the most common disadvantages of using latent heat thermal energy storage (LHTES) is the low thermal conductivity of PCMs. This issue affects the rate of energy storage (charging/discharging) in PCMs. Many researchers have proposed different methods to cope with this problem in thermal energy storage. In this paper, a tubular heat pipe as a super heat conductor to increase the charging/discharging rate was investigated. The temperature of PCM, liquid fraction observations, and charging and discharging rates are reported. Heat pipe effectiveness was deﬁned and used to quantify the relative performance of heat pipe-assisted PCM storage systems. Both experimental and numerical investigations were performed to determine the efﬁciency of the system in thermal storage enhancement. The proposed system in the charging/discharging process signiﬁcantly improved the energy transfer between a water bath and the PCM in the working temperature range of 50 ◦ C to 70 ◦ C.


Introduction
The world energy demand has been increasing fossil fuel usage. However, due to the environmental impacts, the usage of fossil fuels has been discouraged and the use of passive techniques, renewable energies, energy storage, and electric vehicles has increased [1][2][3][4][5][6][7][8][9][10]. Therefore, the usage of thermal energy storage became more popular. Meanwhile, latent heat thermal energy storage (LHTES) is classified as a high energy storage density that decreases the storage volume compared with sensible thermal energy storage (STES) systems, which can result in less expensive thermal energy storage systems [11][12][13][14][15][16][17]. Phase change material (PCM) is known as a famous substance that is widely used for LHTES. PCMs are classified into organic and non-organic materials, like paraffin wax and salts. They can be used in many applications such as solar thermal energy, electronic and battery cooling, waste heat recovery, and building heating and cooling systems [18][19][20][21][22].
Recently, utilization of renewable and clean solar energy has been growing at a quick pace. LHTES is a perfect case in a solar power plant because of its constant storage temperature and high energy storage density [23]. The operation of an LHTES includes the exchange of energy between solar energy and PCM through the charging and discharging processes. Cooling and heating can be produced by solar radiation through one or two energy conversion steps.
Kuravi et al. [24] prepared a review regarding the thermal energy storage technologies for concentrating solar power plants. Behi et al. [25] experimentally and numerically investigated the possibility of using PCM in two different configurations for cold and heat storage. They connected the PCM storage to the evaporator and condenser. They considered the average performance of the system in a cooling/heating capacity, COP, and total efficiency. Nevertheless, the physical design of the LHTES applied in solar energy lacks new changes. Farid et al. [21] classified the thermal storage unit as an indirect or direct contact type in the PCM, in line with the physical design, though the primary heat transfer mechanism for both manners is almost the same. Most LHTES suffers low efficiency of the thermal storage because of the low thermal conductivity of the PCMs [21,26]. The main thermo-physical properties of PCMs, including thermal conductivity and latent heat, highly affect the performance of the LHTES [27][28][29][30][31].
A number of techniques have been utilized by researchers to increase efficiency enhancements of PCMs. Adding highly thermally conductive particles [32], nanomaterials [31,[33][34][35], fins [36], and heat pipes [37][38][39] are some examples of tools used to improve the thermal conductivity of the medium. Heat pipe systems have been widely used in various energy storage and heat transfer systems because of their suitability in the role of heat delivery and passive operation [40][41][42][43][44][45]. They can be used in many thermal storage applications. Nithyanandam and Pitchumani [46] designed gravity-assisted heat pipes for concentrating solar power. They considered the transient numerical simulations and the effect of the design and operating parameters on the system's dynamic charge and discharge performance. Tiari et al. [47] numerically investigated the effect of the finned heat pipes on the discharging process of latent heat thermal energy storage. They studied the effect of heat pipe spacing, natural convection, and fin length on the discharging rate of the PCM. Liang et al. [48] experimentally and numerically considered the latent thermal energy storage effect by flat micro-heat pipe array-metal foam configuration. Wang et al. [49] experimentally studied the heat transfer performance of the heat pipe on Nano PCM thermal energy storage. They experimentally considered the effect of fan power, thermal conductivity, and mass fraction of the nanocomposite.
Moreover, many studies have been conducted [50,51] on structural designs and heattransfer improvement of indirect-contact thermal storage units using numerical simulations. There have been fewer studies regarding direct contact heat storage units than indirect contact ones.
This study considered the charging/discharging of the heat-pipe-assisted thermal storage system so that the evaporator and condenser of the system are in direct contact with the heat pipe. During the charging process, the water tank plays the role of a heat source and the PCM container as heat storage. The heat is efficiently transferred from the surface of the heat pipe to the PCM storage in direct contact. During the discharging process, the heat is transferred from the PCM storage to the water tank. The new design prepares the direct evaporation and condensation in the system, which avoids conduction and convection between materials and makes the thermal storage system very efficient. The RT42 from Rubitherm was used as a PCM in this study. The results revealed that the system prepared in this study has good thermal storage characteristics, indicating that the heat-pipe-assisted PCM has excellent potential for thermal storage applications.

