Thermal Performance Assessment of Heat Storage Unit by Investigating Different Fins Configurations

Abstract

Energy shortage is a significant global concern due to the heavy reliance of industrial and residential sectors on energy. As fossil fuels diminish, there is a pressing shift towards alternative energy sources such as solar and wind. However, the intermittent nature of these renewable resources, such as the absence of solar energy at night, necessitates robust energy storage solutions. This study focuses on enhancing the performance of a thermal storage unit by employing multiple fin configuration with solar salt (NaNO₃-KNO₃) as a phase change material (PCM) and Duratherm 630 as a heat transfer fluid (HTF). Notably, W-shaped and trapezoidal fins achieved reductions in melting time from 162 min to 84 min and 97 min, respectively, while rectangular fins were the least effective, albeit still reducing melting time to 143 min. Reduction in thermal gradients due to well-developed thermal mixing significantly reduced phase transition duration. Impact of fins geometries on localized vortexes generation within the unit was identified. W-shaped and trapezoidal fins were notably efficacious because of greater heat transfer area and better heat distribution through conduction and convection.

1. Introduction

Today, global shortage of energy stands as one of the most formidable challenges facing the world. Energy supply needs to be increased linearly with energy requirements and this dependency is projected to widen further by the century’s end. Traditionally, fossil fuels have served as the primary source of power generation over the past few decades. However, burning these fuels in power plants releases toxic gases that are harmful to both society and the environment. Moreover, the availability of fossil fuels is depleting, with reports predicting their near-complete exhaustion by the middle of this century [1]. Therefore, there is a pressing need to explore alternative, environmentally friendly sources of power. Renewable energy sources such as solar and wind can play a vital role in mitigating global warming [2]. The sun is an immense but intermittent source of energy, with its supply ceasing at night. Therefore, storing energy becomes crucial, especially during the day when massive energy reaches the Earth by sunlight [3]. This excess energy can be effectively utilized by integrating a Thermal Energy Storage (TES) unit with solar collectors [4]. TES stores energy by employing two main techniques: latent heat energy storage (LHES) and sensible energy storage (SHES). Phase change materials (PCMs) are very popular due to transitioning of their state upon exposure to heat, while SHES are also part of LHES when temperature increases to melting point. Beyond melting point, LHES is efficacious due to zero temperature fluctuations [5]. LHES is often preferred because of its greater energy storing capacity per unit volume and the wide availability of diverse PCMs [6].

PCMs are widely used in various applications such as waste heat recovery, building heating and cooling, and energy storage [7]. Hosseini et al. conducted a study to assess the performance of a heat exchanger using paraffin as a PCM. They observed a significant reduction of approximately 38% in melting time with an increase in the inlet temperature of the heat transfer fluid (HTF). The liquid fraction expanded from the HTF tubes toward the shell side, which ultimately improved the storage efficiency [8]. Furthermore, Hosseini and colleagues evaluated the thermal performance of the storage unit by comparing it with experimental results. Their findings indicated that an increase in the inlet temperature of the HTF enhanced both charging and discharging efficiencies. Furthermore, they investigated the impact of fins dimensions on heat flow, which directly affects the charging and discharging times. Their findings revealed that increasing the fin length not only reduced the melting time but also increased the heat density within the storage tank [9]. The rate of solidification is closely linked to the HTF inlet temperature. Ismail et al. conducted a numerical study to enhance the phase transformation of PCM in a cylinder, finding that lowering the HTF inlet temperature accelerated the solidification process [10]. Bathelt and Viskanta studied an analytical approach to assess its effectiveness for a storage unit filled with paraffin. Their results indicated swift change in phase during melting in top region of storage unit as compared to the bottom [11]. Additionally, further analysis of a triple pipe heat exchanger through computational methods identified other critical performance factors. Notably, the space between high temperature carrying fluid and the boundary wall of the storage was deemed a crucial factor for optimizing the unit’s performance [12].

