Performance evaluation of heat sinks with calcium nitrate tetrahydrate phase change material for electronic cooling

Abstract

The study investigates the influence of heat sink designs and phase change material on the passive cooling of integrated circuits, specifically focusing on input power levels ranging from 4 to 12 W. The experimental setup evaluated heat sinks incorporating Calcium Nitrate Tetrahydrate PCM (SH PCM), with a particular emphasis on Triangular Fin Heat Sink (TFHS) and No Fin Heat Sink (NFHS). The TFHS design featured a consistent fin volume fraction of 11%, while the performance of these configurations was assessed across various power inputs. Besides that, SH PCM is evaluated through parameters such as enhancement ratio, heat storage ratio, set point temperature, Fourier number, and Stefan number. Results reveal that both TFHS and NFHS with SH PCM effectively regulate temperature at lower power levels, with NFHS showing a controlled temperature rise of 56.7% at 4 W. However, as power increases, PCM efficiency declines, with NFHS reaching an 89% temperature rise at 12 W, while TFHS experiences a 92.3% increase. Despite this, TFHS consistently maintains lower peak temperatures than NFHS, improving performance by 4.3% at 4 W and 6.7% at 12 W, due to its superior heat dissipation. While TFHS performs well in heat absorption under moderate conditions, it has a 41% performance gap at maximum heat flux compared to NFHS. Additionally, NFHS requires 15–30% longer charging times but releases heat 10–25% faster during discharging. Overall, TFHS combined with SH PCM proves to be the most effective configuration for passive cooling, making it highly suitable for portable electronic devices.

Introduction

As the electronics industry rapidly evolves, managing thermal output is increasingly essential for ensuring device reliability, optimizing performance, and extending lifespan¹. Proper thermal management mitigates the risk of overheating, allowing components to function within their ideal temperature range², thereby enhancing both efficiency and durability. Traditional methods of cooling have included heat sinks and fans, but often substantial challenges in efficiency and compactness must be faced³. To all these challenges, Phase Change Materials have emerged as a promising solution to thermal management: PCMs absorb and release heat at the phase changes between the solid and liquid states⁴. It ensures temperature stability within electronic systems⁵. PCMs are particularly advantageous in electronic cooling due to their ability to absorb excess heat during peak operational periods and release it when the device cools down. This characteristic helps in mitigating temperature fluctuations and protecting sensitive components. Recent developments related to PCM are focused on the enhancement in the thermal conductivity, phase change temperatures, and integration with other cooling systems. Recent studies have highlighted the potential of PCMs for future electronic applications⁶. For instance, the integration of advanced composite PCMs in high-performance computing has shown notable enhancements in thermal management and device reliability. These developments emphasize the increasing role of PCMs in creating efficient, compact, and effective cooling solutions for modern electronic systems⁷.

Environmentally, PCMs contribute to reducing reliance on conventional cooling methods that are often energy-intensive and less sustainable. Its help lower the operational energy requirements of cooling systems, thus potentially reducing greenhouse gas emissions associated with electronic cooling. However, some environmental challenges remain, such as the need to improve the thermal conductivity of PCMs to enhance their effectiveness and reduce their environmental footprint further⁸. Economically, the combination of PCMs in thermal management systems can reduce costs related to energy consumption and equipment maintenance. Hybrid cooling systems that integrate PCMs with materials such as heat pipes and copper foams have been shown to lower device temperatures by as much as 54% under specific conditions. This enhancement improves the reliability and lifespan of electronic devices, leading to long-term cost savings⁹. Yet, despite all these advantages, there are some continuous challenges in the development of PCMs with superior thermal performance and durability, and most importantly, cost-effective methods for production and encapsulation to make them feasible for practical applications in large quantities. Overcoming such barriers demands further studies and developments to fully exploit PCMs potential in sustainable cost-effective thermal management¹⁰.

The network Fig. 1 illustrates keyword co-occurrence related to PCMs and their applications in thermal management, where the size of each node represents the term frequency and intensity of color indicates the strength of association between terms¹¹. The largest nodes comprise PCMs, thermal management, and PCMs that dominate in the central region, signifying the importance of being centrally located in the field¹². Surrounding these primary terms are related keywords, including heat sinks, energy storage, electronics cooling, and thermal conductivity enhancer, highlighting the diverse applications of PCMs in thermal regulation and energy systems¹³. The presence of terms like latent heat storage, solar energy, battery thermal management, and heat pipes shows that so many technologies are using PCMs for effective thermal control. The meaning of each of them is self-explanatory, while the presence of other terms like 3D printing, composites, and metal foam means looking into advanced materials and manufacturing techniques for the betterment of PCMs¹⁴. The usage of keywords like computational fluid dynamics, numerical model, and dimensional analysis pinpoint the importance of simulation and modeling in optimizing PCM-based systems. This network map gives a great overview of the research landscape on PCMs, reflecting broad utilities for thermal performance enhancement across diverse sectors¹⁵.

Fig. 1.

Overview of network flow diagram of phase change materials.

A comprehensive overview between different phase change materials is included in the Table 1, collectively with details on thermal characteristics, and practical applications. It provides inorganic and organic PCMs, from salt hydrates to fatty acids to paraffin wax. Materials such as calcium nitrate tetrahydrate and magnesium nitrate hexahydrate have allegedly increased conductivity and storage capabilities of heat, to create problems that they cause, such as corrosion. Paraffin wax has a durable nature and sufferers from poor thermal conductivity. Biodegradable fatty acids, such as stearic, lauric, and palmitic acid, are commonly used for thermal insulation levels and textiles.

Table 1.

The details of phase change materials properties and applications.

PCM type	Melting point (°C)	Density (kg/m3)	Thermal conductivity (W/mK)	Flash Point (°C)	Applications	Observations	References
Paraffin Wax	46–68	800–900	0.2–0.3	> 200	Thermal storage, packaging	Stable, low thermal conductivity	16
Calcium Nitrate Tetrahydrate (SH)	42–46	1820–1900	0.5–0.6	–	Solar energy, building materials	High heat storage capacity	17
Erythritol	118–120	1290	0.733	–	Electronics cooling, textiles	High latent heat, slightly hygroscopic	18
Stearic Acid	55–69	940	0.15–0.18	> 200	Thermal insulation, packaging	Biodegradable, moderate thermal conductivity	19
Lauric Acid	42–44	880	0.147	> 200	Heating pads, textiles	Good compatibility with various materials	20
Sodium Acetate Trihydrate	58–61	1450	0.57	–	Hand warmers, heat packs	Supercooling tendency, low thermal conductivity	21
Capric Acid	31–32	880	0.153	> 150	Cosmetics, thermal textiles	Low melting point, good thermal stability	22
Myristic Acid	54–56	990	0.17	> 200	Textiles, thermal energy storage	Biodegradable, safe handling	23
Pentaglycerine	82–84	1230	0.45	–	Electronics, medical devices	High phase change enthalpy	24
Sodium Sulfate Decahydrate	32–35	1490	0.54	–	Solar heating, building materials	Phase separation issues, hydration problems	25
Butyl Stearate	18–22	860	0.15	> 200	Cold storage, cosmetics	Low melting point, stable under cycling	26
Octadecane	28–30	776	0.15–0.24	> 150	Electronics cooling, textiles	High latent heat, moderate stability	27
Tetradecane	05-Jul	758	0.14	> 150	Chemical thermal energy storage	Low melting point, flammable	28
Dodecanol	22–24	829	0.14	> 150	Thermal regulation textiles	High heat capacity, odorless	29
Palmitic Acid	62–64	840	0.17	> 200	Thermal energy storage, packaging	Biodegradable, stable phase change properties	30
Capric-Caprylic Acid Mix	21–24	880	0.2	> 150	Cooling textiles, medical	Good thermal conductivity, low toxicity	31
Heptadecane	22–25	774	0.15	> 150	Thermal energy storage, textiles	Low melting point, good for low-temperature storage	32
RT27	27	760	0.2	–	HVAC systems, electronics	Engineered PCM with stable properties	33
Arachidic Acid	75–77	960	0.2	> 200	High-temperature storage, textiles	High latent heat, solid at room temperature	34
1-Hexadecanol	48–50	820	0.16	> 150	Thermal energy textiles, cooling	Good latent heat, stable performance	35
Magnesium Nitrate Hexahydrate	88–90	1540	0.6	–	Heat batteries, solar applications	High thermal conductivity, corrosive	36
Potassium Nitrate	334	2110	0.5	–	Solar power, thermal energy storage	High melting point, good thermal stability	37
Sodium Thiosulfate Pentahydrate	48–50	1700	0.6	–	Heat storage, thermal packs	High latent heat, supercooling issues	38
Hydroquinone	171–173	1320	0.31	–	High-temperature applications	High thermal stability, toxic handling required	39
D-Mannitol	167–170	1490	0.21	–	Electronics cooling, textiles	Non-toxic, high latent heat	40
Magnesium Chloride Hexahydrate	117–118	1568	0.57	–	Heat batteries, heat packs	High thermal conductivity, corrosive	41
Pentadecanol	50–53	823	0.15	> 150	Phase change textiles, electronics	Good stability, moderate thermal conductivity	42
Butyl Palmitate	13–16	850	0.14	> 150	Cosmetics, cooling packs	Low melting point, good thermal stability	43
Caprylic Acid	16–18	910	0.15	> 150	Cold storage, medical applications	Low melting point, biodegradable	44

