Experimental and Numerical Analysis of Thermal Efficiency Improvement in a Hybrid Solar–Electric Water Heating System

Abstract

Many studies on solar heating systems have examined individual techniques to enhance the performance of solar water collectors, such as flow obstructions, increased turbulence, nanofluids, and investment in thermal storage. The benefits of integrating these sustainability strategies into a single, sustainable system have yet to be fully established. This work displays a hybrid water-heating system that contains a solar water collector (SWC) and an electric water heater (EWH), a photovoltaic panel (PV), and nano-additives to increase the outlet water temperature and improve thermal efficiency. Numerical and experimental analyses were used to estimate the influence of water flow rate (2.5, 3.5, and 4.5 L/min) and different Al₂O₃ concentrations (0.1%, 0.2%, and 0.3%) on system performance using U-shaped pipe in SWC model. The results highlight that lower flow rates consistently yield higher ΔT values because water spends a longer time in the collector, allowing it to absorb more heat. Also, when using water only, the collector efficiency increases pro-aggressively with flow rate. A significant performance enhancement is observed upon incorporating Al₂O₃ nanoparticles into the fluid, with a 0.1% Al₂O₃ volume concentration improving efficiency by ~7.4% over water. At 0.3%, the highest improvement is recorded, yielding a ~9.3% gain in efficiency compared to the base case.

1. Introduction

In the past few years, heating systems have needed to find renewable, clean, non-polluting energy from natural sources, rather than using fossil or nuclear fuels that pollute the environment and pose the dangers of explosion and fire [1]. Solar energy, the cleanest and most abundant renewable energy resource, is a suitable alternative for reducing energy consumption. Since the early 1970s, solar water heater (SWH) systems have been tested, and classic solar collectors are made of flat-finned tube panels. Since then, new developments and innovations have led to more efficient collectors, including evacuated-tube collectors (ETC) [2], U-tube collectors [3], and heat-pipe collectors [4]. Heating water using a home SWH system is the most feasible, economical, and popular way to use solar energy in many countries worldwide. Hence, the global market for its use has expanded greatly in recent years [5]. A home solar water heating system consists of a solar collector, a heat storage tank, an auxiliary heater, a heat exchanger, and a series of tubes connecting the solar collector to a storage tank [6,7]. Many homes’ solar water heater systems use flat plate collectors attached to vertical or horizontal storage tanks [8,9]. A SWH significantly reduces electricity consumption for domestic water heating and helps reduce greenhouse gas emissions. Most residential buildings are equipped with water heaters set to 50–60 °C. Because its operating temperature range is well-suited to the melting behavior of Phase Change Material (PCM), it can be used for effective temperature control. So, the temperature of the produced water is regulated by the PCM in combination with the storage capacity [10]. To improve the overall performance of solar water collectors, experts have developed several techniques, including altering the design of heat pipes [11,12], using open geometric channels [13,14], using phase change materials [15,16], improving heat transfer with nano-additives [17,18], etc.

Regarding other investigations, the feasibility of investing in waste heat recovery and performance enhancement of an integrated system with a solar collector for hydrogen production was studied by Khanmohammadi and Saadat-Targhi [19]. They present the thermodynamic analysis and testing of a solar-based integrated energy system for hydrogen production, with and without a thermoelectric generator waste-heat recovery system. The results show that the standard system delivers 66.9 kW of net output power, and the suggested system can generate an additional 14 kW. Also, Zhu et al. [20] proposed a new solar-integrated energy system for power generation, hydrogen production, and combined heat. The system includes four units: a parabolic trough solar collector, a Kalina cycle, a transcritical CO₂ power cycle, and an electrolytic cell. Analysis results indicate that under standard conditions, when the transcritical CO₂ power cycle outlet temperature is 157.35 ° and the hydrogen production rate is 0.51 kg/h, the system achieves maximum exergy and energy efficiencies of 18.62% and 46.52%, respectively.

Abu-Hamdeh et al. [21] studied the thermal performance of a cylindrical solar collector with a curved absorber tube. An improvement in heat absorption has been observed in cylindrical solar collectors. At the same time, Guo et al. [22] reported that an optimal matching between collector area and storage tank volume is essential for space heating applications. Their simulation results for SWH systems indicated that the ideal ratio of storage tank volume to collector area depends on the total collector area. The developed model demonstrated reasonable accuracy, with deviations of ±10% for transient storage temperature distribution and ±3% for accumulated heat flux over the entire heating season. Yari et al. [23] highlighted in their study that the location of the SWH collectors, whether below or above the storage tank during system design, is an important factor in determining system efficiency. When building applications, moving the collector incurs additional installation and implementation costs. Liu et al. [24] investigated space heating using a novel hybrid solar heating system that integrates a Kang solar system (an old Chinese heating method that relies on the heat generated by burning animal waste) with a direct-gain hole and a Trombe wall. The study examined the effects of five operating modes on hourly indoor temperatures in the Qinghai–Tibet Plateau region. The results showed good agreement between numerical simulations and experimental measurements. In addition, unlike the other systems, the Kang solar system operates continuously throughout the day. The combined use of the Kang solar system, direct-gain holes, and Trombe walls was found to provide an optimal indoor thermal environment, particularly for rural residential buildings. Schoebi et al. [25] used CFD simulations to analyze the influence of cooling water and glass on collector performance. A range of operating parameters for the solar system, including water-cooling temperature, cover glass thickness, and water-cooling velocity, was analyzed. The findings revealed that employing water–glass cooling increased solar productivity by approximately 21.53% compared with glass–air cooling.

