2.1 Nano-Enhanced PCM

The preparation of nano-enhanced phase change material (Ne-PCM) using Fe₃O₄ nanoparticles and paraffin wax varies depending on the volume fraction of nanoparticles (0.2 wt.%, 0.4 wt.%, and 0.6 wt.%) to optimize thermal performance. Initially, paraffin wax is melted at 70°C–80°C to ensure a uniform liquid phase for effective nanoparticle incorporation. Fe₃O₄ nanoparticles are first dispersed in ethanol or hexane to prevent agglomeration, with ultrasonication applied for 30 min to achieve uniform dispersion. For 0.2 wt.% Fe₃O₄, a lower concentration ensures minimal alteration of paraffin's latent heat while enhancing thermal conductivity slightly. For 0.45 wt.% Fe₃O₄, a balance between thermal conductivity improvement and phase change enthalpy retention is maintained, making it suitable for moderate thermal applications. For 0.6 wt.% Fe₃O₄, a higher concentration leads to significant thermal conductivity enhancement, but excessive loading may cause particle sedimentation and reduce latent heat storage. Various Fe₃O₄ (iron oxide) nanoparticle weight percentages amounting to 0.2 wt.%, 0.4 wt.%, and 0.6 wt.% served as the strategic selection basis during this investigation because they meshed scientific principles with practical requirements. Several precise concentrations were chosen because they establish a systematic way to analyze the thermal effects of nano fluids while revealing patterns between thermal performance metrics [20]. The experimental conditions of nanoparticle loading consist of three percentages that generate enough data to determine the best concentration that optimizes Ne-PCM performance without compromising its material stability.

Fe₃O₄ nanoparticles maintain exceptional thermal conductivity properties with media fluid stability, which makes them appropriate additives for solar thermal energy system improvement. Too many nanoparticles used in combination may create various adverse effects during the process. When the nanoparticle concentration exceeds 0.6 wt.%, van der Waals attractions cause particles to tend to agglutinate. Such nanoparticle aggregation results in non-homogeneous distribution along with reduced surface area, which leads to poor thermal conductivity enhancement and may negatively affect system performance High concentrations of nanoparticles cause PCM viscosity increases that reduce fluid flow efficiency and heat transfer quantity while increasing pump power needs, thus lowering system operational performance.

Operational needs together with economic aspects sail as important factors in the process. The high cost of nanoparticles becomes a major issue when their concentration is elevated because it affects the overall expenses while potentially nullifying the efficiency benefits achievable in practical implementations. The operational stability of higher concentration suspensions can be negatively affected over time by sedimentation and stability issues that emerge under periodic thermal cycling, which happens frequently in solar thermal systems. Although 0.6 wt.% offers excellent thermal capabilities, the system operates within a stable and reliable economic range that ensures Ne-PCM remains functional throughout its operational lifespan. A maximum practical amount of 0.6 wt.% serves as an optimal boundary to enhance nanoparticle benefits in the system because it strikes a balance between performance and system stability and flow characteristics, and cost-effectiveness. The researcher has deliberately manipulated concentrations of Fe₃O₄ nanoparticles to establish methodical results about performance improvements through nanotechnology in ETSC.

The dispersed Fe₃O₄ nanoparticles are gradually added to the molten paraffin under continuous stirring for 60 min at 1540 rpm (Sesw 0136 3 L Magnetic Stirrer without Hot Plate with Magnetic Bar). To improve stability, a surfactant such as oleic acid or stearic acid is introduced, especially at higher nanoparticle concentrations, to prevent aggregation. Further ultrasonication is applied to maintain homogeneity, ensuring even nanoparticle distribution. The ultrasonication (Verilux 2 Liter Stainless Steel Ultrasonic Cleaner with Digital Timer & Heater) is done at a temperature of 80°C for 90 min. The solvent is evaporated under vacuum at 60°C to eliminate residuals that may affect thermal properties. The solidified Ne-PCM is characterized using DSC to measure phase transition temperatures and latent heat, revealing that 0.2 wt.% has minimal latent heat reduction, whereas 0.6 wt.% shows a slight decrease due to increased solid content. After the preparation, the PCM was incorporated within the heat exchanger to study the experiment of ETSC. Table 2 shows the properties of PCM. Similarly, Figure 1 shows the Ne-PCM preparation steps.