Observed heat sinks with circular fins, using four different pin diameters. These pin fins, representing a 9% volume fraction, served as thermal conductivity enhancers (TCE). The study explored various PCM volumetric fractions (0, 0.3, 0.6 and 0.9), identifying that the heat sinks with 3 mm fin diameter and higher concentrations of n-eicosane offered the best cooling performance⁴⁵. Specifically, when PCM was introduced into the circular fin heat sinks, the combination significantly improved thermal performance, reducing base temperatures as n-eicosane content increased. In another study,⁴⁶ fabricated square pin–fin heat sinks (72 pins) using the same PCM to cool four separate heaters. They applied an optimization method to determine the ideal power levels, aiming to minimize discharge time while extending charge time. Additionally, they also analyzed the effect of each level of heat input and established a correlation to estimate the time required to reach the desired temperature⁴⁷.

There exist three PCMs types that are divided into either organic, inorganic and eutectic category as shown in Fig. 2. The organic type of PCMs are those carbon-containing compounds having stable behavior for more than one phase change cycle: they include both paraffin and non-paraffin categories^48,49. The inorganic type PCMs, such as salt hydrates, metal-based PCMs, have high thermal conductivity but experience problems associated with supercooling and phase separation⁵⁰. Eutectic PCMs comprise two or more components with a mixed, lower melting and solidification temperature compared with any of their individual constituents⁵¹. The organic–inorganic mixtures, inorganic-inorganic mixtures, and organic–inorganic mixtures have very wide melting temperatures that might be appropriate for almost all applications⁵².

Fig. 2.

Categories of phase change materials.

Further research evaluated different fin geometries and configurations (staggered or inline arrays) along with various PCMs. Results indicated that the most effective heat sinks featured inline circular pin-fins with PCM⁵³. For low-power applications, PCMs such as RT44, nicosan and SP31 were most suitable, whereas RT54 was recommended for higher-power systems. In systems operating at power levels of 5 and 8 Watts, SP31 and paraffin wax demonstrated the highest enhancement ratios. To conducted experimental tests, revealing that triangular cross-sectional pin-fins performed better than round and rectangular pins⁵⁴. The performances were enhanced because of the increase in the number of pin fins and the lower surface area ratio. The investigated the thermal performance of a heat sink assembled with copper foam and RT35HC PCM with and without a cooling fan under different heat flux conditions. Results indicated a strong cooling of temperatures by 48%, 52%, and 55% at various heat flux intensities⁵⁵. Hybrid cooling with a fan is also very effective regardless of the level of heat flux tested. In another study, Arshad et al., (2021)⁵⁶ explored the use of a mixture of graphene oxide and silver nanoparticles within the PCM. The inclusion of these hybrid nanoparticles led to a 12.5% reduction in melting time, enhanced heat storage capacity, a smoother melting process, and improved thermal conductivity.

Ahmed Saad Soliman research presents innovative cooling techniques for photovoltaic systems using PCMs. In Soliman et al. (2025)⁵⁷ study, a finned heat sink filled with multiple PCMs, which effectively lowers PV module temperatures by up to 16.7 °C, enhancing power output by over 9% and reducing CO₂ emissions by 9.4%. Soliman et al. (2023)⁵⁸ work focused on a ribbed heat sink with PCM for bifacial PV systems, analyzed through a 4E framework. The findings highlight improved thermal management, higher energy efficiency, and cost-effectiveness while supporting environmental sustainability. These advancements contribute to the enhanced performance and longevity of PV module.

Qin et al.⁵⁹, introduced a new class of dynamic PCMs that significantly improve both energy and power densities. By incorporating external forces; such as magnetic fields and gravity, the PCM maintains consistent contact with heat sources during the phase transition. This method enhances heat transfer efficiency and accelerates charging/discharging cycles. The researchers reported a remarkable temperature stabilization at over 97% under high heat flux, and a power density increase of up to 80% compared to conventional PCMs. These findings mark a major advancement toward thermal storage systems capable of meeting the demands of high-performance energy applications.

Zhang et al.⁴⁸, conducted a detailed study on a dynamic PCM wall system that allows the PCM and insulation layers to switch positions based on external conditions, aiming to improve thermal regulation in buildings. Additionally, by adjusting the position of the PCM layer, the design could extend the duration of thermal comfort by around 60% compared to static wall structures. These results highlight the potential of climate-specific dynamic PCM walls to significantly enhance building energy efficiency.

Ismail and Hassan⁶⁰, presented a dual-PCM strategy for improving air conditioning unit performance throughout different seasons by using SP24E for summer and SP11_gel for winter. Their findings showed that the coefficient of performance of the ACU increased by around 80% during summer and about 40% in winter when compared to systems without PCMs. The study also compared encapsulation designs, revealing that staggered cylinder layouts improved charging and discharging speed, while inline arrangements delivered higher power efficiency. Over a 4-h operation, the dual-PCM setup resulted in energy savings of 11.8% in summer and 12.8% in winter, underlining its effectiveness in enhancing seasonal energy efficiency in HVAC systems.

The current research aims to enhance heat sink efficiency by integrating phase change material for improved thermal management. The study introduces a design with an 11% TCE volume fraction and 25 aluminum (A6063) fins. Unlike conventional approaches, this work systematically compares different heat sink configurations, specifically NFHS and TFHS, to identify the most effective design, as illustrated in Fig. 3. Experimental tests are conducted at constant power levels of 4 W, 8 W, and 12 W, evaluating key performance metrics such as the Enhancement ratio, Heat storage ratio, Set Point Temperature, Fourier number, and Stefan number. The previous research on PCM-based heat sinks has primarily focused on liquid–solid PCMs, higher power levels, or lacked a detailed comparison of different fin configurations. This study bridges these gaps by utilizing SH PCM, which eliminates leakage issues and improves long-term reliability. Additionally, it incorporates insulation to minimize heat loss, ensuring a more precise performance evaluation. Unlike studies that examine a single heat sink design, this research compares NFHS and TFHS under identical conditions. Furthermore, it targets lower power levels, making it relevant for low-power electronics such as IoT devices and wearables. These findings contribute to optimizing heat sink designs for efficient thermal management.

Fig. 3.

Present focused work for thermal management systems.