The melting behavior of PCMs shows that efficiency and heat transfer are strongly influenced by the geometric configuration of fins, including their size and shape. Although PCMs are widely used for energy storage, they have a major limitation: their inherently low thermal conductivity, which restricts the rate of heat transfer during melting and solidification phases [13]. To address this, several strategies have been proposed, such as PCM encapsulation, the use of fins made of different materials, and the incorporation of nanoparticles to enhance thermal properties [14]. Considering the rising importance of energy utilization, storage efficiency has become a critical factor. Recent efforts to improve heat distribution in TES systems have demonstrated that the addition of nanoparticles can significantly enhance performance [15]. In particular, the use of hybrid PCMs has been shown to substantially reduce charging time.

Enhancing the thermophysical properties of PCMs through the use of nanoparticles (NEPCMs) and metal foam composites has shown considerable advantages in heat transfer performance. However, their large-scale adoption remains constrained by several practical limitations. The fabrication of NEPCMs requires advanced facilities, efficient dispersion techniques, and low-cost nanoparticle availability that are particularly challenging in developing regions where such materials are not readily accessible [16]. Likewise, metal foam composites improve thermal conductivity but are associated with higher manufacturing costs and concerns regarding long-term structural reliability. In contrast, finned structures are widely available, easy to manufacture, and economical to incorporate into shell-and-tube latent heat storage systems [17]. Thus, fins provide a more practical and scalable solution for real-world applications, especially in markets where nanoparticles or metal foams are not feasible options [18].

Experimental study conducted to compare the thermal performance of storage units with and without extended surfaces. They found fluid temperature at inlet and quantity of fins was critical for accelerating phase shift. Additionally, extended surfaces mitigate disturbances in fluid movement [19]. Effects of various parameters such as fluid thermal condition, the distance between fins, and mass of fluid on performance of storage system was investigated and found that the average thermal behavior of phase change materials improved with an increase in the number of finned pipes [20]. Numerical approach was employed to analyze the phase change behavior of paraffin in a triple tube type storage system. Their findings indicated that the melting time was reduced by 44% in a triple tube storage setup without fins [21]. The impact of fin positioning on the phase transitioning ultimately influences the performance of triple tube storage by employing both internal and external fins [22]. The role of natural convection in the phase change process has been investigated through various experiments conducted on multi-tube heat storage devices. Findings revealed that the presence of multiple convective positions reduces the solid–liquid conversion time [23]. In addition, a numerical study on the thermal efficiency of heat storage systems indicated that geometric configuration strongly affects both charging and discharging times, leading to improved heat distribution [24]. Furthermore, the impact of device orientation on performance was numerically examined. Results showed that convection plays a crucial role during both charging and discharging phases, with longitudinal orientation significantly enhancing storage efficiency [25].

TES unit featuring two PCMs and a novel shape for fins was studied, a significant reduction of 14% in charging-discharging time compared to traditional setups. Fin shape influenced thermal performance of TES due to improved heat distribution, as tree-shaped and snowflake patterns. These innovative fin designs greatly accelerated the melting process in a shell and tube type storage unit. A comparative analysis between TES systems with and without fins indicated that a tree type fin structure was particularly effective in speeding up the conversion process [26]. Using hybrid organic PCM (paraffin) blending with nanoparticles for an enhancement in efficiency, carbon nanotubes and graphene-based nanoplatelets were added for the improvement of temperature distributions withing TES. These findings linked addition of these nanoparticles and their impact on TES charging durations [27,28].

Blending of inorganic PCMs with nanoparticles imparted positive impact on thermal performance, a 21% reduction in charging time as compared to pure salts, making hybrid salts a preferable option [29,30]. Eutectic salts are considered suitable due to better thermal properties; performance of a TES system using KNO₃-NaNO₃ as PCM and Duratherm as HTF was investigated using numerical analysis. The analysis focused on the effect of geometric configuration, such as the number of HTF tubes, on the melting time. Results demonstrated that increasing the number of HTF tubes significantly decreased charging time; with four HTF tubes, melting occurred in 162 min compared to 234 min with just one HTF tube [31].