Experimental Material Setup
To consider the performance of the heat pipe-assisted PCM storage system, an experimental test rig was built. The schematic of the setup and the illustration of the actual structure are shown in Figure 1a,b, respectively. The test rig comprised a transparent glass cylinder with an inner diameter and height of 42 mm and 190 mm. A cylindrical aluminum structure are shown in Figure 1a,b, respectively . The test rig comprised a transparent glass  cylinder with an inner diameter and height of 42 mm and 190 mm. A cylindrical aluminum block with a diameter of 70 mm and a height of 100 mm with a hole diameter of 25  mm, and a height of 97 mm drilled from the bottom was selected as a holder. The holder  was placed in the source with a constant temperature  A length of 190 mm of the heat pipe was put inside the PCM cylinder and the remaining (100 mm) was exposed to the thermal bath at a constant temperature. The plastic washer was used to control the leaks. The top of the cylinder was enclosed with a lid with a hole for adding the PCM. The storage and the lid were connected to the block by three long pins. A thermal insulation cover was used to insulate the PCM storage to minimize ambient heat transfer. Figure 2 displays the schematic of the test setup. A cylindrical copper heat pipe with distilled water as a working fluid was used to perform the experiment. Table 1 represents the main features of the heat pipe. A length of 190 mm of the heat pipe was put inside the PCM cylinder and the remaining (100 mm) was exposed to the thermal bath at a constant temperature. The plastic washer was used to control the leaks. The top of the cylinder was enclosed with a lid with a hole for adding the PCM. The storage and the lid were connected to the block by three long pins. A thermal insulation cover was used to insulate the PCM storage to minimize ambient heat transfer. Figure 2 displays the schematic of the test setup. A cylindrical copper heat pipe with distilled water as a working fluid was used to perform the experiment. Table 1 represents the main features of the heat pipe.
A total of eleven K-type thermocouples were utilized to record all temperatures. In order to record the temperature at a different location of the PCM, six thermocouples were attached in a radius of 6 mm and 13 mm from the center of the cylinder and heights of 50 mm, 100 mm, and 150 mm of PCM cylinder. Thermocouples A, B, and C were placed for the radius of 6 mm and α, β, and θ for the radius of 13 mm for mentioned heights. In addition, three thermocouples were attached on the surface of the heat pipe at heights of 50 mm, 100 mm, and 150 mm, which have been specified by AH, BH, and CH. Holder constant temperature was measured by the average of two thermocouples attached to the holder. All thermocouples were cautiously calibrated, and the expected error of temperature was ±0.2 • C.   A total of eleven K-type thermocouples were utilized to record all temperatures. In order to record the temperature at a different location of the PCM, six thermocouples were attached in a radius of 6 mm and 13 mm from the center of the cylinder and heights of 50 mm, 100 mm, and 150 mm of PCM cylinder. Thermocouples A, B, and C were placed for the radius of 6 mm and α, β, and θ for the radius of 13 mm for mentioned heights. In addition, three thermocouples were attached on the surface of the heat pipe at heights of 50 mm, 100 mm, and 150 mm, which have been specified by AH, BH, and CH. Holder constant temperature was measured by the average of two thermocouples attached to the holder. All thermocouples were cautiously calibrated, and the expected error of temperature was ±0.2 °C.
The melting process has been measured for 50 °C, 60 °C, and 70 °C temperatures. The experiments were limited to a single PCM (RT42) from Rubitherm Company. A number of essential properties of RT42 are provided in Table 2.   The melting process has been measured for 50 • C, 60 • C, and 70 • C temperatures. The experiments were limited to a single PCM (RT42) from Rubitherm Company. A number of essential properties of RT42 are provided in Table 2.