Materials and method

Aluminum heat sinks

With the best combination of physical and thermal properties, A6063 alloyed heat sinks are highly recognized in both electronic and thermal managing fields. Aluminum features a great balance between strength and lightweight with good corrosion resistance; thus, it has become a priority for several heat dissipation applications. The mechanical strength of this alloy is good enough for the majority of applications involving heat sinks, having a tensile strength of about 150–250 MPa and yielding at 110–150 MPa. Also, it has a relatively low density at 2.7 g/cm³, hence being lightweight enough to make efficient heat sinks with an overall low weight, which is very desirable in portable electronic devices and automotive applications for reasons of weight savings. A6063 possesses thermal conductivity properties of approximately 201 W/m.K, the effectiveness, although relatively lower than pure aluminium, is still highly effective at dissipating heat from electronic components. This property is essential to maintain the performance and lifetime of the devices by preventing overheating. Among its many impressive qualities, aluminium alloy offers great extrudability, opening up the possibility of manufacturing very intricate heat-sink designs with elaborate fin structures to maximize surface area for enhanced thermal performance. The ease of machining, cutting, and finishing of this alloy makes it quite versatile for the production of custom shapes of heat sinks to cater for specific needs. The other beneficial property is a smooth surface finish, which is suitable for anodizing-a process that enhances corrosion resistance and generally improves its appearance. This provides further protection against environmental factors like moisture and chemicals.

The good corrosion resistance, particularly in environments prone to moisture or other corrosive elements, is one of the most characteristic properties of A6063. These applications include outdoor LED lighting, solar power systems, and automotive electronics. Especially for these applications, key factors such as reliability and durability are needed to ensure long lifespan. To further enhance the natural corrosion resistance of A6063 heat sinks, a protective oxide layer can be added through the anodizing process. The emissivity of the heat sink is improved, which enhances the overall thermal performance. The alloy elongation, usually in the range of 8–10%, maintains adequate ductility for the material, absorbing mechanical stresses without fracturing optimistic attribute at installation and during operational life. Additionally, aluminum has a melting point of around 615–650 °C, suitable for applications involving moderate temperature environments. This property ensures that heat sinks will not experience loss in structural integrity and performance under high operating temperatures. Typical applications involving A6063 heat sinks would include LED lighting, power electronics, telecommunications equipment, computer hardware, and sundry automotive components where efficient heat dissipation is required to avoid component failure and to improve the efficiency of the device. Good thermal conductivity, combined with light weight, corrosion resistance, and ease of manufacturing, makes a very good material choice for heat sinks in a wide variety of industries. With an increasing number of manufacturing processes, that customized capability enables the device to optimize heat sinks for an exact cooling challenge as highly reliable and efficient thermal management solutions as given in Table 2.

Table 2.

Dimensions of the materials in the fabrication of the heat sink.

S. no	Name of the materials	Dimensions
1	Wood panel	(8 × 8 × 0.5) cm3
2	Silicone rubber	(7.5 × 7.5 × 0.5) cm3
3	Heating element	(6 × 6 × 0.2) cm3
4	Thermal heat sink dimensions	(7 × 7 × 3) cm3
5	Effective area of the heat sink	(6 × 6 × 2.5) cm3

As shown in Table 3, all configurations maintain a consistent fin volume fraction of 11%, functioning as thermal conductivity enhancers (TCEs). The volume fraction of TCEs is determined using Eq. (1), which represents the ratio of the total heat sink volume to the volume taken up by the fins (Fig. 4).

1

Table 3.

Testing heat sinks fin configuration details.

Fin configuration	Dimension	Total fins	γt
Triangular fin	6.1 mm side length	25	11%

Fig. 4.

Fabricated aluminum heat sink using CNC machine (a–f).

To calculate volumetric fraction of the fin

The vol% of the fin calculated using the following formula.

2

3

4

5

6

where, ‘P’ represents the input power supply, such as 4, 8, and 12 W. The area of the heating plate (A) is 60 mm × 60 mm which is equal to 3600 mm².

Table 4 shows list the various power levels that were implemented in this study, along with their respective heat fluxes.

Table 4.

Constant input power values and the heat flux that results.

Power (W)	4 Watts	8 Watts	12 Watts
Heat flux (q)	1.12 kW/m2	2.23 kW/m2	3.23 kW/m2

Heating plate

The heater plate is made in the shape of 60 mm × 60 mm and is designed to simulate thermal energy produced by microchips. This includes a spiral-patterned nichrome wire situated a top a mica sheet. Nichrome is an alloy 20% chromium and 80% nickel, known for being resistant, hence it produces fine efficiencies in heating. When electrical current passes through the nichrome wire, it transfers electrical energy successfully into heat. It is a mica sheet that comprises complex silicate minerals and offers significant thermal insulation and electrical resistance that ensures balanced heating over the entire plate surface as shown in Fig. 5. It has an input power of 15 W, and this heater plate is very effective in delivering high precision temperature control in electronic cooling systems and industrial heating applications. Mica can withstand temperatures to 1000 °C without substantial degradation and also has its own high dielectric strength, ensuring that high voltage transmission can be handled safely. Mica also presents with a high degree of flexural properties and is relatively easy to shape, so it finds industrial and electronic uses in plenty of applications. Nichrome wire can sustain continuous operation to a temperature of 1200 °C because an outer layer of chromium oxide prevents oxidation. In addition, low thermal expansion increases the protection of the heater against changes in dimensions when exposed to fluctuating temperatures; this ensures constant heater structural integrity when repeatedly cycled through different temperatures. This resilient combination of materials and a well-designed structure ensures the heater plate works reliably under high temperature conditions.

Fig. 5.

Heater plate.

Calcium nitrate tetrahydrate phase change material (SH PCM)

Calcium nitrate tetrahydrate, among all PCMs, is one of the most used and studied PCM materials because of its performance in thermal energy storage application. Being an inorganic PCM, it characteristically possesses high latent heat capacity with excellent thermal conductivity. This material actually has a phase change from the solid to the liquid state at relatively low temperatures between 42 °C to 45 °C as shown in Fig. 6. It is therefore particularly suitable for applications requiring the supply of temperatures in this range-such as passive solar heating systems, building energy management, and waste heat recovery from the industry. One of the notable features of SH is its relatively high latent heat of fusion that lies in the range of 171 to 179 kJ/kg. This enables it to store and release significant thermal energy with respect to phase transitions, hence turning it into a very effective medium for energy storage; details of properties are shown in Table 5. Besides, its thermal conductivity is moderate, which is enough for allowing heat transfer and thus important for consistent temperature regulation in many applications. It provides excellent thermal stability, good chemical compatibility with many different metals and non-metals, and generally extends its usage in a wide range of applications. However, like many inorganic hydrates, SH is prone to subcooling, where the material cools below its melting point without solidifying. This phenomenon can affect the predictability of its thermal performance, but it can often be mitigated through the use of nucleating agents or by carefully controlling the operational environment.

Fig. 6.

SH PCM at (a–b).

Table 5.

The materials properties of calcium nitrate tetrahydrate PCM.

Name of the property	Values	References
Molecular weight	236.15 g/mol	61
Temperature of Melting point	42–45 °C	16
Latent heat fusion	171–179 kJ/kg	21
Density (Solid)	1.82 g/cm3	20
Density (Liquid)	1.82 g/cm3	20
Thermal conductivity of solid	0.5–0.7 W/mK	16
Specific heat capacity of solid	1.6–1.8 kJ/kgK	21
Specific heat capacity of liquid	2.0–2.2 kJ/kgK	16
Thermal expansion coefficient	0.00041 K−1	61
Stability	Good	16
Heat of crystallization	~ 210 kJ/kg	16
Volume change on phase transition	~ 10%	21

On the practical application side, SH is considered quite well for building materials with thermal mass enhancement due to its ability to maintain stable indoor temperatures by absorbing excess heat taken up during daytime and then releasing at night. It has also been said to take several repeated thermal cycles without degradation, and therefore may be used for materials for long-term energy storage applications. Overall, Calcium Nitrate Tetrahydrate is a versatile and efficient PCM with potential in various thermal management applications, this is due to its high latent heat, suitable phase transition temperature, and stability during repeated thermal cycles. However, challenges such as subcooling need to be addressed to fully harness its capabilities in practical applications.