Numerous studies have been conducted to improve the thermal performance of TES units through various techniques. In this study, an innovative method is proposed for enhancing the performance of latent heat energy storage (LHES) system. Hence, this paper examines the impact of different fin configurations on reducing charging time. Geometric configurations such as rectangular, C-shaped, double J-shaped, W-shaped, and trapezoidal fins are employed. To enhance convective heat transfer, this study emphasized increasing the surface area and promoting local vortex generation by employing different shapes for extended surfaces inside storage tank. A thermal assessment was performed to compare the simple rectangular fins with the proposed fin designs. The complete study is conducted regarding fins configuration effect on charging durations of triple tube heat exchanger mentioned in ref study [31]. The charging time, temperature variations, and the quantity of liquid phase across the length of the storage unit are evaluated in this study. Melting/charging duration is the direct measure of storage efficiency and thermal variations inside storage system are the ultimate cause of this phase shift.

2. Materials and Methods

2.1. Geometric Configuration

Figure 1 illustrate the complete working methodology of this study. The HTF, Duratherm oil circulates in a closed-loop system, moving from a solar energy collecting device to an overhead hot fluid supply tank and then to a heat storage tank. Figure 2 displays the geometric configuration of fins used to improve the performance of the LHES system. Overhead supply tank is employed to accommodate oil expansion caused by temperature fluctuations. However, the focus of this study is on evaluating the performance of a latent heat storage tank with different fin configurations. The dimensional specifications are presented in

Table 1. Geometry dimensions.

Dimensions of Storage Tank (mm)
Length	1000
Outer Diameter	200
Diameter of central pipe	150
Diameter of HTF pipe	15
Maximum height of fin	15

and are consistent with those of the reference study, except for the fin design. The fins are 15 mm high to increase the surface area of the HTF tubes. A uniform thickness of 2 mm was maintained for the fins, tubes, and storage tank. Copper fins and copper HTF tubes were selected to facilitate rapid heat dissipation toward the PCM.

Table 2. Thermo-physical properties of PCM (KNO₃-NaNO₃) [30]. Reproduced with permission from Atif Shazad, Thermal performance enhancement of latent heat energy storage unit, published by Journal of Thermal Analysis and Calorimetry, 2025.

Properties	Values
Density	1796 kg/m3
Thermal Conductivity	0.55 W/(m.K)
Thermal Expansion Coefficient	54.7 × 10−6 °C−1
Cp	0.75 if T ≤ 383 K 4.1 if 383 < T ≤ 388 K 1.4 if 388 < T ≤ 488 K 12 if 488 < T ≤ 498 K 1.6 if T > 498 K
Liquidus Temperature	495 K
Solidus Temperature	487 K
Pure Solvent Melting Heat	102 kJ/kg

and

Table 3. Thermo-physical properties of Duratherm 630 oil [30]. Reproduced with permission from Atif Shazad, Thermal performance enhancement of latent heat energy storage unit, published by Journal of Thermal Analysis and Calorimetry, 2025.

Properties	Value	Temperature Range
Thermal Expansion Coefficient	0.001012 °C−1	-
Thermal Conductivity	0.143–0.13 W/m·K	298 K–500 K
Density	0.684 d/mL	-
Specific Heat	1.9–2.90 kJ/kg·K	308 K–580 K

demonstrate the thermophysical properties of the PCM and HTF, respectively. KNO₃-NaNO₃ (40/60) was used as the PCM due to its suitable melting point. Figure 2 displays the fin configurations; five different configurations were used to explore improvements in heat distribution within the LHES unit.

2.2. Boundary Conditions

To minimize volume variations across all fin models, the height of each fin was carefully selected. The W fin and the trapezoidal fin were made a little shorter than the other three types, while taking into account their increased surface area and its impact. The number of extended surfaces enhances heat distribution and reduces temperature discrepancies. The central pipe of the storage tank was filled with PCM, whose thermophysical properties are summarized in Table 2. Two paths for the HTF were chosen: an external tank and four HTF tubes. Duratherm 630 (manufactured in USA) and known for its excellent properties at high temperatures, was used as the HTF. The flow rate of the HTF and the initial conditions were kept constant across all numerical simulations.