Diyoko et al. [26] conducted an experimental and ancillary theoretical study to enhance the convective heat transfer coefficient in a solar water heater by increasing the effective area between the heat transfer fluid and the contact surface area. Rectangular and square fins were used to improve the collector’s thermal performance. The results showed that the rectangular fin gives more power and energy efficiency. The efficiency of the rectangular fin is 18–20% higher than that of an ordinary tube at different mass flow rates. The efficiency of a square fin is 3–5% lower than that of a rectangular fin. Zhao et al. [27] conducted an experimental and theoretical study to investigate the Dynamic Phase Change Material Solar Collector (DPSC) integrated with walls. This study was conducted to control indoor temperature. The experimental and numerical results were compatible. The experiments show that about 3.43 °C can increase the room’s air temperature during winter. At the same time, the DPSC’s energy consumption reached 3.5 kWh when the room’s air temperature was set to 18 °C. The numerical results showed that the DPSC’s daily thermal efficiency was 44.3%. Lokhande and Dubey [28] used a heat exchanger to enhance the performance of a solar water heater. In the experiments, distilled water was used as the working fluid in the collector, and tests were conducted under both sunny and cloudy conditions from 9:00 am to 5:00 pm. The results showed that the system reached a temperature above 50 °C on sunny days. When the weather was cloudy, the system reached good results. Santos et al. [29] analyzed a vertical solar dryer by using the COMSOL Multiphysics software version 6.1, and performed another test by simulating a conventional solar dryer system, and compared the results. Abdelsalam et al. [30] proposed a solar steam generator for treating artificial seawater; they also used COMSOL Multiphysics in the numerical analysis. Their results showed a constant efficiency of 94% with a water salinity weight of 3.5%. In ambient conditions, a new model can produce 2.2 L of pure water per day from seawater. Sami et al. [31] applied the method of integrating a solar flat-plate heating system with clean-energy housing. Their economic analysis included four houses in different locations across distinct climatic regions in Algeria. They used the FChart method (an empirical method for assessing the long-term performance of solar systems). The study aimed to identify a suitable area for solar energy investment and reduce costs. The results showed that solar energy helped minimize traditional energy consumption by 46% and 57% in the northern and southern zones, respectively. Additionally, the annual cost savings for the solar system were 51% and 69%.

Nanofluids are prepared by homogeneously mixing nanoparticles in the working fluid. Adding solid-phase nanoparticles to the working fluid improves its thermal properties, enhancing direct absorption and heat transfer. Recently, scientific research has increased on the use of nanofluids in solar collectors to investigate their efficiency [32]. Shalal et al. [11] improved the thermal properties of the working fluid in PV/T systems by adding Al₂O₃ nanoparticles to enhance heat dissipation using a new solar collector design. Luo et al. [33] used nanofluids to increase the absorption of the solar radiation at low nanoparticle concentrations. They demonstrated that these additives improve the collector’s temperature and performance. They showed that nanofluids enhanced collector efficiency by 5–25% compared to the base fluid. An experimental and numerical study by Otanicar et al. [34] examined the influence of three nanofluids (silver, carbon, and graphite) on direct heat absorption rate in a solar collector. Their results showed that performance improved with increasing nanoparticle concentration beyond a volume fraction of 5%. Subramani et al. [35] investigated the addition of TiO₂ nanoparticles to water in a parabolic trough collector at concentrations of 0.05, 0.1, and 0.2% under turbulent flow conditions. The thermal efficiency was recorded at about 8.66% with 0.2% TiO₂ nanoparticles.

Generally, researchers have investigated various techniques to improve the performance of solar water heaters, including different pipe configurations within the collector, thermal energy storage (TES), nanofluids, and flow obstructions systems. The need to integrate these technologies into a comprehensive, unified system has recently become a research priority to address the significant gap in solar energy systems. Specifically, this involves reducing the daily fluctuations in absorbed energy resulting from the water exiting the solar water heater’s unstable temperature by combining it with another sustainable energy source. This work integrates two elements into a unified system. The validation included a rigorous dual approach, obtaining both experimental and computational fluid dynamics (CFD) results. While earlier research often reported efficiency trends without accounting for the coupled power water heaters powered by various solar energy sources, our study systematically examines a hybrid solar system including a solar water heater integrated with an electric water heater powered by a PV panel, with the adoption of nanofluid as the working fluid, and focusing on their combined effect on thermal performance and release cycles.