To calculate contact thermal resistance

Thermal paste is applied to the bottom of the heatsink and the top of the heating plate in order to avoid contact thermal resistance, contact thermal resistance (R_c) is still existing in between the inner sides of the heatsink to the PCM, even when the surfaces appear smooth, microscopic knocks create air gaps, which reduce conductivity. This resistance can greatly affect transfer systems efficiency, especially for applications such as electronics cooling and energy storage. Lower R_c values are preferred, indicating efficient heat flow as a result of better thermal contacts. Factors affecting R_c involve surface roughness, materials-profiles, contact pressure, thermal interface materials and the ambient conditions. Minimized R_c in thermal management systems is essential for achieving effective dissipation of heat and stable operational temperatures. Thermal resistance is calculated using Eq. (7), following the formulas:

7

where, ‘R_c’ is contact thermal resistance (K m²/W), ‘ΔT’ is temperature drop across the interface (K), ‘q’ heat flux through the interface (kW/m²).

The calculation details for contact thermal resistance across different power inputs and heat sink design are comprehensively listed in Table 6.

Table 6.

The contact thermal resistance details at different input power.

Power (W)	NFHS (ΔT)	TFHS (ΔT)	q (kW/m2)	NFHS, Rc (Km2/W)	TFHS, Rc (Km2/W)
4	2.7	2.5	1.12	0.00245	0.00225
8	4.04	3.6	2.23	0.00182	0.00166
12	5.4	5.06	3.34	0.00163	0.00152

The Fig. 7 shows that the contact thermal resistance (R_c) decreases as power input increases, suggesting better thermal interaction at greater heat fluxes. Interestingly, at all power levels, TFHS continuously shows a lower R_c than NFHS. In comparison to NFHS, TFHS has a slightly lower 7% at 4 W, 6.5% at 8 W, and 4.2% at 12 W. The triangular fins better heat dispersal and larger effective contact area are the primary explanations of this significant improvement. In order to decrease temperature gradients and improve contact between the heat sink and PCM, the fins lessen thermal obstacles resulting in more uniform heat transfer.

Fig. 7.

The contact thermal resistance of NFHS and TFHS at different input power.

Experiment procedure

The experimental setup for evaluating heat dissipation in electronic devices is illustrated in Fig. 8a–c. Experiments were conducted both with PCM under various constant heat inputs. Two types of heat sink were used in the study: a triangular fin heat sink with 25 fins, and a finless heat sink. The heat sinks were filled with SH PCM, occupying 11% of their volume, as depicted in Fig. 8c. Baseline comparisons were made using a finless, PCM-filled heat sink. All tests employed a section with core dimensions of (70 × 70 × 30) mm³ and a fin height of 25 mm as shown in Table 2. The Fig. 4 shows provide 3D views of the heatsink configurations: finless, and triangular fins. To reduce heat loss to the surroundings, silicone rubber insulation was applied to all sides of the heat sink. While copper has twice the thermal conductivity of aluminum, its density is over three times greater, making it less practical for many applications, especially in the thermal management of portable electronics. The materials used in the study are described as follows: a fiberglass box measuring (200 × 200 × 120) mm³ was constructed to maintain stable temperatures. To ensure the heatsink assembly remains level, a spirit level and two adjustment screws were used, as shown in the attached photo. The upper surface was coated with silica film. A heater plate, (60 × 60) mm² and 2 mm thick, was used to simulate heat generation typical of microchips. This heater utilizes a conventional spiral-type nichrome wire mounted on a mica sheet. The input power of the experiments was between 4 and 12 W, with a step of 4 W corresponding to heat fluxes of 1.12 kW/m² at 4 W, 2.23 kW/m² at 8 W, and 3.32 kW/m² at 12 W. K-type thermocouples, calibrated according to ASTM standards, the thermocouples are strategically positioned at various locations to accurately monitor the thermal behavior of the PCM. These positions include the bottom of the heat sink, where heat is initially applied, and the four side walls, which help assess heat distribution along the boundaries.

Fig. 8.

(a–c): The Experimental setup process.

Additionally, a thermocouple is placed at the center of the PCM to capture the core temperature response, while another is positioned at the corner of the PCM to observe temperature variations in less exposed regions. Finally, a thermocouple is mounted at the top of the fin to evaluate heat dissipation efficiency and the impact of the fin structure on thermal performance. This arrangement ensures a comprehensive understanding of temperature distribution and phase transition dynamics within the system. These thermocouples were interfaced to the Data logger, which logged temperature data every 10 s during the experiments. The heater plate was powered by a separately regulated DC power module, which can handle a voltage (V) and current (A) range of 0 to 230 V and 0–2 amp respectively. Different power input supplies were studied for voltage and current regulation, as shown in Table 7. For 4 Watts, the voltage and current were set at 40 V, 0.106 amps; for 8 W at 55 V, 0.146 amps; and for 12 W at 67 V, 0.180 amps.

Table 7.

The details of various input power supply.

S. no	Power supply	Voltage and current settings
1	4 W	40 V × 0.106 A
2	8 W	55 V × 0.146 A
3	12 W	67 V × 0.180 A

Uncertainty analysis

In assessing the thermal performance of heat sinks, measurement uncertainties arise from both instrumentation limitations and human factors. Key measured parameters such as temperature, thermocouples, voltage and current contribute to the overall uncertainty in calculated results. To quantify this, the root sum square method is employed to evaluate error propagation. For a given result Z that depends on multiple variables, the total uncertainty​ is determined by incorporating the uncertainties of each contributing parameter. For instance, the precision of the temperature recorder (± 0.6 °C), thermocouple (± 0.4 °C), volts meter (± 0.06 V), and ammeter (± 0.2 A) significantly impact the calculated convection heat transfer coefficient, while variations in power input influence the computed thermal resistance and efficiency as mention in Table 8. A systematic uncertainty analysis enhances the reliability of heat sink performance evaluation, allowing for accurate comparisons between different heat sink designs. The error propagation is determined using the root sum square method. For a given specific result Z, the uncertainty is calculated (Eq. 8) as described in Soliman et al. (2023)⁵⁸.

8

Table 8.

Summary of direct and indirect measurement components and their associated uncertainties.

S.no	Parameter	Type	Uncertainty (%)	Source
1	Ambient temperature	Direct	± 0.4	Measured using calibrated thermocouples
2	Surface temperature of heat sink	Direct	± 0.75	The sensor accuracy and placement
3	Temperature of PCM	Direct	± 0.85	Multiple sensors used within PCM volume
4	Input power	Direct	± 2.4	Power = voltage × current
5	Voltage	Direct	± 0.06	Measured using multimeters loggers
6	Current	Direct	± 0.2	Ammeters
7	Thermal conductivity of PCM	Indirect	± 2	Measured via steady-state methods
8	Specific heat capacity	Indirect	± 3	DSC calibration
9	Latent heat of PCM	Indirect	± 3.5	Derived from DSC
10	Heat flux	Indirect	± 4.1	Derived from temperature gradients
11	Mass of PCM	Direct	± 0.5	Precision scales required
12	Density of PCM	Indirect	± 1.5	Calculated from mass and volume
13	Volume of PCM	Direct	± 0.75	Determined geometrically
14	Heat transfer coefficient	Indirect	± 12.5	Estimated using correlations
15	Thermal resistance	Indirect	± 6.5	Derived from temperature difference and heat input
16	Thermal diffusivity	Indirect	± 5	Inferred from material tests
17	Melting point of PCM	Direct	± 0.5	Accurate from DSC

For an independently measured quantity x_i​, the associated uncertainty ω_i represents the uncertainty in the independent variables. The overall uncertainty ω_z in the result Z is determined using the following expression (Eq. 9):

9

The overall uncertainty in power (P) is ± 2.4 W, while the uncertainty in thermal resistance (R_θ) is ± 0.13 K/W. Additionally, the total uncertainty in temperature measurement is ± 0.72 °C. Considering these factors, the total uncertainty (ω_z) is determined to be ± 2.51.