The inlet temperature of the HTF was maintained at a constant 300 °C in all cases to evaluate the impact of different fin geometries. Tank external surface was designated as an adiabatic boundary to prevent heat loss. The boundary conditions are appended in Equation (1) to Equation (7) below:

• Internal heating of HTF pipe:

$$\mathrm{i}\mathrm{n}\mathrm{n}\mathrm{e}\mathrm{r} \mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{H}\mathrm{T}\mathrm{F} \mathrm{p}\mathrm{i}\mathrm{p}\mathrm{e}, r=r_{1i} \to T=T_{HTFT}$$

(1)

$$\mathrm{a}\mathrm{t} \mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{o}\mathrm{f} \mathrm{H}\mathrm{T}\mathrm{F} \mathrm{p}\mathrm{i}\mathrm{p}\mathrm{e}, r=r_{1m } \to {\displaystyle \frac{\partial T}{\partial r}}=0$$

(2)

• External heating of HTF pipe:

$$\mathrm{i}\mathrm{n}\mathrm{n}\mathrm{e}\mathrm{r} \mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{o}\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{p}\mathrm{i}\mathrm{p}\mathrm{e}, r=r_{3i} \to {\displaystyle \frac{\partial T}{\partial r}}=0$$

(3)

$$\mathrm{a}\mathrm{t} \mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{o}\mathrm{f} \mathrm{o}\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{p}\mathrm{i}\mathrm{p}\mathrm{e}, r=r_{3m} \to T=T_{HTFT}$$

(4)

• Internal and external heating:

$$\mathrm{i}\mathrm{n}\mathrm{n}\mathrm{e}\mathrm{r} \mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{l} \mathrm{p}\mathrm{i}\mathrm{p}\mathrm{e}, r=r_{2i} \to T=T_{HTFT}$$

(5)

$$\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{H}\mathrm{T}\mathrm{F} \mathrm{p}\mathrm{i}\mathrm{p}\mathrm{e}, r=r_{1out} \to T=T_{HTFT}$$

(6)

• Initial temperature:

$$\mathrm{a}\mathrm{t} t=0 \to T=T_{ini}$$

(7)

2.3. Validation of Current Study with Experimental and Numerical Studies

Validation was performed to assess variation between melting performance of an experimental study [32] with this current study. Figure 3 depicts phase shifting of PCM (RT-82) using an experimental setup by Ref. [32] and a numerical approach. The physical model utilized for this experimental and numerical study is represented in Figure 4, a triple tube heat exchanger which contains PCM in the central pipe. Mushy zone constant value is set for 10⁵ for validating this study. The PRESTO scheme was employed for pressure correction, while the SIMPLE algorithm was used for pressure–velocity coupling. Relaxation factors were assigned as 0.3 for pressure, 0.2 for velocity, and 1 for energy. A time step of 0.5 s yielded the most accurate simulation results, and a residual value of 10⁻⁶ was considered as the convergence criterion. Flow rate HTF was set at 8.3 L/min. Results shown in Figure 3 representing good agreement between both studies.

Another validation was performed for assessing PCMs melting and solidification behavior using an enthalpy-porosity approach on Ansys 2024 R2 software (CFD Fluent) for validating numerical study by Mahad et al. Ref. [31]. SIMPLE, QUICK, and PRESTO schemes are used for solving governing equations and pressure correction, respectively. Figure 5 demonstrates the melting profile of both studies, and findings illustrated that the liquid profile of the current study was following very closely to liquid profile of reference study [31]. The mesh convergence study represented in Figure 6 shows that difference in results output was negligible beyond 12 million mesh. Simulations were performed as shown in Figure 7 by comparing results of some initial runs with melting data of Ref. [31]. Red color in these initial runs represented complete liquid transition while blue color indicated solid phase. Fine mesh with inflation layers as represented in Figure 8 was used for independence study. Inlet temperature of HTF for base model validation was set at 300 °C and inlet mass flow rate of HTF was maintained at 0.03 kg/s. The unconditional stability of the implicit solver enabled the use of a consistent time step of 0.5 s for all solidification/melting simulations, ensuring both accuracy and stability. For high accuracy, the residual convergence criteria were set to 1 × 10⁻⁶ for continuity, momentum, and energy.

2.4. Governing Equations

In mathematical formulation, following assumptions are important to consider:

i.

Laminar flow approach

ii.