Figure 2 shows the Fourier transform infrared (FTIR) spectrum of the Ne-PCM. The broad absorption band observed in the range of 3200–3500 cm⁻¹ corresponds to the OH stretching vibration, indicating the presence of hydroxyl (-OH) groups, which could be due to hydrogen bonding or moisture absorption. Peaks at 2916.5 cm⁻¹ and 2852.9 cm⁻¹ indicate CH stretching vibrations from aliphatic hydrocarbons, indicating the existence of long-chain organic molecules in the PCM. A peak at 1735.1 cm⁻¹ signifies the CO (carbonyl) stretching vibration, typical of ester or carboxyl functional groups, indicating the PCM includes organic substances like fatty acids or esters.

Peaks at 1635.4 cm⁻¹ and 1462.7 cm⁻¹ indicate structural alterations in the PCM, caused by CC stretching vibrations in alkenes or aromatic rings and bending vibrations of –CH₂ or –CH₃ groups. Further, the peak at 1381.7 cm⁻¹ is associated with the symmetric bending vibration of CH bonds in alkanes, indicating the organic character of the PCM. Strong absorption bands at 1103.4 cm⁻¹ and 1018.7 cm⁻¹ indicate CO stretching vibrations in ether or ester bonds, suggesting Fe₃O₄ nanoparticles and PCM may interact chemically. The FeO peaks at 580.2 cm⁻¹ and 628.8 cm⁻¹ indicate the existence of Fe₃O₄ nanoparticles, confirming their effective incorporation into the PCM. Additional peaks (900–1300 cm⁻¹) in the fingerprint region indicate complicated bond bending and stretching vibrations, bolstering the PCM's structural stability. The existence of FeO bonds and organic functional groups indicates that Fe₃O₄ nanoparticles are evenly distributed throughout the PCM, improving its thermal characteristics. Spectral measurements suggest Fe₃O₄ nanoparticles efficiently interact with the PCM, potentially enhancing thermal conductivity, phase shift, and energy storage.

Similarly, Figure 3 shows the result of X-ray diffraction (XRD) of Ne-PCM, which provides crucial information about their crystalline structures and the impact of Fe₃O₄ nanoparticle incorporation. The XRD spectrum of pure PCM exhibits a broad diffraction peak in the range of 15°–30°, indicating its amorphous or semi-crystalline nature. This broad peak is characteristic of organic PCM materials, which generally lack a well-defined crystalline structure. In contrast, the Ne-PCM spectrum shows a significant difference with distinct sharp peaks, particularly at 2θ values of approximately 30.1°, 35.5°, 43.2°, 53.7°, 57.2°, and 62.8°. These peaks correspond to the characteristic diffraction planes (220), (311), (400), (422), (511), and (440) of Fe₃O₄ nanoparticles, confirming their presence in the modified PCM. The high-intensity peak at around 35.5° indicates strong crystallinity in the Fe₃O₄ phase, suggesting that the nanoparticles are well dispersed within the PCM matrix.

The incorporation of Fe₃O₄ nanoparticles results in an overall increase in crystallinity, as seen in the Ne-PCM pattern, which exhibits sharper peaks compared to the broad amorphous hump of the pure PCM. This enhanced crystallinity contributes to improved thermal conductivity, as crystalline structures facilitate better heat transfer pathways. Furthermore, the suppression of the amorphous peak in Ne-PCM suggests strong interactions between the PCM molecules and Fe₃O₄ nanoparticles, leading to structural modifications that enhance phase change behavior.

2.2 Experimental Details

Experimental equipment includes an ETSC, flow meter, control valve, data logger, data recording system, and solar weather station. ETSC has 15 evacuated tubes and a 1.49 m² collection area. Each tube has a 47-mm inside and 60-mm outside diameter and a length of 1.9 m. Enclosing a heating conduit with an aluminum fin improves tube thermal conductivity and heat transfer. To distribute heat efficiently, a manifold is attached to the heat conduit, which is filled with a high-conductivity liquid. A vacuum barrier between the tubes and the outside glass lowers conduction heat loss, improving thermal efficiency.