Table 1. The summary of the previous studies and the current work.

Authors	Used Technique	Performance
Morrison et al. [2]	ETC, a non-selective flat plate system (NFPS)	The efficiency was about 1.8 times that of NFPS.
Ma et al. [3]	U-tube solar collector, copper fin.	The efficiency decreases by 10%, and the outlet fluid temperature decreases by 16%.
Shalal et al. [11]	PV/T system, spherical bulges in an open flow flat collector, and Al2O3 nanofluid.	With nanofluid, the electrical efficiency has increased by 6.5% to 10%.
Yari et al. [23]	SWH and TES, with PCM	The maximum thermal efficiency was 74%.
Sharma et al. [32]	Solar collector, TES, Nano-enhanced-PCM-based energy storage	Charging and discharging efficiencies are enhanced by 24% and 28%, respectively.
Luo et al. [33]	Direct absorption collection, TiO2, Al2O3, Ag, Cu, SiO2, graphite nanoparticles, and carbon nanotubes.	Improved the efficiency by 2–25% for the base fluid.
Otanicar et al. [34]	Direct-absorption solar collector, nanofluids—silver, carbon, and graphite.	Efficiency improvements of up to 5% by utilizing nanofluids.
Subramani et al. [35]	Parabolic trough collector, TiO2 nanofluid	Collector efficiency is enhanced by up to 8.66% with nanofluids compared to water.
Current work	SWH, EWH powered by PV, Al2O3 nanofluid	Improving efficiency by 7.4–9.3% compared to the base case.

summarizes the comparison between the methods used in previous studies and those in our current work. This combined experimental and numerical methodology enables a deeper investigation of key physical processes, particularly the interactions among flow resistance, improved thermal conductivity, and thermal stability, which have been insufficiently explored in previous studies. By elucidating these processes and assessing their influence on heater performance, the work offers new insights that advance the design and optimization of integrated solar thermal systems.

On the economic side, integrating solar collectors, electric water heaters, and nano-additives into solar systems directly enhances heat transfer and reduces thermal losses. Furthermore, investing in PV panels to supply the system’s electrical power supports sustainable integration. These enhancements lead to higher thermal efficiency and more stable energy delivery, reducing the collector surface area needed to meet a given energy demand. Finally, by minimizing system size and nano-material use, the fabrication costs of solar thermal systems are reduced, and operational costs decrease due to lower auxiliary heating needs. More so, improved system reliability and lifetime performance minimize maintenance costs, resulting in a shorter payback period and a higher return on investment. These factors make the technology more attractive for large-scale applications in industrial process heating, building heating, and cooling.

2. Experimental Implementation

In this section, all experimental requirements to study the performance of the hybrid solar system are presented. A new design of a SWC and an EWH powered by a PV panel was used in experiments. The SWC was designed to include U-shaped copper tubes as a heat-absorbing medium. Also, the EWH was integrated with the SWC unit, using isolated copper tubes. This section presents how these heaters were fabricated and tested. The measurement system for limiting SWC and EWH unit performance, uncertainty analysis, and data collection will also be described.

2.1. Design and Fabricate a Hybrid Solar System

The hybrid solar system consists of two main parts: a new SWC design and an EWH. The solar radiation incident on the collector’s front surface directly affects its efficiency, as this depends on the absorber material’s properties and the collector’s surface area. To achieve maximum heat gain, the SWC is placed in a suitable area free of obstructions to solar radiation and uses water with nano additives (the working fluid) as the absorption medium to absorb solar energy. The SWC was fixed at a 45° inclination to ensure the collection of solar energy during the day. The new collector design features U-shaped tubes that provide a suitable path for the working fluid and a longer absorption period for solar energy. In experiments, different concentrations of Al₂O₃ nanoparticles and flow rates were tested. The geometry of the hybrid system is detailed as follows:

The hybrid solar system comprises several parts that work together to perform a specific function. The radiation is the system’s power unit. Using a SWC, solar energy is converted into thermal energy and transferred to the working fluid. Collector dimensions are 1000 × 2000 × 100 mm, Glass cover thickness is 3.2 mm, thickness of aluminum absorber plate is 1 mm, triangular face dimensions in the absorber plate are 140 × 120 × 100 mm, Inclination angle is 45ᵒ, copper water pipe is 13 mm in diameter, there is 150 mm spacing between the copper pipes, length of the water pipe is 7.5 m, and the thickness of glass wool insulation is 25 mm, as shown in Figure 1a.