Navier–Stokes and thermal energy equations are recommended for incompressible viscous flow and heat dissipation in circular area due to very low value of viscous dissipation

iii.

Incompressible and unsteady flow

iv.

Pressure drops assumed to be negligible because of no resistance offered to HTF flow as pipe internal area is free from any obstacles

v.

Boussinesq approximation for melting due to convection (natural). This approximation is expressed as Equation (8).

$$\rho ={\rho }_1\left(1-\beta (T-T_1)\right)$$

(8)

Continuity and momentum terms are expressed as Equations (9) and (10)

➢

Continuity Equation:

$$\nabla .\stackrel{⃑}{V}=0$$

(9)

➢

Momentum Equation:

$${\displaystyle \frac{\partial V}{\partial t}}+\stackrel{⃑}{V}.\nabla \stackrel{⃑}{V}={\displaystyle \frac{1}{\rho }}\left(-\nabla P+\mu {\nabla }^2\stackrel{⃑}{V}+\rho \stackrel{⃑}{g}\beta \left(T-T_{ref}\right)\right)+\overrightarrow{S}$$

(10)

$$\overrightarrow{S}={\displaystyle \frac{({1-\lambda )}^2}{{\lambda }^3}}{A}_{mush}\stackrel{⃑}{V}$$

(11)

Equation (11) demonstrated a term relevant with damping. This term is a part of Darcy law and employed with momentum equation to produce smooth phase shift in convection mode. Mushy zone constant A_mush ranges between 10⁴ to 10⁷; in this study, it is assumed to be 10⁶.

➢

Equation (12) is used as the energy equation:

$${\displaystyle \frac{\partial h}{\partial T}}+{\displaystyle \frac{\partial H}{\partial T}}+\nabla .\left(\stackrel{⃑}{V}h\right)=\nabla .({\displaystyle \frac{K}{\rho C_{p }}}.\nabla h)$$

(12)

where H represents Material Enthalpy, and it is calculated using Equation (13):

$$H=h + ∆H$$

(13)

and h can be measured by using Equation (14)

$$h=h_{ref}+{\int }_{T_{ref}}^T{C}_{p}dT$$

(14)

Latent energy part in total heat can be replaced by L, as shown in Equation (15):

$$∆H=\lambda L$$

(15)

$∆H$ ranges from zero to maximum, zero in solid phase and maximum in liquid phase. Equation (16) is utilized for liquid fraction (LF).

$$\lambda =\left\{\begin{array}{cc}{\displaystyle \frac{∆H}{L}}=0& if T< T_s\\ {\displaystyle \frac{∆H}{L}}={\displaystyle \frac{T-T_s}{T_{liq-}{T}_s}}& if T_s<T<T_{liq}\\ {\displaystyle \frac{∆H}{L}}=1& if T>T_{liq}\end{array}\right.$$

(16)

3. Results

In this study, various fin configurations were employed to enhance both sensible and latent heating. Initially, the PCM is in a solid state, where sensible heating dominates, raising its temperature from room level to the melting point primarily through conduction. Once the melting point is reached, latent heating begins, and the dominant mode of heat transfer shifts from conduction to convection.

Table 4. Increment in surface area.

Serial. No	Fin Configuration	Effective Surface Area for Single Fin (mm2)
1	Rectangular	17,030
2	Double J-shaped	22,880
3	C-shaped	26,400
4	Trapezoidal-shaped	28,160
5	W-shaped	31,680

presents the corresponding increase in surface area.

3.1. Rectangular Fins

Evaluation of impact of fin geometry (rectangular shape) on the melting behavior of phase change materials was conducted and fins were mounted to HTF pipes. Results were then compared with those in reference [31] to accurately assess thermal performance. Figure 9 illustrates the phase change of PCM over time. The melting process was closely monitored at different points within the tank.