Results and discussion

The NFHS with SH PCM at different input power 4 W, 8 W and 12 W

In the Fig. 9 shows, the temperature response of a NFHS with SH PCM at different input powers 4 W, 8 W, and 12 W. Thermal response to each power level is shown through the curves in green, red, and blue, respectively. The green curve is for operation at 4 W: the temperature rises monotonically from about 30 °C to a maximum of about 47 °C at about 7000 s, then decreases very slowly. This indicates a slow rate of heat absorption due to the relatively low power input, which aligns with the limited energy available for heating the system. The SH PCM absorbs and stores heat through its phase change, which moderates the temperature increase and results in a lower peak compared to higher power settings. The red curve, corresponding to 8 W, starts similarly at around 30 °C but shows a much steeper increase, reaching a peak temperature of approximately 60 °C at about 5000 s. The sharper rise in temperature reflects the higher energy input, which accelerates the heating rate. The presence of SH PCM plays a crucial role by absorbing excess heat during its phase transition, helping to smooth out the temperature rise but allowing for a higher peak due to the increased power level. The PCM thermal energy storage properties help manage the heat load but are challenged more significantly at this power setting than at 4 W. The blue curve represents the highest power setting at 12 W. It begins at the same initial temperature but rises most rapidly, reaching a peak of about 75 °C around 4000 s. This curve exhibits the steepest slope, indicating the fastest heating rate due to the substantial power input. At this level, the SH PCM phase change capability is quickly reached, and while it initially absorbs heat, the system temperature continues to climb sharply due to the overwhelming energy influx. This results in the highest peak temperature among the three power levels, demonstrating that the PCM thermal management effect is more limited as power increases. The differences in the thermal response are primarily governed by the amount of power supplied to the system. Higher power inputs deliver more energy, thus increasing the heating rate and the maximum temperatures achieved. SH PCM acts as a thermal buffer due to its ability to absorb and releases heat through its phase change. This characteristic helps to manage and stabilize temperature fluctuations. However, as the power input rises, the PCM capacity to control the temperature diminishes because the material can only absorb a finite amount of heat before its phase change potential is exhausted. This is evident from the progressively higher peaks as power increases from 4 to 12 W. In all cases, after the peak temperatures are reached, the curves exhibit a gradual decline, reflecting the cooling phase of the system. This cooling can be attributed to heat dissipation to the surroundings or the gradual release of stored heat from the PCM as it reverts to its original phase. The study of these temperature profiles underscores the importance of PCM in thermal management, demonstrating how it can moderate temperature increases under various power conditions but also highlighting its limitations when faced with high energy inputs.

Fig. 9.

The charging and discharging cycles of NFHS with PCM at 4 W, 8 W, and 12 W.

The TFHS with SH PCM at different input power 4 W, 8 W, and 12 W

The Fig. 10 shows, the temperature response of a TFHS with SH PCM under different power inputs; (4, 8, and 12) W. The three curves, green for 4 W, red for 8 W, and blue for 12 W demonstrate how varying power levels influence the heating and cooling behavior of the heat sink system. For the 4 W input, represented by the green curve, the temperature starts around 30 °C and gradually increases, reaching a peak of approximately 47 °C at around 7000 s before slowly declining. This results in an overall temperature rise of about 56.7% from the initial temperature. The gradual increase and moderate peak reflect a slower rate of heat absorption due to the lower power input. The SH PCM absorbs thermal energy during its phase change, effectively stabilizing the temperature and preventing rapid increases. The slower and sustained temperature profile suggests that the PCM is well-suited to managing the heat load at this power level, allowing for efficient thermal regulation. The red curve, corresponding to the 8 W power input, shows a steeper rise in temperature, peaking at around 60 °C at approximately 5000 s. This is an 85% increase from the initial 30 °C, indicating a significantly faster heating rate compared to the 4 W arranging. The higher energy input leads to a more rapid temperature rise, with the PCM absorbing heat during the phase change but reaching its capacity more quickly due to the increased power. As a result, the peak temperature is higher, reflecting the PCM reduced efficiency in heat absorption under these conditions. The curve demonstrates the PCM continued role in temperature moderation, although with diminished effectiveness as the power level increases. The blue curve, representing the 12 W setting, shows the most rapid and steep temperature increase, peaking at around 70 °C at approximately 4000 s. This peak represents a 92.3% increase from the initial temperature of 30 °C, the highest among three power levels. The steep rise is due to the substantial power input, which causes the system to heat up quickly and exceed PCM capacity to absorb and manage heat effectively. The PCM initially mitigates the temperature rise, but the large energy input overwhelms the material’s phase change capability, leading to a sharp peak and rapid cooling afterward. The performance at 12 W highlights the limitations of PCM at high power levels, where its ability to stabilize temperature diminishes significantly.

Fig. 10.

The charging and discharging cycles of TFHS with PCM at 4 W, 8 W and 12 W.

The differing temperature profiles are primarily influenced by the varying power inputs. High power output increased from 4 to 12 W was used to demonstrate the increased energy supplied to the system. Correspondingly, this increases heating rates with peak temperatures. The SH PCM manage temperature by absorbing heat through phase change while operating, which introduces a delay in the rise of temperature and dampens fluctuation. However, as the power input increases, the PCM capacity to manage the heat becomes increasingly limited. At 4 W, the PCM effectively absorbs heat, maintaining a relatively low and steady peak temperature. At 8 W, the PCM still absorbs significant heat, but the faster energy input results in a higher peak. At 12 W, the high-power input leads to a rapid temperature increase quickly surpassing the PCM ability to moderate the system temperature effectively. The triangular fin design of the HS enhances heat dissipation by increasing the surface area in contact with the surrounding air, facilitating more efficient heat transfer away from the PCM. The m combination of the HS geometry and the PCM phase change properties work together to regulate the system’s temperature, but the effectiveness of this combination is most apparent at lower power levels. As power increases, the limitations of the PCM heat absorption capacity become more evident, resulting in higher and more pronounced temperature peaks.

The comparison of NFHS and TFHS with SH PCM at input power 4 W

The Fig. 11 shows, the thermal performance comparison between the TFHS and NFHS, both utilizing SH PCM under a 4 W constant power input. Starting at an initial temperature of 30 °C, the TFHS demonstrates a sharper rise in temperature, reaching approximately 55 °C in about 10000 s, reflecting an 83.3% increase from the initial temperature. This faster rise is due to the finned design, which provides a larger surface area, allowing more efficient heat absorption and transfer to the PCM. In contrast, the NFHS shows a slower increase, peaking at around 50 °C in 12000 s, indicating a 66.7% increase, with its simpler design limiting heat absorption. Both systems cool down after peaking, but TFHS cools faster due to its fins enhancing convective heat dissipation, whereas NFHS cools more gradually. The enhanced thermal performance of TFHS over NFHS is primarily due to the triangular fins, which improve both the rate of heat transfer into the PCM during charging and the efficiency of heat release during discharging. The added surface area and better thermal connectivity provided by the fins significantly improve overall thermal management compared to the finless configuration. The TFHS superior performance, attributed to its finned design, improves both heat absorption and dissipation, making it more effective for applications requiring rapid thermal management. The NFHS, with its lower surface area, shows slower and less efficient thermal responses, making it less suited for situations that demand quick heat regulation.

Fig. 11.

Comparison of NFHS and TFHS with SH PCM at 4 W.