The working fluid is accurately guided to the absorber by a flow meter and control valve. A 1 HP pump maintains fluid circulation pressure. J-type thermocouples with a broad operating range of −300°C–1500°C are mounted at the inlet and egress to assess thermal efficacy and detect fluid temperature variations. In addition, a pyranometer and anemometer are employed to continuously monitor wind speed and solar radiation to ascertain the extent to which environmental conditions affect the system's performance. The Keysight 34970A data gathering system facilitates precise thermal analysis by collecting real-time temperature data. The experimental structure of the ETSC system is illustrated in Figure 4, which illustrates the integration of the solar collector with the measuring devices. Additionally, the ETSC specification is delineated in Table 3.

Additionally, the PCM material was retained in the heat exchanger to ensure a consistent heat supply to the air, thereby mitigating the temperature fluctuations caused by passing clouds. This, in turn, led to intermittent heat transmission to the operating fluid. Paraffin wax was selected as the PCM for this investigation due to its thermal stability, high latent heat storage capacity, and non-corrosive characteristics. The heat exchanger contained 3.8 kg of paraffin wax, which occupied 75% of the available capacity. The remaining 25% was left unoccupied to accommodate the volumetric expansion of PCM during its transition from solid to liquid.

To maximize heat transfer, the heat exchanger used a cylindrical copper coil. Copper tubes with 10 mm diameters and 2.8 m lengths transmitted heat between the ETSC's working fluid and the stored PCM. ETSC heat was stored in paraffin wax during peak sun radiation. For consistent air heating, this heat was gradually released. Copper's strong thermal conductivity improves heat exchange efficacy to reduce heat losses and improve system performance. Due to its thermal buffering effect, this setup maintained heat output regardless of solar radiation, improving the system's thermal performance.

2.3 Experimental Procedure

To assess the thermal efficiency of the ETSC, the experiment was conducted with the Nee-PCM with varying mass fractions of nanoparticles 0.2 wt%, 0.4 wt%, and 0.6 wt%. The experimentation was conducted at Saveetha University in Chennai (13.0802°N, 80.2011°E), where the ambient temperature ranged from 30°C–38°C and solar irradiance oscillated between 50 and 950 W/m². The ETSC was initially evaluated using water without PCM conditions, and its efficacy was compared to water with PCM and Ne-PCM conditions. For precise thermal analysis, J-type thermocouples were employed in conjunction with a data-logging system to collect temperature measurements. The study examined critical performance parameters, such as the fluid temperature profile, heat accumulation, thermal efficiency, and exergy efficiency. The experimental setup's photocopy is illustrated in Figure 5.

Figure 5 displays an experimental procedure that measures the performance outcomes of an ETSC system along with its Ne-PCM Fe₃O₄ nanoparticle-enhanced PCMs. As a highly efficient solar thermal system, the ETSC operates mainly for water heating purposes and thermal energy storage needs. The system has parallel vacuum-sealed glass tubes that work as individual solar collectors. The vacuum-sealed tubes achieve solar heat absorption through a reduction in conductive and convective heat losses. Each tube represents 1800 mm in length while measuring 58 mm around its outside and 47 mm around its inside diameter, is constructed using borosilicate glass with selective coating applied to the inner surface to boost solar absorption.

A nanofluid storage tank operated by Fe₃O₄ nanoparticles and water solutions exists at the top portion of the ETSC. The system uses the nanofluid as it travels from the storage tank through the fluid inlet and then sends it into the evacuated tubes for solar energy absorption. The nanofluid circulation flow run is marked as “Nanofluid Circulation” in the representation. After heat absorption from solar energy, the nanofluid exits the system through the fluid outlet to reach the heat exchanger. The closed-loop pattern of circulation enables continuous heat absorption as well as heat transfer activities.

The thermocouple sensors track temperatures along the nanofluid route starting from the collector inlet and extending to the outlet and potentially extending to the storage device and heat exchanger units. The sensors interface with a data logger system which maintains continuous temperature measurement for thermal measurement purposes. Data analysis consisting of heat absorption and thermal and exergy efficiency calculations depends on the measurements obtained under changing nanoparticle concentrations. The results of the reaction depend on data obtained when the nanoparticle concentration levels change. The setup contains a weather monitoring station that collects measurements of solar irradiance together with wind speed and temperature levels because these environmental elements impact the system output. These measurement variables enable precise connection of system production data to external inputs.