Table 2. Specifications of the solar water collector, the electric water heater, and the PV panel system.

Specification of SWC	Values
Collector body dimensions	1000 × 2000 × 100 mm
Copper pipe diameter	13 mm
length of the water pipe	7500 mm
Space between the U pipe	150 mm
Collector frame	Wooden
Tilt angle	45°
Frame cover, Emissivity	Glass, 0.89
Specification of EWH	Values
Copper twist pipe length	1500 mm
Copper twist pipe diameter	13 mm
Twist turn	150
Strip heater length	5000 mm
Heater power	3000 watts
Specification of PV system	Values
Model of PV panel	MSM150S, Magnizon Power Systems, Dubai, United Arab Emirates
Cell efficiency	17.7%
Maximum power voltage and current	17.5 V and 8.63 A
Solar generator model	BLUETTI AC200P, PowerOak Technology Co., Ltd., Shenzhen, China
Battery capacity	~2000 Wh

shows all technical specifications of the SWC selected for the experiments.

Another part of the hybrid solar system is the EWH, a copper twist pipe with a 13 mm diameter and 1500 mm length, fabricated to have 150 turns. A 30 mm wide, 5000 mm long strip heater with a power of 3000 W is wound on the outer wall of a twist pipe, powered by a PV panel, as shown in Figure 2. All specifications of the EWH selected for the experiments are shown in Table 2.

2.2. Experimental Setup

The experiments were conducted on sunny days with moderate winds during daytime at the solar site of the University of Technology, Baghdad, Iraq. The experimental setup is shown in Figure 2. The hybrid system consists of several parts: the SWC, the EWH, the electric generator from a PV panel, the water-cooling tower, and the water pump. The specifications of the hybrid solar system are shown in Table 1. The hybrid solar heating system is equipped with a cooling tower to achieve a closed cycle. The water pump circulates the working fluid, and the control valve stabilizes the flow through a Rotameter at the required rate. The pump features were a model KF-10, 370 W, and 30 L/min flow. Also, a solar-powered generator from a PV panel provides the electrical energy used to heat the working fluid in an EWH to the required temperature.

In experiments, γ-Al₂O₃ nano-powder (20 nm, 99.6% purity, from SkySpring Nanomaterials, Houston, TX, USA) was used to prepare the nanofluid. The Al₂O₃–water nanofluids were prepared at different volume fractions (0.1–0.3%) by dispersing γ-Al₂O₃ nanoparticles in deionized water. Initially, the mixture was stirred magnetically for 60 min to ensure uniform dispersion, followed by ultrasonication for 90 min using a probe sonicator (400 W, 20 kHz, Omni International/Revvity, Kennesaw, GA, USA). During preparation, the fluid temperature was maintained below 30 °C using an external cooling bath to prevent nanoparticle agglomeration from excessive heating. The dispersion stability of prepared Al₂O₃ nanofluids was evaluated by zeta potential at 1 h and 48 h. At 1 h, the nanofluid exhibited a zeta potential of −38.4 mV, indicating strong electrostatic repulsion and excellent initial dispersion stability. After 48 h, the zeta potential remained relatively high at −36.6 mV, demonstrating only a slight decrease and confirming that the nanoparticles maintained a stable suspension over time. In addition to the electrokinetic analysis, visual inspection showed no signs of sedimentation or agglomeration even after 48 h, further validating the good long-term dispersibility of the Al₂O₃ nanofluids.

Table 3. Thermophysical properties of Al₂O₃ nanoparticles and Al₂O₃-water nanofluids at different volume concentrations.

Nanoparticle	Density (kg/m3)	Thermal Conductivity (W/m·k)	Specific Heat Capacity (J/kg·k)
Al2O3 (20 nm)	3970	40	765
Nanofluid (water + Al2O3)
0.1%	1025.4	0.867	4051
0.2%	1055.2	1.11	3926
0.3%	1084.9	1.78	3808

shows the direct effect of increasing the volumetric concentration of nanoparticles on their physical properties: density and thermal conductivity increase with concentration, while specific heat decreases gradually.

2.3. Measuring Instruments and Calculations

The measurement included type K thermocouples (Shanghai Weilian Electronic Technology Co., Ltd., Shanghai, China) to record the temperatures in the SWC. On the solar collector’s surface, two thermocouples were installed to measure the collector cover temperature. The second group has two thermocouples to record water temperature at the SWC inlet and outlet. The third group of thermocouples measures water temperature by passing through an electric water heater; thermocouples were used to record data at both ends of the EWH. The fourth group was installed to measure temperatures in the remaining system components and the ambient temperature (T_amb). The calibration of thermocouples was at 100 °C, with a maximum error of ±1.21 °C, and the flow meter recorded the required flow rate through the hybrid solar system.