Physical Model
As shown in Figure 3, the system consisted of a cylindrical heat pipe and PCM storage that covered 190 mm of the heat pipe. The storage part was filled with RT42 as PCM. The radius and length of PCM storage were 21 mm (rs) and 190 mm (ls), respectively. Additionally, the radius and length of the heat pipe were 3 mm (rh) and 290 mm (lh), respectively.

Physical Model
As shown in Figure 3, the system consisted of a cylindrical heat pipe and PCM storage that covered 190 mm of the heat pipe. The storage part was filled with RT42 as PCM. The radius and length of PCM storage were 21 mm (rs) and 190 mm (ls), respectively. Additionally, the radius and length of the heat pipe were 3 mm (rh) and 290 mm (lh), respectively.

Performance of the Heat Pipe
The heat pipe as a super heat conductor can transfer heat with high efficiency. Figure  4a describes the temperature variation of the heat pipe in a constant hot temperature of the bath. In the charging process, the bath temperature provided a constant 70 °C, whereas the PCM storage had a temperature of 23 °C. On the other hand, Figure 4b presents the wall temperatures of the heat pipe with a constant cold temperature of the bath. In the discharging process, the PCM was fully charged (70 °C), whereas the thermal bath was set at 23 °C. According to Figure 4a, at the beginning of the charging process, the heat pipe wall temperature increased rapidly due to its high thermal conductivity. Thus, it can explain the rapid rise of the heat pipe wall temperature during this step. However, as soon as the wall temperature of the heat pipe was more than the PCM phase change temperature, heat was transferred to the PCM through pure conduction. Therefore, the temperature rise rate slowed as the process continued. Figure 4b represents the discharging process. At the beginning of the process, the heat pipe wall cooled very quickly and transferred the heat from the PCM to cold water. Some non-uniformity can be seen in the heat pipe surface temperature during the discharging process. In this manner, the temperature gradient was low on the surface of the heat pipe. However, the heat pipe working flow

Performance of the Heat Pipe
The heat pipe as a super heat conductor can transfer heat with high efficiency. Figure 4a describes the temperature variation of the heat pipe in a constant hot temperature of the bath. In the charging process, the bath temperature provided a constant 70 • C, whereas the PCM storage had a temperature of 23 • C. On the other hand, Figure 4b presents the wall temperatures of the heat pipe with a constant cold temperature of the bath. In the discharging process, the PCM was fully charged (70 • C), whereas the thermal bath was set at 23 • C. According to Figure 4a, at the beginning of the charging process, the heat pipe wall temperature increased rapidly due to its high thermal conductivity. Thus, it can explain the rapid rise of the heat pipe wall temperature during this step. However, as soon as the wall temperature of the heat pipe was more than the PCM phase change temperature, heat was transferred to the PCM through pure conduction. Therefore, the temperature rise rate slowed as the process continued. Figure 4b represents the discharging process. At the beginning of the process, the heat pipe wall cooled very quickly and transferred the heat from the PCM to cold water. Some non-uniformity can be seen in the heat pipe surface temperature during the discharging process. In this manner, the temperature gradient was low on the surface of the heat pipe. However, the heat pipe working flow had to flow against gravity because the condenser part of the heat pipe was located in the bath. had to flow against gravity because the condenser part of the heat pipe was located in the bath.

Charging Curves and Phase Change Interfaces
In order to do the charging test, the PCM storage was filled with liquid PCM several times to confirm the absence of air bubbles. Next, the storage was kept at 23 °C for 24 h to reach the uniform temperature. To start the charging process, the bath temperature was set at 70 °C. Broad experiments were performed to test the performance charging of the PCM storage system embedded with a vertical heat pipe. Therefore, many melting curves of the PCM were obtained. Figure 5 displays the typical PCM temperatures at different radii of A, B, C, α, β, and θ in the axial direction, which were given in Figure 1, for a bath water temperature of 70 °C. As it can be seen, the phase change happened approximately between t = 600 s to t = 800 s in Figure 5a; however, it happened almost at t = 1000 s in Figure 5b. This phenomenon was more evident in comparison to thermocouples in the radius of 6 mm and 13 mm in Figure 5c-e.