Notably, 90% of the PCM melted in 135 min, with complete melting observed around the 143 min mark. Rapid melting occurred near the HTF pipes due to a significant temperature differential, whereas the central region, hindered by the PCMs poor thermal conductivity as began to melt after 60 min. The rectangular fins promoted heat dissipation due to enhancement in thermal conductivity shown in Figure 9a,b. After 60 min, the mode of heat transfer shifted from conduction to convection as the amount of liquid PCM increased. Natural convection, driven by buoyancy forces, accelerated heat transfer as the less dense liquid moved toward the top of the storage tank. Localized vortices at the solid–liquid interface may promote a rapid phase transition, but they are not very pronounced due to PCMs higher viscosity. Thermal variations are illustrated in Figure 10, where the heat gradients highlight the phase transition behavior with respect to temperature. In Figure 10a, the PCM remains in the solid state; however, temperature distributions indicate effective heat transfer.

3.2. Double J-Shaped Fins

The melting of PCM was significantly influenced by the shape of the extended surfaces, employing double J-shaped fins resulting in enhanced melting rates with complete melting achieved within 128 min. Figure 11 demonstrates the melting and charging process, showing that double J-shaped fins outperformed rectangular fins, with more than 80% of the PCM transitioned to a liquid state under 120 min. PCM adjacent to HTF tubes shifted their phase swiftly as compared to rectangular fins due to improvement in thermal conductivity because surface area was increased.

Mode of conduction was responsible for PCM melting in close vicinity of HTF tubes, however liquid salt starts exhibiting temperature driven buoyancy effects which ultimately promoted convective heat transfer. Major quantity of PCM was in liquid and plastic state within 90 min due to enhanced thermal distribution. Temperature gradient in Figure 12 within the tank illustrates the distribution of heat from HTF to PCM. Figure 12a,b represent transition of PCM after 60 min and 90 min, respectively. Most of the liquid after 90 min was shifted to a viscous state.

Hence, Figure 11 witnessed major phase transition from solid to viscous PCM. Temperature after 120 min was almost equal to liquidus point, which indicate complete phase shift to liquid. The change in shape significantly ameliorated thermal performance of storage tank by reducing melting time from 143 min to 128 min for rectangular and double J type fins, respectively.

3.3. C-Shaped Fins

C-shaped fins facilitated the charging/melting of the PCM within 116 min. Localized vortex generation intensified due to swirl effect. The orientation of rectangular fins was modified into a curved, C-shaped design, resulting in an increased surface area. This geometric configuration enhanced both conduction and convection heat transfer, with natural convection arising from buoyancy forces caused by temperature-dependent density gradients, as illustrated in Figure 13. A major portion of the PCM completed its phase transition within 90 min of charging. Thermal gradients observed at 30 min indicated a more uniform heat distribution within the storage tank, primarily due to the effectiveness of conduction.

After 90 min of charging, temperature raised far enough to shift the state of large proportion of solid PCM into viscous and liquid form, as shown in Figure 14. The shapes of these fins were selected intentionally to possess greater surface area due to its direct impact on heat distributions. However, shapes can influence the convective mode by generating very minute localized vortices. These thermal gradients are corroborated by liquid fraction results. C-shaped fins enhanced thermal performance as compared to double J-shaped fins by mitigating charging duration from 128 min to 116 min.

3.4. Trapezoidal Fin

Figure 15 illustrates that the melting process occurred significantly faster with the incorporation of trapezoidal fins, achieving complete melting within 97 min. The trapezoidal fin design offers a larger heat transfer surface area compared to previously discussed geometries. The broader contact surface facilitates more efficient conduction of heat from the heat sources to the solid PCM, particularly during the initial stages.

Thermal conduction was improved which ultimately resulted in rapid heat transfer and faster charging process. Faster thermal distribution due to large surface area of these fins generated stronger buoyancy-driven convection currents, where the molten PCM rises while the cooler PCM descends. The solid–liquid interface indicated very localized vortexes which are responsible for swift convection due to improved thermal mixing, reduced thermal resistance in the liquid PCM, and ensured more uniform heat distribution throughout the system.

The study revealed increment in thermal performance due to reduction overall melting duration from 116 min for C-shaped fins to 97 min for trapezoidal fins. Thermal distribution represented in Figure 16 confirmed the variations in liquid fraction for different charging durations.