The comparison of NFHS and TFHS with SH PCM at input power 8 W

The Fig. 12 shows, the comparison of the thermal performance of NFHS and TFHS configurations, both using SH PCM under an 8 W thermal load. Initially, both systems start at 30 °C, but TFHS shows a faster rise in temperature due to its finned design, this improves heat transfer by increasing the surface area and hopeful more efficient airflow. TFHS reaches a peak temperature of 73 °C, about 5.8% higher than NFHS, which peaks at 69 °C. This suggests that while TFHS can quickly absorb heat, it also reaches its thermal limit sooner. During cooling, TFHS initially dissipates heat faster, but both configurations eventually show similar cooling rates. The key difference between the curve’s deceits in the presence of TFHS. These fins not only accelerate heat absorption during charging by spreading the heat more effectively into the PCM but also enhance heat release during cooling by offering better conduction and convective interaction with the surroundings. This results in better overall thermal regulation for TFHS compared to NFHS. The NFHS maintains a higher temperature for longer, providing a more gradual release of heat, which may be beneficial for applications requiring stable, sustained cooling. The choice between TFHS and NFHS depends on the specific cooling needs, with TFHS suited for faster thermal regulation and NFHS for more consistent, long heat dissipation.

Fig. 12.

Comparison of NFHS and TFHS with SH PCM at 8 W.

The comparison of NFHS and TFHS with SH PCM at input power 12 W

The Fig. 13 shows, a comparison between the thermal performance of NFHS and TFHS, both incorporating SH as a PCM under 12 W thermal load. Initially, both configurations start at around 30 °C. The TFHS, represented by the solid red line, exhibits a slower temperature rise compared to the NFHS, indicated by the dashed black line. This slower increase in TFHS is attributed to its finned design, which enhances heat distribution and absorption by increasing the surface area, allowing more efficient heat transfer to the PCM. Consequently, During the heating period, both configurations show a temperature rise, but TFHS heats up more quickly and reaches a peak temperature of approximately 72.3 °C, compared to 71.2 °C for NFHS. This 1.5% increase is due to the improved heat conduction and greater surface area provided by the triangular fins, which allow heat to transfer more efficiently to the PCM. In the cooling stage, TFHS also demonstrates a faster drop in temperature. Around 9000 s, its temperature is about 8.7% lower than that of NFHS, and by 15000 s, it remains roughly 4.2% lower. These differences are primarily attributed to the fin design, which enhances both heat absorption during charging and heat dissipation during discharging. The added surface area not only improves contact with the PCM but also promotes better thermal exchange with the environment, resulting in more effective temperature regulation in the TFHS compared to the NFHS. During cooling, TFHS shows a steady and gradual decline, suggesting more controlled heat dissipation, while NFHS cools rapidly at first but slows down as it approaches ambient temperatures. TFHS more consistent cooling process makes it ideal for applications where stable thermal regulation is essential, while NFHS may be better suited for environments that can tolerate faster heat fluctuations and higher temperatures. Finally, TFHS provides superior thermal management through its design, making it more suitable for applications requiring consistent and moderate temperature control, while NFHS simpler structure may be beneficial in scenarios where rapid heat absorption and release are prioritized.

Fig. 13.

Comparison of NFHS and TFHS with SH PCM at 12 W.

The comparison of heat sinks with SH PCM at input power 4 W, 8 W and 12 W

The Fig. 14 illustrates, a comprehensive comparison of the thermal performance between NFHS and TFHS configurations using SH PCM under varying thermal loads of 4 W, 8 W, and 12 W. Each curve corresponds to the performance at a different configuration. Besides this, analysis has also shown variations in the heating/cooling behaviors of the said conditions. During the initial heating phase, both NFHS and TFHS configurations start from a baseline temperature of about 30 °C. At a 4 W load, TFHS (dashed green line) reaches a peak temperature of approximately 44 °C, while NFHS (solid pink line) peaks slightly higher at around 46 °C, showing a 4.3% lower peak for TFHS. This suggests that the TFHS, with its extended surface area due to fin structures, enhances heat absorption and distribution, making it more efficient in managing low power loads. As the power load increases to 8 W, the difference becomes more pronounced. NFHS (dotted red line) peaks at around 70 °C, whereas TFHS (solid orange line) peaks at approximately 67 °C, indicating again a 4.3% reduction in peak temperature for TFHS. This demonstrates that TFHS is more effective at dissipating increased heat loads, likely a result of enhanced convective heat transfer provided by the increased surface area from the fins. At the highest tested load of 12 W, the performance gap widens further; NFHS (dashed blue line) reaches a peak temperature of about 75 °C, while TFHS (solid purple line) peaks at ~ 70 °C, which is about 6.7% lower. This significant difference highlights TFHS superior ability to manage high thermal loads by delaying the saturation of the PCM, benefiting from the enhanced phase change process facilitated by its finned design. In the cooling phase, TFHS consistently shows a more gradual and controlled temperature decline compared to NFHS across all power levels. For example, at 12 W, the TFHS configuration (solid purple line) exhibits a steady cooling curve that maintains higher temperatures longer, gradually approaching ambient conditions. Conversely, NFHS (dashed blue line) experiences a rapid initial drop but slows down significantly, indicating less effective long-term heat dissipation. Similarly, at lower power levels of 4 W and 8 W, TFHS demonstrates sustained heat release, which is beneficial in applications that require continuous and stable thermal control. This is evidenced by the slower cooling rates of TFHS (dashed green line for 4 W and solid orange line for 8 W), compared to the more rapid but less consistent cooling of NFHS (solid pink line for 4 W and dotted red line for 8 W).

Fig. 14.

Comparison of NFHS and TFHS with SH PCM at 4 W, 8 W, and 12 W.

The overall superior performance of TFHS can be attributed to its increased surface area from the fins, which enhances both convective and conductive heat dissipation. This structural advantage not only lowers peak temperatures but also results in a more stable cooling process. The fins support to attain a more uniform temperature distribution throughout the PCM, improving the efficiency of the phase change process and resulting in better overall thermal regulation. TFHS consistently maintains peak temperatures that are lower by approximately 4.3% at 4 W, 4.5% at 8 W, and 6.7% at 12 W compared to NFHS, highlighting its superior ability to prevent overheating and manage heat loads effectively. In conclusion, TFHS with SH PCM offers a more reliable and effective solution for thermal management, especially in scenarios that demand sustained cooling performance and stability. Its ability to maintain lower peak temperature and provide a controlled cooling rate makes it particularly suitable for applications where prolonged thermal management is crucial. In contrast, NFHS, while effective at rapidly absorbing and releasing heat, tends to reach higher peak temperatures and exhibits a less steady cooling profile, making it less ideal for applications sensitive to temperature fluctuations. Therefore, the choice between these configurations should be guided by the specific cooling requirements, with TFHS being the preferred option for more demanding thermal management tasks.

Enhancement ratio (ξ)

The enhancement ratio with PCM is defined as the ratio of the time it takes for a PCM-based heat sink to reach the SPT, compared to the time required for the same heat sink without PCM. This can be calculated using Eq. (10), as referenced by Arshad et al.⁵⁶.

10

The Fig. 15a–d illustrate, comparison between NFHS and TFHS across various heat fluxes and temperature settings highlights the effectiveness of finned designs in enhancing heat transfer, especially during charging phases. At lower set-point temperatures (SPT 40 °C), TFHS benefits from a larger temperature gradient, which amplifies its heat absorption capability, allowing it to maintain relatively high performance despite being around 41% less efficient than NFHS at maximum heat flux. As the temperature rises to 50 °C, the efficiency gap between NFHS and TFHS narrows, with NFHS showing only about 50% better performance. In the discharging phase, the finned structure of TFHS contributes less to performance, as heat dissipation is more uniform between the two configurations. Still, NFHS maintains a slight edge, with a 6–13% higher enhancement ratio at higher heat fluxes. Overall, TFHS design is particularly advantageous in scenarios requiring efficient heat absorption at moderate heat fluxes, while NFHS tends to perform better under extreme conditions, particularly in heat release phases. This suggests that finned heat sinks like TFHS are more suited for applications where rapid heat absorption is required, while NFHS may be preferable in environments with high heat dissipation demands.