To determine the heat transfer coefficient (h) and Nusselt number (Nu) [11,36]:

$$h={\displaystyle \frac{Q_u}{A_c\times ∆T}}$$

(1)

$$∆T=T_c-T_{av}; T_{av}={\displaystyle \frac{(T_{in}+T_{out})}{2}}$$

(2)

$$Nu={\displaystyle \frac{h\times d_e}{k}}$$

(3)

where Q_u is the useful heat gained by the collector, T_c is the collector surface temperature, Ac is the collector surface area, T_av is the average temperature between the inlet and outlet flows in the SWC, de is the hydraulic dimension of the collector cross-section, and k is the thermal conductivity.

The useful heat gain was determined by calculating the efficiency curve slope parameter, FcU, and the absorbed energy parameter, F_c(τα) [24]:

$$Q_u={\dot{m}}_{w}cp(T_{out}-T_{in}{)}_w=A_c{F}_c\left[G\left(\tau \alpha \right)-U(T_{in}-T_a)\right]$$

(4)

To determine the collector efficiency (ηc), Equation (5) was used [24,25]:

$${\eta }_c={\displaystyle \frac{Q_u}{G\times A_c}}=F_c\left(\tau \alpha \right)-F_{c}U{\displaystyle \frac{(T_{in}-T_a)}{G}}$$

(5)

$${\eta }_c={\displaystyle \frac{{\dot{m}}_w{Cp}_w(T_{out}-T_{in}{)}_w}{G\times A_c}}$$

(6)

where U is the total heat transfer coefficient, G is the incident solar radiation, $\dot{m}$ is the mass flow rate, cp is the heat capacity, and $(T_{out}-T_{in}{)}_w$ is the change in the water temperature.

The efficiency of the EWH unit was calculated using Equation (7) [25,26]:

$${\eta }_{EWH}={\displaystyle \frac{heat gained}{V\times I}}={\displaystyle \frac{\dot{m_w}{cp}_w{\left(T_{out}-T_{in}\right)}_{EWH}}{V\times I}}$$

(7)

2.4. Data Collection and Uncertainty Analysis

The experiments were carried out in several steps sequentially. Initially, the instruments were set up and insulated from the surroundings. Secondly, working fluid was circulated in the SWC and the EWH unit, and all data were recorded. Thirdly, further experiments were conducted by varying the flow rates and the working fluid at different nanofluid concentrations, and the data were recorded.

Table 4. Data collection for the hybrid solar system, SWC, and EWH.

Measurement Steps
Collector surface temperature	2 points	7:00 am to 7:00 pm
Inlet and outlet temperatures from SWC	2 points	7:00 am to 7:00 pm
Inlet and outlet temperatures from EWH	2 points	7:00 am to 7:00 pm
Direct solar irradiance	-	7:00 am to 7:00 pm
Al2O3 volume concentrations	0.1%, 0.2%, and 0.3%
Flow rate	2.5, 3.5, and 4.5 L/min

describes the experimentally recorded readings.

The Root Mean Square (RMS) uncertainty method was applied to determine the minimum and maximum uncertainty values [1], based on the measured values of the solar system parts and the accuracy value.

$${\epsilon }_i=\sqrt{{\left({\epsilon }_{sensor}\right)}^2+{\left({\epsilon }_{instrument}\right)}^2}$$

(8)

$$Minimum \& Maximum Uncertainty \left(\mathrm{\%}\right)=100\times \left({\displaystyle \frac{{\epsilon }_i}{Min.\&Max.reading}}\right)$$

(9)

Table 5. Uncertainty values of the measured parameters.

Parameter	Accuracy	Minimum Reading Value	Maximum Reading Value	Min. & Max. Uncertainty Value (%)
Temperature of collector surface, °C	±1.11°	23 °C	79 °C	1.18–0.952%
Inlet and outlet temperatures from the SWC	±1.21°	29 °C	72 °C	1.19–1.06%
Inlet and outlet temperatures from the EWH	±1.21°	34 °C	94 °C	1.32–1.02%
Flow rate, L/min	±0.13	2.5	4.5	0.264–0.179%

shows the uncertainty values for the parameters measured in the experiments. These parameters included working fluid temperatures and all hybrid system temperatures at both the SWC and the EWH.

3. Numerical Analysis

The performance enhancement and heat transfer behavior of a hybrid system were analyzed using the COMSOL Multiphysics v6.1 computational tool. The assessment criteria for nanofluid with concentrations (1%, 2%, and 3%) were investigated when the maximum efficiency was achieved. This analysis provides a valuable economic overview of the potential future commercial uses of a hybrid solar heating system. Also, the simulation goal is to record the maximum possible heat gain from a hybrid system containing an SWC and an EWH powered by PV-generated electricity.