The system contains a heat exchanger that serves as a crucial device for moving thermal energy from nanofluid to stored or used water. The system uses spiral coil heat exchangers because they provide both compactness and efficient heat transfer performance for this application. For this application, the heat exchanger has its copper tubes approximately 2 to 3 m long, with an outer coil diameter of 300 mm, an inner diameter of 200 mm, and a tube diameter of 10 mm Such a system design creates high heat transfer surface capacity from limited space while properly functioning for solar thermal applications.

The experimental framework enables thorough analysis of fluid temperature changes, heat transfer behavior, along with thermal and exergy performance at 0.2 wt.%, 0.4 wt.%, and 0.6 wt.% Fe₃O₄ nanoparticle dosages for validating PCM-based improvement in solar power applications.

2.4 Thermal Modeling

The equations provided for analyzing the thermal and exergy performance of an ETSC are based on a set of underlying assumptions that ensure the validity and applicability of the models. Firstly, it is assumed that the solar radiation I_T is uniformly distributed across the collector surface and that the collector area A_c is effectively exposed to this radiation. The transmittance–absorptance product (τα) is considered constant, reflecting stable optical properties of the collector during operation. The heat loss coefficient U_L is treated as constant over the range of operating temperatures, implying that the thermal losses through convection, conduction, and radiation are linear with respect to the temperature difference between the absorber surface and ambient air.

In the derivation of the heat removal factor F_R, the fluid properties such as specific heat C_p and mass flow rate m are considered steady and uniform, ensuring a consistent heat transfer throughout the collector. The temperature distribution within the working fluid is assumed to be one-dimensional, neglecting any radial gradients, and the flow is considered to be fully developed and steady-state. It is also assumed that there are no heat losses along the flow path inside the tubes apart from the predefined losses accounted for by U_L.

For the thermal efficiency equation, the assumption is that the system operates under steady-state conditions with no energy accumulation, and all absorbed energy is either transferred to the fluid or lost through heat transfer to the surroundings. The exergy efficiency equation assumes that the irreversibility in the system can be quantified through entropy generation S_gen, and that the average surface temperature T_s of the collector is well-defined and stable. The ambient temperature T_a is also considered constant during the period of analysis. Additionally, the second law efficiency calculation presumes that the energy conversion processes follow ideal thermodynamic behavior where exergy destruction is solely due to heat transfer across finite temperature differences.

These assumptions simplify the real system into a tractable analytical model, allowing for performance evaluation and comparison, while recognizing that deviations may occur under dynamic or transient operational conditions.

2.5 Uncertainty Analysis

The instrument's uncertainty in Table 4. Moreover, Figure 6 shows the graphical flow of the current study. Uncertainty in temperature measurements (±1%) had a negligible impact on efficiency calculations, as confirmed by error propagation analysis (Equation 5). In general, all uncertainties measured and the sum of them were less than 5%. This confirms a 95% confidence level. The uncertainties were mentioned in the results at 95% CI, ±1 SD with the use of error bars (Figures 7-11).

3.1 Fluid Temperature

The thermocouple measured the fluid outlet temperature, which is illustrated in Figure 7. It clearly shows that the fluid temperature increases with the solar radiation increasing and decreases with solar radiation decreasing. Also, the maximum fluid temperature was recorded at noon due to peak radiation availability. The fluid temperature of water under the PVCM (pure PCM) condition is recorded as the lowest, at approximately 58.4°C. This is primarily due to the limited thermal conductivity of conventional PCM materials, which results in slower heat absorption and release rates. In contrast, the addition of Fe₃O₄ nanoparticles into the PCM matrix (Ne-PCM) significantly enhances thermal conductivity, thereby improving heat transfer efficiency and raising fluid temperature. The increase in fluid temperature with varying concentrations of Fe₃O₄, Ne-PCM is evident, with values of 83.2°C, 88.8°C, and 94.5°C for 0.2 wt.%, 0.4 wt.%, and 0.6 wt.% nanoparticle concentrations, respectively. The uncertainties were mentioned in the results at 95% CI, ±1 SD in error bars on the graph in Figure 7.