Charging Curves and Phase Change Interfaces
In order to do the charging test, the PCM storage was filled with liquid PCM several times to confirm the absence of air bubbles. Next, the storage was kept at 23 • C for 24 h to reach the uniform temperature. To start the charging process, the bath temperature was set at 70 • C. Broad experiments were performed to test the performance charging of the PCM storage system embedded with a vertical heat pipe. Therefore, many melting curves of the PCM were obtained. Figure 5 displays the typical PCM temperatures at different radii of A, B, C, α, β, and θ in the axial direction, which were given in Figure 1, for a bath water temperature of 70 • C. As it can be seen, the phase change happened approximately between t = 600 s to t = 800 s in Figure 5a; however, it happened almost at t = 1000 s in Figure 5b. This phenomenon was more evident in comparison to thermocouples in the radius of 6 mm and 13 mm in  Figure 6 displays the temperature profile of the heat pipe and PCM for the charging process at t = 1200 s. It is obvious that the temperature difference in the axial direction of the heat pipe was less than 0.5 • C, which was tremendously smaller than the radial direction (more than 2 • C). This phenomenon demonstrates high efficiency, excellent temperature leveling ability, and minimal applied heat pipe thermal resistance in the axial direction [51].

Influences of Increasing Bath Water Temperature
As was expected, the hot water temperature had an imposing effect on the melting operation processes. Therefore, a significant number of experiments were done to study this effect. Figure 7a,b summarizes a number of typical results and shows the effect of hot water temperature on PCM temperature variation. Figure 6 displays the temperature profile of the heat pipe and PCM for the charging process at t = 1200 s. It is obvious that the temperature difference in the axial direction of the heat pipe was less than 0.5 °C, which was tremendously smaller than the radial direction (more than 2 °C). This phenomenon demonstrates high efficiency, excellent temperature leveling ability, and minimal applied heat pipe thermal resistance in the axial direction [51].

Influences of Increasing Bath Water Temperature
As was expected, the hot water temperature had an imposing effect on the melting operation processes. Therefore, a significant number of experiments were done to study this effect. Figure 7a,b summarizes a number of typical results and shows the effect of hot water temperature on PCM temperature variation. According to Figure 7, the increasing bath water temperature had a significant and direct influence on PCM temperature. Increasing the water temperature directly affected the inlet temperature of the evaporator, which was influenced by PCM temperature. It is observable that phase change time for the temperature of 70 °C decreased tremendously for both radii. The experimental results in Figure 7 demonstrate that the phase change the time for inlet temperature of 60 °C was less than 1600 s, which reduced to 800 s for 70 °C. On the other hand, the phase change time for a temperature of 50 °C was more than 2400 s.

Discharging Curves and Phase Change Interfaces
The solidification process is an application of the PCM that results from heat pipe cooling. In this manner, a section of the heat pipe located in the PCM plays the role of the evaporator. The group of solidification curves for different heights and radius can be seen in Figure 8. According to Figure 7, the increasing bath water temperature had a significant and direct influence on PCM temperature. Increasing the water temperature directly affected the inlet temperature of the evaporator, which was influenced by PCM temperature. It is observable that phase change time for the temperature of 70 • C decreased tremendously for both radii. The experimental results in Figure 7 demonstrate that the phase change the time for inlet temperature of 60 • C was less than 1600 s, which reduced to 800 s for 70 • C. On the other hand, the phase change time for a temperature of 50 • C was more than 2400 s.