3.5. W-Shaped Fin

Figure 17 demonstrates that the use of W-shaped fins reduced the PCM melting time to 62 min. The improved thermal conduction is attributed to the increased fin surface area as shown in Table 4. The larger surface contact with the heat source allowed for a faster initiation of melting compared to other fin configurations, ensuring rapid heat penetration into the PCM. This proved particularly beneficial in regions previously identified as thermal dead zones when using trapezoidal fins. The complex geometry of the W-shaped fins further enhanced the formation of stronger and more numerous localized vortices at the solid–liquid interface.

Initially, conduction was the dominant heat transfer mode due to the solid state of the PCM; however, as melting progressed, convection became increasingly significant and accelerated the phase transition process after 30 min of charging. Complete melting was achieved in 84 min because of W-shaped fins. W-shaped fins effectively enhanced heat transfer by conduction and convection modes. Charging duration was reduced from 97 min for trapezoidal fins to 84 min for W-shaped fins. Figure 18 illustrates variation in thermal content, after 75 min of charging; it is clearly depicted that temperature reached its highest limit beyond viscous temperature range. In viscous range, the behavior of PCM changed from solid PCM to highly viscous PCM; this state is very close to liquid PCM.

4. Discussion

This comparison illustrates impact of different fins shape on charging duration and amount of liquid PCM. Melting time comparison of different fins as shown in Figure 19 revealed that approximately 47% of the PCM melted under 90 min and remaining 53% melted within 53 min due to strong convection mode and localized mixing of PCM near tip of rectangular fins. The results show that 68% of the PCM transitioned from a solid to a viscous liquid state by utilizing double J-shaped fin during 90 min of charging, where conduction was the dominant mode of heat transfer.

The line curve for double J-shaped fin illustrated that a higher proportion PCM change to liquid compared to the case with simple rectangular fins. The charging duration for C-shaped fins was also significantly shorter than that of rectangular fins, reducing the total charging time from 143 min to 116 min. During the early stage of the charging process in C-shaped fins, conduction dominated, with 34% of the PCM undergoing phase transition. However, an abrupt slope change, as observed in Figure 19, indicates the increasing influence of convection, which became the prominent mode of heat transfer as melting progressed. Melting contours depicted small and localized vortexes near tip of fins which promoted natural convection currents and thermal mixing. About 80% of phase change was achieved after 90 min for C-shaped configuration of fin. This represented improvement in thermal performance of heat storage tank because charging duration was significantly reduced. Almost 19% increment in thermal performance was attained due to utilization of C-shaped fins as compared to rectangular fins. Table 4 clearly displays the increment in surface area; if surface area increased, heat transfer rate was directly augmented. PCM phase transition in the case of trapezoidal fins showed that 51% PCM converted to viscous liquid form within 60 min. Complete charging was achieved in 97 min, high thermal conductivity leads to rapid melting of PCM in close vicinity of HTF tubes in initial stages of charging. Thermal performance of a heat storage tank employing trapezoidal fins was increased from 19% to 32.2% because of the large heat transfer area. The change in slope after 60 min indicated heat transfer mode change because convection is fairly fast due to the force of buoyancy and minute quantity of localized vortices.

The melting time comparison for W-shaped fins revealed rapid charging, with 36% of the PCM transitioning to a viscous liquid state within 30 min. The dominant conduction mode, supported by the larger surface area compared to other fin designs, highlighted the importance of extended surfaces in heat storage tanks. Unlike other configurations, the slope of the curve in Figure 20 did not exhibit sudden slope variations, indicating improved heat distribution through both conduction and convection. The total charging duration was recorded as 84 min, demonstrating a significant enhancement in thermal performance. A notable 41.3% increase in thermal efficiency was achieved, while 90% of the PCM completed its phase transition within 75 min due to the fin geometry, which facilitated rapid heat distribution through both conduction and convection modes.

Analysis of thermal variations revealed how temperature changes during the melting process. In Figure 20, the temperature rose steadily for 90 min, indicating heat was transferred primarily by conduction. After this period, the heat transfer mode abruptly shifted to convection, causing the temperature to rise more sharply.