This improvement can be attributed to the superior thermal conductivity of Fe₃O₄ nanoparticles, which facilitate rapid heat absorption and storage within the PCM, leading to more effective thermal energy exchange with the fluid. Dispersed nanoparticles improve convective heat transmission, resulting in more uniform and efficient energy distribution. Higher nanoparticle concentrations raise fluid temperature due to better thermal diffusivity and reduced thermal resistance. Additionally, Fe₃O₄ nanoparticles maintain stable dispersion in PCM, minimizing agglomeration and maintaining heat transfer performance. Nanomaterials and PCM synergistically reduce subcooling, ensuring a more constant phase transition and heat storage. Due to its higher specific heat capacity, the hybrid Ne-PCM retains energy and releases heat slowly, maintaining high fluid temperatures for longer. The magnetic characteristics of Fe₃O₄ nanoparticles may enhance thermal performance by promoting micro-convective currents. The pattern shows that nanoparticles and PCM optimize heat transfer fluid thermal regulation. This helps solar thermal systems, where heat storage and retrieval are crucial to performance. Incorporating Fe₃O₄ Ne-PCM shows promise in improving thermal behavior and heat transmission between PCM and water [27].

3.2 Heat Absorption

The temperature differential between the fluid inlet and outlet is measured to compute the heat absorption rate. Figure 8 depicts the heat absorption value for the different PCM integration conditions. The uncertainties were mentioned in the results at 95% CI, ±1 SD in error bars on the graph in Figure 8. The maximum heat absorption capacity of the PCM and Ne-PCM composites varies significantly depending on the concentration of Fe₃O₄ nanoparticles. The pure PCM exhibits the lowest heat absorption, at approximately 2516.9 W, due to its inherently low thermal conductivity, which restricts the rate of heat transfer. However, the introduction of Fe₃O₄ nanoparticles into the PCM matrix enhances its thermal performance, leading to higher heat absorption values. At 0.2 wt.% of Ne-PCM, the heat absorption increases to 3084.8 W, indicating an improvement in thermal conductivity due to the dispersion of nanoparticles, which facilitates better heat distribution. As the concentration of Fe₃O₄ nanoparticles rises to 0.4 wt.%, the heat absorption further increases to 3298.5 W, demonstrating the effectiveness of the nanoparticle-enhanced PCM in improving energy storage and transfer efficiency. The highest recorded heat absorption, at 3804.1 W, corresponds to the Ne-PCM with 0.6 wt.% Fe₃O₄, highlighting the substantial role of nanoparticles in promoting thermal conductivity and reducing thermal resistance within the PCM. This progressive increase in heat absorption capacity can be attributed to the enhanced specific heat and improved latent heat storage properties of the nanocomposite PCM [27].

Fe₃O₄ nanoparticles induce micro-convective currents, enhancing heat dispersion and thermal management. Nanoparticles also reduce subcooling, improving phase transition and heat absorption. Ne-PCM is ideal for thermal energy storage applications, especially solar thermal systems, where heat absorption and storage are important to system performance. Ne-PCM can be used in sophisticated methods of storing energy since it absorbs and stores more heat than pure PCM [12]. Applications demanding high energy density and effective temperature regulation need this increase. Integrating Fe₃O₄ nanomaterials into PCM enhances heat absorption, thermal energy usage, and ETSC system efficiency.

3.3 Thermal Efficiency

The heat input and output ratio gives the thermal efficiency profile of the ETSC system, and it is illustrated in Figure 9. It also follows the same trend of heat absorption profile. The peak thermal efficiency was recorded at peak fluid temperature and heat absorption values. The uncertainties were mentioned in the results at 95% CI, ±1 SD in error bars on the graph in Figure 9. The thermal efficiency of the system exhibits a significant improvement with the integration of Fe₃O₄ nanoparticles into the PCM. Pure PCM demonstrates the lowest thermal efficiency at approximately 46.1%, primarily due to its limited thermal conductivity, which restricts heat transfer rates and results in suboptimal energy utilization. However, the addition of Fe₃O₄ nanoparticles enhances the thermal properties of PCM, leading to a notable increase in efficiency. At 0.2 wt.% Ne-PCM, the efficiency rises to 61.7%, indicating improved heat absorption and distribution due to enhanced thermal conductivity.