Discharging Curves and Phase Change Interfaces
The solidification process is an application of the PCM that results from heat pipe cooling. In this manner, a section of the heat pipe located in the PCM plays the role of the evaporator. The group of solidification curves for different heights and radius can be seen in Figure 8. According to Figure 8, PCM cooled down and changed from the liquid to the solid state, which represents a normal solidification process. The discharging process was divided into three different areas, which are shown in Figure 8c. In the initial area, heat extracted from the PCM via the heat pipe (1500-2000 s) reached the phase change point. The heat that was absorbed by cold water was mainly the sensible heat of liquid PCM.
Due to the fact that heat storage capacity in the sensible area (1, 3) was really lower than latent heat area (2), the diminishing rate of the PCM temperature was quicker. In the next step, the process entered the second period (2000-6000 s). The temperature of the PCM diminished tremendously slower than in the initial period because of the latent heat effect. Finally, when the solidification of the PCM was complete, again, the heat was extracted as sensible heat from the PCM, which sped up the decline of the PCM temperature. According to Figure 8, PCM cooled down and changed from the liquid to the solid state, which represents a normal solidification process. The discharging process was divided into three different areas, which are shown in Figure 8c. In the initial area, heat extracted from the PCM via the heat pipe (1500-2000 s) reached the phase change point. The heat that was absorbed by cold water was mainly the sensible heat of liquid PCM.
Due to the fact that heat storage capacity in the sensible area (1, 3) was really lower than latent heat area (2), the diminishing rate of the PCM temperature was quicker. In the next step, the process entered the second period (2000-6000 s). The temperature of the PCM diminished tremendously slower than in the initial period because of the latent heat effect. Finally, when the solidification of the PCM was complete, again, the heat was extracted as sensible heat from the PCM, which sped up the decline of the PCM temperature.

Numerical Modeling
In this study, Fluent 14.5 software was used to simulate the PCM storage system's temperature distribution and liquid fraction. The geometry of the test setup was drawn in two dimensions and meshed using the Gambit software. The experimental test section was modeled using a 2D axisymmetric geometry. Boundary and initial conditions were defined and transferred into the Fluent software for further process. The liquid fraction and temperature contour of PCM have been described during the melting and solidification processes.

Descriptive Equations for PCM
The basic and fundamental governing equations for the PCM are divided by the following continuity, momentum, and energy equations [53]:

Numerical Modeling
In this study, Fluent 14.5 software was used to simulate the PCM storage system's temperature distribution and liquid fraction. The geometry of the test setup was drawn in two dimensions and meshed using the Gambit software. The experimental test section was modeled using a 2D axisymmetric geometry. Boundary and initial conditions were defined and transferred into the Fluent software for further process. The liquid fraction and temperature contour of PCM have been described during the melting and solidification processes.

Descriptive Equations for PCM
The basic and fundamental governing equations for the PCM are divided by the following continuity, momentum, and energy equations [53]: The scaled temperature of the PCM can be defined as follows: T 1 as a primary temperature, T m as a phase change temperature, T 2 as a final temperature (T 2 = T m + ∆T). A phase change (mushy zone) occurs between the solid and liquid zone within the time interval of ∆T. The phase of the PCM can be defined as below.
T * T 1 (Solid phase)T 1 < T * <T 2 (Mushy phase).T * T 2 (Liquid phase). The heat capacity can be defined as a value of phase change function, which depends on the PCM temperature [54]: The heat that the PCM can absorb is evaluated using the following equation: In Equation (7), m represents the mass of the PCM, while its thermal conductivity can be obtainable as follows: For the heat pipe simulation, it was replaced by a solid copper, and the effective thermal conductivity of components was used in the simulation [41][42][43][44]55].

Validation and Verification
To validate the simulation, the experimental results of the system were compared with the numerical ones. For both charging and discharging modes, the temperatures of PCM versus time were validated with experimental results. Figure 9a,b illustrates the average temperatures of the charging and discharging process versus time. As can be seen, the numerical results had an acceptable agreement with experimental ones.

Charging Process
Pictures taken in this configuration were compared with liquid fractions and temperature contours obtained with Fluent in Figure 10.