Fig. 15.

Enhancement ratio of charging and discharging phase at SPT 40 °C and 50 °C (a–d).

Set point temperature (SPT)

The Fig. 16a–d shows, the performance differences between NFHS and TFHS with PCM during charging and discharging are clear. In the charging phase Fig. 16a–b shows, NFHS takes longer to charge than TFHS with PCM at both 40 °C and 50 °C set point temperatures. Specifically, at 40 °C, NFHS takes 15–20% longer, and at 50 °C, this increases to 25–30%, due to the PCM capability to absorb more amounts of latent heat with minimal temperature increase, allowing faster energy storage. In the discharging phase Fig. 16c–d shows, NFHS releases heat faster than TFHS with PCM. At 40 °C, NFHS discharges 10–15% faster and at 50 °C, by 20–25%, since the stored heat is released by PCM gradually without the temperature varying excessively. Increasing the heat flux from 1.12 to 3.34 kW/m² decreases charging and discharging times by 40–50%, since the higher heat flux enhances the temperature gradient, therefore accelerating the heat transfer process. Similarly, it continues increasing the SPT from 40 to 50 °C for minimizing those times by 10–15% because of the larger temperature difference, which accelerates more heat transfer.

Fig. 16.

The charging and discharging at SPT 40 °C and 50 °C (a–d).

Effect of Stefan number

To evaluate the comparative effect of SH PCM, spider charts are used to depict the relationship between time and the Stefan number (Ste) at various set point temperatures (SPTs), specifically 0.022, 0.065, 0.174, 0.23, and 0.27 for SPTs of (40, 45, 50, 55, and 60) °C, respectively. Figure 17a–c demonstrates the behavior of low melting point PCM at an SPT of 40 °C up to a high melting point at an SPT of 60 °C. The Stefan number, a dimensionless measure of the superheat absorbed by the PCM, is defined by Eq. (11) as referenced by⁵⁵.

11

Fig. 17.

The effect of Stefan number during charging phase at constant power (a) 4 W, (b) 8 W, (c) 12 W, and (d) Compare 4, 8, and 12 W.

where, ‘Ste’ represents the Stefan number, ‘Q’ refers to the heat input (W), ‘c_p’ denotes the PCM’s specific heat capacity, ‘k_PCM’ signifies the PCM thermal conductivity, ‘l’ stands for the length of the heat sink (m), and ‘ʎ_PCM’ indicates the latent heat of the PCM. The Fig. 17a–c displays radar plots comparing the Stefan number for NFHS and TFHS at different thermal loads (4 W, 8 W, and 12 W). The analysis examines various parameters like time and Stefan number to evaluate the heat sink performance in both configurations. Figure 17a shows at a 4 W load, NFHS and TFHS show similar trends in Stefan number distribution. However, TFHS presents a more compact graph, indicating superior heat absorption efficiency. TFHS maintains lower Stefan numbers, signifying a slower temperature rise in comparison to NFHS, which spans a broader area at lower Stefan numbers, implying it takes longer to achieve thermal thresholds. TFHS outperforms NFHS by approximately 7–10% around the 0.22, due to its increased surface area, which enhances heat transfer and allows better heat absorption before significant temperature increase.

Figure 17b shows under an 8 W load; the performance difference becomes more apparent. TFHS, once again, maintains lower Stefan numbers across most regions, with about a 5–7% improvement over NFHS at the 0.174 and 0.065. TFHS compact profile indicates better thermal regulation, while NFHS displays larger deviations, especially around 0.27 and 0.23. The optimized design and larger surface area of TFHS enable more efficient heat dissipation, allowing the PCM to absorb more heat and delay temperature increases. Figure 17c shows at a higher load of 12 W, the gap in performance widens further. TFHS continues to show lower Stefan numbers, exhibiting around 10–12% better performance, particularly at the 0.22 and 0.174. TFHS also reaches thermal stability faster, peaking around 4000 s, whereas NFHS peaks later, around 4500 s. The fins in TFHS aid in maintaining a lower Stefan number by maximizing convective cooling, while NFHS simpler structure struggles to manage the heat effectively under higher loads. Figure 17d shows the performance across all three loads, with TFHS consistently showing lower Stefan numbers at every power level. The largest performance difference is observed at 12 W, where TFHS outperforms NFHS by 10–15% at the 0.27. Even at lower loads, TFHS maintains about 10% better efficiency than NFHS. The fins in TFHS facilitate superior heat dissipation, allowing for more effective absorption and release of heat, particularly as the thermal load increases. The spider plots clearly demonstrate that TFHS performs better than NFHS in heat management across different power loads. TFHS consistently exhibits lower Stefan numbers, highlighting its ability to manage heat more efficiently due to its finned design, which enhances surface area and convective heat transfer. NFHS, while functional, shows higher Stefan numbers, indicating faster temperature rises and less effective heat dissipation. This makes TFHS a preferable choice for applications requiring stable and extensive thermal regulation, especially at higher loads.

Effect of Fourier number

The Fourier number (Fo), a dimensionless measure of time, is described by Eq. (12) as follows⁴⁵.

12

where, ‘α_PCM’ stands for the thermal diffusivity of the PCM (m²/s), ‘L’ represents the heat sink length (m), and ‘t_set’ refers to the time taken to reach the SPT. These parameters are linked to the dimensionless temperature ‘θ’, which is expressed in Eq. (13) as follows.

13

In the equation, T_SPT indicates the set point temperature measured at the base of the heat sink, while T_max refers to the peak temperature observed during the charging and discharging stages under varying heat flux inputs. T_a represents the ambient temperature, which is set at 30 °C. The Fig. 18a–c shows as comparison between NFHS with PCM and TFHS with PCM highlights how the inclusion of triangular fins drastically improves thermal performance. At lower heat flux levels, such as 1.12 kW/m², the NFHS system demonstrates a slower, more gradual increase in dimensionless temperature (θ), indicating limited heat absorption capacity. In contrast, the TFHS system quickly absorbs and transfers heat, achieving approximately 85% of the dimensionless temperature at a Fourier number of 0.10, while the NFHS system only reaches around 72%. This showcases a notable 15–20% improvement in thermal efficiency, attributed to the fins role in enhancing the conduction process. As the heat flux increases to 2.23 kW/m² and 3.34 kW/m², the performance gap between the two systems becomes even more apparent. The TFHS system consistently outperforms the NFHS system, achieving higher temperature values at lower Fourier numbers. This trend underscores the fact that triangular fins not only improve initial heat absorption but also maintain efficiency as the system is exposed to greater thermal loads.

Fig. 18.

Fourier number during charging phase of SPT 70 °C at various heat flux rate (a) 1.12 kW/m², (b) 2.23 kW/m², and (c) 33.34 kW/m².

The triangular fins in the TFHS system act as extended surfaces that facilitate quicker heat dispersion into the PCM, enabling faster phase change and more effective thermal management. On the other hand, the NFHS system relies solely on conduction through the PCM, which is inherently slower and less efficient. This results in slower PCM melting and less uniform heat distribution. Overall, the TFHS system proves to be more advantageous in applications requiring rapid and efficient thermal control, especially under higher heat flux conditions. The ability of the fins to increase heat transfer rates and promote uniform temperature distribution makes the TFHS with PCM system a significantly better solution for scenarios involving high thermal loads, leading to faster charging cycles and improved energy storage capacity. The comparative performance of these systems demonstrates the critical importance of with fin heat sink in optimizing PCM for thermal regulation.

Heat storage ratio

The Heat Storage Ratio (HSR) of a heat sink using SH PCM defined as the total amount of heat the entire system was made to store by the PCM. It can be well defined as the ration of heat stored by the PCM to the total amount of heat storage by the entire heat sink system as presented in Eq. (14) below.