3.1. Geometric Design and Mesh Discretization

The initial stage in evaluating any technical system is developing a geometric model that defines the computational domain for subsequent analysis. Examining thermal systems through their geometric configurations is crucial—particularly for energy-efficient designs—where consistent element dimensions and various shapes, such as uniformly distributed twisted pipes, play significant roles. Consequently, geometric extrapolation using advanced engineering software becomes essential. In this study, the modelling approach comprised two components: the SWC and EWH models. Figure 3 illustrates the simulated domain for both models.

A CFD model was employed to investigate heat transfer via absorption in a U-shaped copper pipe embedded within a zigzag aluminum plate. Owing to the system’s complex geometry, the water domain was discretized using unstructured tetrahedral meshes. An irregular tetrahedral mesh was selected to capture geometric details accurately. Mesh independence was assessed to eliminate the influence of mesh size on the numerical solution, and the optimal mesh density was determined when further refinement produced no significant change in results. Figure 4 illustrates the three-dimensional meshed geometry of the hybrid solar heating system models. The finalized mesh demonstrated sufficient numerical accuracy to evaluate heat gain within the collector and to examine the velocity and temperature fields of the working fluid. As a result, the fine-mesh model was selected for all simulations.

Mesh independence was assessed using five grid sizes for both the SWC and EWH models. The outlet water temperature predicted for the SWC showed negligible variation when meshes with the numbers of nodes 2,978,022 and 3,890,774 were used. Therefore, the mesh with a number of nodes 2,978,022 was selected to ensure sufficient computational accuracy while reducing computational cost. Similarly, the outlet water temperature results for the EWH were nearly identical for meshes containing 308,342 and 388,664 nodes. Figure 5 demonstrates mesh independence validation by showing the convergence of simulated outlet water temperatures with increasing mesh density (i.e., number of nodes).

3.2. Governing Equations

The analysis employs the core fluid-dynamics governing equations, including conservation of mass, momentum, and energy. They were formulated for a three-dimensional, steady, incompressible, viscous flow regime to represent the system’s physical characteristics accurately. The computations were performed using COMSOL Multiphysics’ commercial CFD software version 6.1, employing the finite-volume method. The solver configuration and simulation parameters were selected in accordance with established methodologies and previous studies, as referenced in [11,22]. This approach enables a comprehensive evaluation of fluid flow behavior, heat transfer processes, and thermal energy storage performance in the hybrid solar heating system models.

Continuity equation,

$${\displaystyle \frac{\partial u}{\partial x}}+{\displaystyle \frac{\partial v}{\partial y}}+{\displaystyle \frac{\partial w}{\partial z}}=0$$

(10)

The representation of the momentum equations in Cartesian coordinates is shown in Equations (11)–(13).

$$\rho \left(u{\displaystyle \frac{\partial u}{\partial x}}+v{\displaystyle \frac{\partial u}{\partial y}}+w{\displaystyle \frac{\partial u}{\partial z}}\right)=-{\displaystyle \frac{\partial p}{\partial x}}+\mu ({\displaystyle \frac{{\partial }^{2}u}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}u}{\partial y^2}}+{\displaystyle \frac{{\partial }^{2}u}{\partial z^2}})$$

(11)

$$\rho \left(u{\displaystyle \frac{\partial v}{\partial x}}+v{\displaystyle \frac{\partial v}{\partial y}}+w{\displaystyle \frac{\partial v}{\partial z}}\right)=-{\displaystyle \frac{\partial p}{\partial y}}+\mu \left({\displaystyle \frac{{\partial }^{2}v}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}v}{\partial y^2}}+{\displaystyle \frac{{\partial }^{2}v}{\partial z^2}}\right)+\rho g_y$$

(12)

$$\rho \left(u{\displaystyle \frac{\partial w}{\partial x}}+v{\displaystyle \frac{\partial w}{\partial y}}+w{\displaystyle \frac{\partial w}{\partial z}}\right)=-{\displaystyle \frac{\partial p}{\partial z}}+\mu ({\displaystyle \frac{{\partial }^{2}w}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}w}{\partial y^2}}+{\displaystyle \frac{{\partial }^{2}w}{\partial z^2}})$$

(13)

where u, v, and w are the velocity components in x, y, and z directions. g_y is the gravity effect in the y-direction, and ρ is the working fluid density. For a stable fluid, the assumption is that the liquid is incompressible. For the slight temperature change, the fluid viscosity μ is assumed to be constant, and the fluid is Newtonian [22]. At the same time, the viscosity effect cannot be neglected when the flow occurs inside a relatively long conduit.