Charging Process
Pictures taken in this configuration were compared with liquid fractions and temperature contours obtained with Fluent in Figure 10. The PCM first melted surround the heat pipe wall, as expected. At the beginning of the charging process, PCM received the heat as a sensible form, which was mainly used to increase the temperature of the PCM to the phase change temperature. The melting process began when the PCM temperature reached the phase change temperature. First, a thin vertical PCM layer melted along the heat pipe wall from the bottom to the top, as noted in the liquid fraction contour at t = 800 s. As seen in the temperature contour at t = 800 s, the thermocouples in the radius of 6 mm passed the phase change area and reached 45 °C. However, the temperature of the thermocouples in the radius of 13 mm was 33 °C and still is in solid form. At t = 2400 s, thermocouples in a radius of 6 mm reach 55 °C and those in a radius of 13 mm, located in the mushy zone area, reached 42 °C. The mentioned modes are presented in the experimental temperature in Figure 5. Obviously, at t = 800 s, all the thermocouples that were located in radii of 6 mm and 13 mm, were located in a The PCM first melted surround the heat pipe wall, as expected. At the beginning of the charging process, PCM received the heat as a sensible form, which was mainly used to increase the temperature of the PCM to the phase change temperature. The melting process began when the PCM temperature reached the phase change temperature. First, a thin vertical PCM layer melted along the heat pipe wall from the bottom to the top, as noted in the liquid fraction contour at t = 800 s. As seen in the temperature contour at t = 800 s, the thermocouples in the radius of 6 mm passed the phase change area and reached 45 • C. However, the temperature of the thermocouples in the radius of 13 mm was 33 • C and still is in solid form. At t = 2400 s, thermocouples in a radius of 6 mm reach 55 • C and those in a radius of 13 mm, located in the mushy zone area, reached 42 • C. The mentioned modes are presented in the experimental temperature in Figure 5. Obviously, at t = 800 s, all the thermocouples that were located in radii of 6 mm and 13 mm, were located in a thin layer of melted PCM and solid PCM, respectively. They were approximately at temperatures of 45 • C and 33 • C, respectively. Moreover, at t = 2400 s, all the thermocouples in radii 6 mm and 13 mm were almost at the temperature of 55 • C and 42 • C, respectively.

Discharging Process
Pictures taken during the discharge process are compared with liquid fraction and temperature contours in Figure 11.

Discharging Process
Pictures taken during the discharge process are compared with liquid fraction and temperature contours in Figure 11.  Pictures taken during the discharge process are compared with liquid fraction and temperature contours in Figure 11. The temperature of the cold water was 23 • C. The PCM was heated to a given temperature (70 • C) with hot water in order to prepare the PCM storage for the discharging process. When the whole PCM temperature was steady and uniform, the test rig was put in cold water (23 • C), and the discharging experiment started. The discharging process began when the wall temperature of the heat pipe was equal to or lower than the solidification point. After a while, a thin layer of solid PCM covered the heat pipe wall from the bottom to the top, as noted in the liquid fraction contour at t = 1000 s. As seen in the temperature contour at t = 1000 s, the thermocouples in a radius of 6 mm were almost located in the phase change area (mushy zone) and reached 43 • C. Instead, the temperature of the thermocouples in the radius of 13 mm was 57 • C and they were still in the liquid form. As seen at t = 4200 s, thermocouples in a radius of 6 mm reached 31 • C and radius of 13 mm, located in mushy zone area, reached 40 • C. The mentioned numbers can be proven by the temperature evolution plots in Figure 8. As specified by dashed lines at t = 1000 s, all the thermocouples that were in the 6 mm radius were approximately located in the mushy zone PCM. They were almost at a temperature of 43 • C. Moreover, at t = 4200 s, all the thermocouples in the radii of 6 mm and 13 mm were almost at the temperatures of 57 • C and 40 • C, respectively.