As the concentration increases to 0.4 wt.%, the efficiency further improves to 75.5%, highlighting the role of nanoparticles in facilitating better heat transfer and reducing thermal resistance within the material. The highest recorded thermal efficiency, at 83.5%, corresponds to the Ne-PCM with 0.6 wt.% Fe₃O₄, emphasizing the synergistic effect of nanoparticles in enhancing both sensible and latent heat storage capabilities. This progressive increase in efficiency can be attributed to several factors, including improved thermal diffusivity, reduced subcooling effects, and better phase transition characteristics. The Fe₃O₄ nanoparticles act as thermal conductivity enhancers, promoting faster and more uniform heat distribution throughout the PCM matrix [28]. Additionally, their presence induces micro-convective currents, further optimizing the heat transfer process. Another contributing factor is the increased specific heat capacity of Ne-PCM, which allows for greater energy storage and a more sustained heat release. The observed trend suggests that an optimized concentration of nanoparticles significantly improves the overall thermal performance of PCM, making it more effective for thermal energy storage applications. Higher thermal efficiency improves energy conversion and system reliability in solar thermal systems. Ne-PCM's higher performance over traditional PCM shows its promise for enhanced energy storage technologies, maximizing heat source usage. Adding Fe₃O₄ nanoparticles to PCM can improve thermal efficiency, leading to more sustainable thermal management systems.

3.4 Exergy Efficiency

Figure 10 shows time-dependent exergy efficiency for different PCM settings. The uncertainties were mentioned in the results at 95% CI, ±1 SD in error bars on the graph in Figure 10. The addition of Fe₃O₄ nanoparticles to the PCM improves energy usage and reduces irreversibility, resulting in increased exergy efficiency. Due to its limited thermal conductivity and heat transfer rate constraints, pure PCM has the lowest exergy efficiency of 31.2%. Thermal resistance and poor phase transitions waste much of the absorbed energy. The inclusion of Fe₃O₄ nanoparticles significantly enhances exergy efficiency. Nanoparticles boost thermal conductivity, which improves heat absorption and utilization, increasing exergy efficiency to 36.6% at 0.2 wt.% Ne-PCM. As the concentration climbs to 0.4 wt.%, thermal diffusivity, subcooling, and phase transition kinetics improve, resulting in 43.7% exergy efficiency. The Ne-PCM with 0.6 wt.% Fe₃O₄ had the highest exergy efficiency of 45.2%, highlighting the synergistic benefits of nanoparticles in reducing entropy and optimizing thermal performance. Good heat distribution, lower thermal resistance, and increased latent heat storage capacity increase exergy efficiency. Fe₃O₄ nanoparticles improve heat transmission by generating micro-convective currents in the PCM matrix, resulting in better thermal energy conversion. Additionally, Ne-PCM's increased specific heat capacity retains energy, reducing exergy destruction. The trend shows that PCM-based thermal storage systems with adequate nanoparticle concentration improve exergy efficiency, making them more practicable for solar thermal energy systems [28]. Higher exergy efficiency converts thermal energy into productive work, maximizing heat source use. Solar collectors, heat exchangers, and thermal energy storage devices need this innovation for efficient thermal management. Adding Fe₃O₄ nanoparticles to PCM can improve energy efficiency, reduce losses, and improve thermal storage and conversion processes [29].

Figure 11 displays the average thermal and exergy efficiency curve for different PCM settings. As nanoparticle concentration increases, PCM and Ne-PCM composite thermal and exergy efficiency improve. Due to phase change heat storage and release, the base PCM has 48.7% thermal efficiency and 15.2% exergy efficiency. Lower exergy efficiency indicates higher system irreversibility. With the addition of 0.2 wt.% nanoparticles, thermal efficiency increases to 52.6% as nanoparticles enhance thermal conductivity, leading to better heat absorption and release. The exergy efficiency also rises to 19.7% due to reduced thermal resistance and improved energy utilization [30]. At the Ne-PCM concentration of 0.4 wt.%, thermal efficiency further improves to 55.9% because of enhanced thermal diffusivity, allowing quicker heat transfer. Correspondingly, exergy efficiency reaches 22.4% as the system becomes more thermodynamically efficient with reduced entropy generation. The highest performance is observed at 0.6 wt.% Ne-PCM, where thermal efficiency reaches 62.6% due to superior heat transfer characteristics, ensuring rapid energy storage and retrieval. Exergy efficiency peaks at 26.5% as heat utilization is optimized, minimizing exergy destruction [31]. The uncertainties were mentioned in the results at 95% CI, ±1 SD in error bars on the graph in Figure 11. Table 5 shows the comparative analysis of previous studies with current research.