The energy equation is

$$\rho cp{\displaystyle \frac{DT}{Dx}}=\nabla .\mathrm{k}\nabla T+\beta T{\displaystyle \frac{DP}{Dx}}+\mu \mathrm{\varnothing }$$

(14)

$$\beta =-{\displaystyle \frac{1}{\rho }}{\left[{\displaystyle \frac{\partial \rho }{\partial T}}\right]}_p$$

(15)

where β is the coefficient of thermal expansion, k is the thermal conductivity, and cp is the heat capacity of water, and

$$\mathrm{\varnothing }=2\left[{\left({\displaystyle \frac{\partial u}{\partial x}}\right)}^2+{\left({\displaystyle \frac{\partial v}{\partial y}}\right)}^2+{\left({\displaystyle \frac{\partial w}{\partial z}}\right)}^2\right]+\left[{\left({\displaystyle \frac{\partial u}{\partial y}}+{\displaystyle \frac{\partial v}{\partial x}}\right)}^2+{\left({\displaystyle \frac{\partial v}{\partial z}}+{\displaystyle \frac{\partial w}{\partial y}}\right)}^2+{\left({\displaystyle \frac{\partial w}{\partial x}}+{\displaystyle \frac{\partial u}{\partial z}}\right)}^2\right]-{\displaystyle \frac{2}{3}}{\left({\displaystyle \frac{\partial u}{\partial x}}+{\displaystyle \frac{\partial v}{\partial y}}+{\displaystyle \frac{\partial w}{\partial z}}\right)}^2$$

(16)

where ϕ is the dissipation rate function (also called viscous dissipation or strain-rate invariant) used in fluid mechanics and turbulence modeling, this function measures the amount of energy loss due to fluid deformation. It removes the contribution from pure volumetric change.

4. Results and Discussion

4.1. Experimental Results

Figure 6a shows the variation in the temperature difference (ΔT) in the SWC model throughout the day for three water flow rates: 2.5 L/min, 3.5 L/min, and 4.5 L/min. The trends indicate a strong influence of mass flow rate on heat transfer and thermal performance. The results show that lower flow rates consistently yield higher ΔT values because water spends a longer time in the collector, allowing it to absorb more heat. At 2.5 L/min, the system exhibits the highest temperature rise, peaking around 8–8.5 °C near midday, followed by the 3.5 L/min flow rate, which reaches approximately 7–7.5 °C. The highest flow rate, 4.5 L/min, produces the lowest ΔT—about 5.5–6 °C at peak conditions—because the water moves more quickly and gains less temperature per unit mass. So, the results highlight the inverse relationship between water flow rate and temperature rise, emphasizing the trade-off between achieving higher outlet temperatures at low flow and maximizing heat extraction at higher flow. Figure 6b presents the variation of absorbed energy in SWC at different water flow rates. Figure 6b presents the variation of absorbed energy in SWC at different water flow rates. The absorbed energy rate increased with higher water flow rates, due to increased pumping power. So, in practical solar thermal applications, the trade-off between thermal gain and hydraulic penalty must be considered.

Figure 7 illustrates the effect of working fluid flow rate (2.5–4.5 L/min) on the maximum temperature difference (ΔT) at different Al₂O₃ concentrations. The results clearly demonstrate that adding nanoparticles significantly improves the system’s thermal performance, with ΔT increasing with nanoparticle concentration. At all flow rates, pure water exhibits the lowest temperature rise, while the nanofluid with 0.3% Al₂O₃ achieves the highest ΔT, reaching nearly 9.5 °C at 2.5 L/min. As the flow rate increases, ΔT decreases for all fluids due to reduced residence time within the collector; however, the performance advantage of nanofluids persists. The enhancement becomes particularly noticeable at lower flow rates, where heat absorption per unit mass is more pronounced. Generally, the results highlight both the beneficial impact of nanoparticle concentration on heat transfer and the inverse relationship between flow rate and temperature rise.

Figure 8 compares the thermal efficiency of the SWC under three different flow rates (2.5, 3.5, and 4.5 L/min). The efficiency is plotted as a function of the dimensionless temperature parameter (Ti-Ta)/G (m²·K/W). The results indicate that collector efficiency decreases as (Ti-Ta)/G increases. This is consistent with classical solar collector theory, in which higher temperature differences between the inlet fluid and ambient air result in greater thermal losses, thereby lowering efficiency. The steeper decline in efficiency at higher flow rates is due to insufficient fluid–matrix contact, which limits heat absorption. At low values of (Ti–Ta)/G, efficiency is higher (~0.48 at 2.5 L/min), but drops to ~0.37 at the far right of the curve. This behavior is commonly observed in solar water collectors, where thermal losses increase as the temperature difference rises. The 4.5 L/min flow rate shows the highest thermal efficiency ~0.56 at lower values of (Ti-Ta)/G, due to increased heat absorption, which aligns with the results reported by Shalal et al. [11].