Temperature and Liquid Fraction Contours during the Charging Process
The PCM's numerical temperature and liquid fraction contours during the charging process (T = 70 • C) can be seen in Figure 12. The vertical axes show the heat pipe wall (right side) and the horizontal axes show the radius of PCM storage (downside). Thermal transport was happening between the hot water and the liquid surface of the PCM. At the beginning time of the melting process, PCM received the heat via the heat pipe from the hot water in a sensible form. Utilizing this heat, the temperature of PCM gradually increased to the melting point. The melting process started once the wall temperature of the heat pipe was equal to or higher than the melting point of PCM. The heat was transferred to the PCM by pure conduction before melting, and the temperature increased almost linearly with time.
According to the contours in primary time, due to the high efficiency of the heat pipe and low thermal conductivity of PCM, the temperature of the heat pipe increased very quickly. It is noticeable that the temperature rise inside the PCM storage increased with time, and solidified layer thickness of PCM storage decreased. It can be seen that after t = 2400 s, 50% of the PCM temperature was more than the melting point, and finally, at t = 6600 s, the total PCM storage temperature was more than the melting point. Figure 13 depicts the PCM's numerical temperature and liquid fraction contours during the solidification process (T = 23 • C) from the beginning until the end of the process. Temperatures contours show the solidification process for seven different periods. According to the colors, the solidified and melted parts are defined from the blue to red areas, respectively. Thermal transport occurred at the interface of the liquid surface of the PCM and cooling water bath. According to Figure 13, PCM was cooled from the liquid to the solid state. Utilizing the heat pipe, the temperature of PCM decreased to the solidification point. The solidification process started once the wall temperature of the heat pipe was equal to or less than the phase change temperature of PCM. Temperature decreased inside the PCM storage by increasing the time and solidified layer thickness of PCM increased. It can be seen that more than 50% of PCM was solidified after t = 4200 s and, finally, at t = 8000 s, total PCM temperature was less than phase change temperature. transport was happening between the hot water and the liquid surface of the PCM. At the beginning time of the melting process, PCM received the heat via the heat pipe from the hot water in a sensible form. Utilizing this heat, the temperature of PCM gradually increased to the melting point. The melting process started once the wall temperature of the heat pipe was equal to or higher than the melting point of PCM. The heat was transferred to the PCM by pure conduction before melting, and the temperature increased almost linearly with time. According to the contours in primary time, due to the high efficiency of the heat pipe and low thermal conductivity of PCM, the temperature of the heat pipe increased very quickly. It is noticeable that the temperature rise inside the PCM storage increased with time, and solidified layer thickness of PCM storage decreased. It can be seen that after t = 2400 s, 50% of the PCM temperature was more than the melting point, and finally, at t = 6600 s, the total PCM storage temperature was more than the melting point. Figure 13 depicts the PCM's numerical temperature and liquid fraction contours during the solidification process (T = 23 °C) from the beginning until the end of the process. Temperatures contours show the solidification process for seven different periods. According to the colors, the solidified and melted parts are defined from the blue to red areas, respectively. Thermal transport occurred at the interface of the liquid surface of the PCM and cooling water bath. According to Figure 13, PCM was cooled from the liquid to the solid state. Utilizing the heat pipe, the temperature of PCM decreased to the solidification point. The solidification process started once the wall temperature of the heat pipe was equal to or less than the phase change temperature of PCM. Temperature decreased inside the PCM storage by increasing the time and solidified layer thickness of PCM in-

Conclusions
In this study, a heat-pipe-assisted PCM system was built to improve the rate of energy storage (charging/discharging). Experiments were performed to investigate the thermal behavior of PCM in the presence of the heat pipe. A 2D axisymmetric numerical model was built and validated by experimental data. The following conclusions were drawn.

•
The wall temperature profile along the heat pipe length at 100 mm, 150 mm, and 200 mm was experimentally considered in the charging and discharging processes. It was found that the faster temperature changes in the heat pipe may result in higher thermal efficiency.
• The PCM temperature evolutions as a function of the axial position in charging and discharging processes were monitored using the six thermocouples in the radii of 6 mm and 13 mm.

•
The influence of the thermal bath temperature (50 • C, 60 • C, and 70 • C) on the phase change time of the PCM has been investigated. It was found that the hotter temperature resulted in lower phase change time.

•
The PCM storage picture, liquid fraction, and temperature contour have been compared in different charging and discharging times.

Future Work
The advantage of using the energy storage embedded with a heat pipe was considered in the present study. Since the heat pipes are gravity-dependent, the heat transfer efficiency of the presented system can be considered in different inclination angles for future studies. Moreover, the role of fin, graphite, nanomaterial, mesh, and so on can be considered to increase the rate of energy storage.