14

where, ‘Q_PCM’ is the amount of heat stored by the PCM during its phase change process. ‘Q_HS​’ represents the sensible heat stored by the heat sink material. This equation provides a way to determine the proportion of heat storage by the PCM in relation to the overall system, which includes both PCM and heat sinks base material. The Fig. 19a–c illustrating the Heat Storage Ratio (%) during the charging phase reveal notable differences between NFHS and TFHS across various SPTs and power levels. At lower power levels (4 W), NFHS demonstrates a slight edge over TFHS in heat storage efficiency, showing up to 6.6% higher storage at 50 °C. However, as power levels increase to 8 W and 12 W, TFHS consistently surpasses NFHS, with TFHS exhibiting up to 28.8% higher heat storage at 12 W and 70 °C compared to NFHS.

Fig. 19.

Heat storage ratio during charging phase at (a) SPT 50 °C, (b) SPT 60 °C, and (c) SPT 70 °C.

This trend indicates that TFHS efficiency improves with higher power inputs and temperatures, unlike NFHS, which experiences a decrease in heat storage ratio as power rises. The superior performance of TFHS at elevated power levels can be attributed to its more effective utilization of PCM, likely higher thermal conductivity, and enhanced heat transfer mechanisms. TFHS design appears to optimize SH PCM behavior and thermal mass distribution, making it more adaptable and efficient under varying or high-energy conditions. Conversely, NFHS may face challenges related to thermal resistance and restricted heating, which diminish its effectiveness at higher power levels. Finally, TFHS ability to maintain or improve performance with increasing power and temperature suggests it is better suited for applications requiring efficient heat storage in dynamic or high-energy environments.

Conclusion

The study examined several factors influencing the passive cooling of integrated circuits, focusing on input power levels ranging from 4 to 12 W. The experimental setup included heat sinks with SH PCM and utilized triangular cross-sectional designs. For the TFHS, the fin volume fraction was consistently set at 11%. The key findings highlight differences in thermal management performance based on these configurations, showing how fin design and the presence of PCM affect the cooling efficiency of the heat sinks under varying power loads.

• The temperature profiles of NFHS with SH PCM analysis in managing heat under varying power inputs. At 4 W, the system shows a controlled temperature rise of approximately 56.7%, indicating efficient heat absorption by the PCM. At 8 W, the peak temperature increases by about 80%, reflecting a higher heating rate that partially exceeds the PCM capacity. At 12 W, the peak temperature climbs by roughly 89%, the highest among the three scenarios, showcasing the PCM diminished effectiveness at higher power levels. Finally, while SH PCM effectively moderates temperature at lower power inputs, its capacity to absorb and stabilize heat decreases significantly as power increases, leading to progressively higher peak temperatures.

• The performance of the TFHS with SH PCM varies significantly with power input. At 4 W, the PCM effectively absorbs heat, resulting in a moderate temperature rise of about 56.7%. At 8 W, the peak temperature increases by 85%, indicating a faster heating rate and reduced PCM efficiency. At 12 W, the system exhibits the steepest temperature rise of 92.3%, showing the PCM limitations under high power conditions. Overall, the PCM provides effective thermal regulation at lower power levels, but its capacity diminishes significantly as the power increases, leading to higher peak temperatures and reduced thermal management efficiency.

• The TFHS with SH PCM consistently outperforms the NFHS across all tested power levels. TFHS achieves lower peak temperatures, reducing them by approximately 4.3% at 4 W and 8 W, and by 6.7% at 12 W compared to NFHS. This improved performance is attributed to the enhanced heat dissipation from the fins, which effectively distribute thermal energy and delay the saturation of the PCM. Furthermore, TFHS demonstrates a more stable and controlled cooling rate, making it a superior option for applications requiring sustained and reliable thermal management, especially under higher thermal loads.

• The Enhancement ratio of the TFHS performs well in heat absorption at lower temperatures and moderate heat fluxes but is less efficient than NFHS at maximum heat flux, with a 41% performance gap. As temperatures rise, the difference decreases, though NFHS still leads in both charging and discharging phases, especially under high heat flux. TFHS is ideal for efficient heat absorption, while NFHS is better suited for high heat dissipation needs.

• The SPT during charging and discharging phases. In charging, NFHS takes 15–20% longer at 40 °C and 25–30% longer at 50 °C compared to TFHS, due to PCM efficient latent heat absorption. In the discharging phase, NFHS releases heat 10–15% faster at 40 °C and 20–25% faster at 50 °C, as PCM releases heat more gradually. Increasing the heat flux from 1.12 to 3.34 kW/m² shortens both charging and discharging times by 40–50%, and raising the SPT from 40 to 50 °C reduces these times by 10–15%, thanks to enhanced temperature gradients.

• The Stefan number of TFHS consistently outperforms NFHS across various thermal loads. At a 4 W load, TFHS shows approximately 7–10% better performance by maintaining lower Stefan numbers and achieving faster heat absorption. At 8 W, TFHS improves efficiency by 5–7% and displays better thermal regulation, with smaller deviations in Stefan numbers. Under a 12 W load, the performance gap widens to about 10–12%, with TFHS reaching thermal stability faster and showing a significant advantage in heat management. Overall, TFHS demonstrates up to 15% better efficiency at higher loads, thanks to its enhanced surface area and convective cooling, making it superior in heat management compared to NFHS.

• The Fourier number of TFHS outperforms NFHS, especially at higher heat flux levels. At 1.12 kW/m², TFHS achieves about 85% of the dimensionless temperature, 15–20% better than NFHS 72%. With increasing flux, TFHS continues to excel, demonstrating superior heat transfer and phase change efficiency, underscoring the 15–20% gain of finned designs in managing high thermal loads.

• The TFHS shows superior heat storage ratio, especially at higher power levels and temperatures. While NFHS performs better at 4 W with up to 6.6% higher storage at 50 °C, TFHS outperforms NFHS by up to 28.8% at 12 W and 70 °C. This indicates that TFHS is more effective in high-energy conditions, optimizing PCM behavior and heat transfer for better performance as power and temperature increase.

• The results shows that the TFHS distributes superior thermal management compared to the NFHS, especially under heat fluxes up to 3.33 kW/m². At 12 W, TFHS reduced peak temperatures by up to 6.7% and reduced charging and discharging times by 20–30%, allowing faster thermal response. It also achieved a 10–12% gain in Stefan number efficiency, indicating more effective latent heat usage. Additionally, Fourier number improvements of 15–20% suggest enhanced heat transfer, while the heat storage ratio increased by 28.8% at 12 W and 70 °C.

• In conclusion, the TFHS is the best heat sink configuration, and SH PCM is suitable for use in portable electronic cooling.

Abbreviations

HS

Heat sink

NFHS

No fin heat sink

PCMs

Phase change materials

SH

Salt hydrates as calcium nitrate

SPT

Set point temperature

TCE

Thermal conductance enhancer

TFHS

Triangular fin heat sink

List of symbols

A

Heating plate base area

c_p

Specific heat capacity

F_o

Fourier number

g

Grams

K

Kelvin

L

Heat sink length (m)

P

Input power (W)

q

Heat flux (W/m²)

Q

Input heat capacity

s

Seconds

Ste

Stefan number

T

Temperature (°C)

t

Time (s)

V

Volume

W

Watts

Greek letters

k

Thermal conductivity

λ

Latent heat

α

Thermal diffusivity

γ

Volume fraction of the fins

θ

Dimensionless temperature

ξ

Enhancement ratio

ψ

Volume of fraction of the PCM

Subscripts/superscripts

a

Ambient

b

Base

max

Maximum

set

Set point temperature

t

Triangular fin

tf

Total fins

ts

Total heat sink

tt

Total triangular fins

Author contributions

G.M. investigated, conducted the experimental trials, Data cured and written original draft. M.S., project administration supervised, given methodology along with resources. A.C.B., performed result validation and reviewed. M.S. acquired the funding E.L. used software and Designed.

Data availability

The datasets used and analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.