Similarly, Figure 21 shows that double J-shaped fins experienced stronger conduction, reaching a higher temperature of 431 K in the same 90 min timeframe. As shown in Figure 22, increasing the surface area directly influenced this, as evidenced by C-shaped fins reaching 344 K within the first 30 min, compared to 332 K for rectangular fins. This demonstrates that a larger surface area promotes a more dominant conduction mode, which significantly reduces the time needed for charging.

During the melting process, conduction seems to be the dominant heat transfer mode early on in trapezoidal fins, causing the temperature to shift from a lower to a higher level. As shown in Figure 23, there was a swift 18 K temperature increase compared to rectangular fins, with the average temperature reaching 478 K within 90 min. This rapid heat dissipation suggests that a significant amount of the solid PCM has transitioned to a liquid state, particularly near the fins and HTF tubes. Meanwhile, Figure 24 shows a major temperature rise initially due to superior conduction, followed by dominant convection after just 30 min of charging. The average temperature in this case reached 479 K within 75 min, further highlighting how conduction’s prominence at the start significantly reduces the overall charging duration. Figure 25 illustrates a significant reduction in charging duration, with the percentage decrease improving from 11% for rectangular fins to 48% for W-shaped fins. This trend highlights the effectiveness of different fin configurations. It can also be observed from Figure 25 that the performance-to-area ratio progressively improves as the fin geometry evolves from rectangular to W-shaped.

The presence of multiple fins can enhance nucleation during the discharging process, as they act as localized heat sinks. When the cold fluid circulates through HTF tubes during discharging, the extended fin surfaces provide additional sites for heterogeneous nucleation. This mechanism reduces the degree of supercooling and promotes more uniform solidification of the PCM.

A detailed exergy analysis was conducted to evaluate the impact of various fin geometries on the maximum useful energy transfer. As illustrated in Figure 26, the energy graphs for the rectangular and J-shaped fins exhibited an abrupt change in slope after 90 min. Similarly, the C-shaped fin showed a similar shift after 75 min. These changes are attributed to a fluctuation in the dominant heat transfer mode. The quantitative analysis confirmed that the energy transferred in the form of heat from the HTF to the PCM was sufficient to overcome both the latent heat and sensible heat requirements. This was observed after 60 min for both the trapezoidal and W-shaped fins.

The total energy content of the HTF was assessed to determine the fraction of energy not utilized for phase transformation. As illustrated in Figure 27, a significant portion of the HTF energy was neither extracted nor transferred to the supply tank. Heat losses to the surroundings occurred due to the large temperature gradient. The variations in energy, along with the HTF outlet temperature, highlight the effectiveness of each fin geometry. Among the tested designs, the W-shaped and trapezoidal fins demonstrated superior performance, as their higher temperature differences indicate more efficient heat transfer to the PCM. This enhanced dissipation of heat into the PCM is particularly critical in thermal storage systems, given the inherently low thermal conductivity of PCM materials.

5. Conclusions

The study evaluated the influence of fin configurations on the thermal performance of a TES unit.

• The results showed that, in comparison with base model from a referenced study, rectangular fins reduced the charging time from 162 min to 143 min, enhancing the system’s efficiency by 11.8%.
• The thermal response of the TES unit was further analyzed using double J fins and C fins. About 85% phase transition from solid to viscous liquid was noted under 115 min duration due to double J fins.
• As localized regions transition to liquid, convection begins in the molten salt near HTF tubes. Orientation of fins from rectangular fins to C-shaped rapidly transforms heat and reduces thermal gradients due to proper thermal mixing and localized vortexes because of natural swirl effect.
• Convection mode of heat transfer was dominant in most cases due to temperature driven buoyancy effects, leading to the development of natural convectional currents and minute vortexes. To further enhance conduction mode, trapezoidal and W-shaped fins were employed possessing large heat transfer area.
• These modifications led to further significant reductions in charging time from 143 min to 97 min and 84 min for trapezoidal and W-shaped fins, respectively.
• The performance-to-area ratio was augmented from basic rectangular shape to W-shaped fin; these results are reinforced by rapid thermal distribution.
• This notable enhancement in heat transfer efficiency was attributed equally to conduction mode in initial stages, then promotion of convective component of heat transfer. Localized vortices generation and enhancement in natural convection because of buoyancy effect definitely improved the thermal performance of the TES tank.