Figure 9 presents a comparative analysis of the impact of varying flow rates and Al₂O₃ nanoparticle concentrations on the thermal efficiency of a solar water collector. The results showed that, for the base case using water only, the collector efficiency increases progressively with flow rate, from approximately 0.57 at 2.5 L/min to around 0.63 at 4.5 L/min. A significant performance enhancement is observed upon incorporating Al₂O₃ nanoparticles into the fluid, with 0.1% Al₂O₃ volume concentration improving efficiency by ~7.4% over water. At 0.2%, efficiency increases further by ~8.8%. Also, at 0.3%, the highest improvement is recorded, yielding a ~9.3% gain in efficiency compared to the base case. This performance increase is attributed to the higher thermal conductivity and enhanced heat transfer properties of Al₂O₃ nanofluids, especially when U-shaped pipes are used, which promote turbulence and improve thermal exchange. The absorber’s ability to transfer heat to the working fluid is strong even with plain water. When nanofluids are added, the relative enhancement is the greatest because the performance indicates nanofluid enhancements (higher k, better heat absorption).

Figure 10 shows the dual impact of flow rate and nanoparticle concentration on the thermal performance of SWCs. The results show that higher concentrations of Al₂O₃ increase the absorbed energy parameter Fc(τα) while decreasing the slope parameter FcU, reflecting higher energy retention and lower losses. Increasing the flow rate improves the effect by promoting better convective heat transfer, as evidenced by the rising FcU at each concentration level. Figure 10a illustrates the variation in the absorbed solar energy parameter, denoted as, across a range of Al₂O₃ volume fractions (from 0% to 0.3%) at three distinct flow rates (2.5, 3.5, and 4.5 L/min). The Fc(τα) increases steadily with increasing nanoparticle concentration and flow rate, indicating improved solar energy absorption by the nanofluid medium compared to pure water.

Figure 10b illustrates the behavior of the efficiency curve slope parameter, FcU (the overall heat loss coefficient multiplied by the collector efficiency factor), for the same flow rates and Al₂O₃ concentrations. Unlike the absorbed energy parameter, the FcU parameter shows a decreasing trend with increasing Al₂O₃ volume fraction, particularly at lower flow rates. This suggests that heat losses are mitigated when using nanofluids compared to water, likely due to improved thermal conductivity and better heat retention within the collector system. For any given concentration, increasing the flow rate increases the FcU value. This indicates that forced convection at higher flow rates improves heat removal, helping balance the increased thermal absorption.

Figure 11 illustrates the daily variation of outlet water temperature from the EWH integrated with the SWC. Figure 11a presents the effect of different water flow rates (2.5, 3.5, and 4.5 L/min). Across all flow rates, the outlet temperature rises during the morning hours, attains its maximum near solar noon, and then gradually declines toward the evening as solar irradiance decreases. At the minimum flow rate of 2.5 L/min, the outlet water temperature peaks at approximately 90.6 °C around midday. This behavior is attributed to the longer water residence time in the absorber, which allows greater thermal energy absorption. In contrast, increasing the flow rate to 3.5 L/min and 4.5 L/min results in lower peak outlet temperatures of approximately 75.3 °C and 64.7 °C, respectively. This reduction is due to enhanced convective heat removal, in which the absorbed thermal energy is distributed over a larger water mass, resulting in a smaller temperature rise per unit mass.

Figure 11b shows the influence of Al₂O₃ nanoparticle additives at concentrations of 0.1%, 0.2%, and 0.3%. For all Al₂O₃ concentrations, the outlet water temperature follows a similar trend: it increases from morning until around midday, then slowly decreases toward evening as solar radiation declines.

4.2. Numerical Results

Figure 12 presents the temperature contours of the SWC at 12:00 pm for different water flow rates: (a) 2.5 L/min, (b) 3.5 L/min, and (c) 4.5 L/min. The results indicate that the water temperature increases as it flows through the collector due to heat absorption, with higher temperatures observed at the outlet resulting from suction and thermal uptake within the U-shaped pipe. At the lowest flow rate of 2.5 L/min, the temperature distribution shows higher temperatures along the entire U-shaped flow path, indicating slower heat removal and greater thermal accumulation within the fluid. As the flow increases to 3.5 L/min, the contours show slightly lower temperatures, indicating enhanced convective heat transfer at the higher fluid velocity. At the highest flow rate of 4.5 L/min, the temperature distribution shows a notable overall decrease, with heating zones appearing later along the coil and reduced thermal gradients throughout the domain. This heating effect reflects the decreased heat-carrying capacity of the faster-moving water. Overall, the figure clearly shows that increasing the water flow rate enhances heat transfer performance in the SWC system, resulting in lower, more uniform temperature fields.

Figure 13 presents the temperature contours for the SWC model at three Al₂O₃ nanoparticle concentrations, 0.1%, 0.2%, and 0.3%, showing how increasing nanoparticle content affects the thermal performance of the working fluid. At the lowest concentration of 0.1%, the temperature field exhibits relatively higher temperatures along the U-shaped pipe, particularly in the upper regions, indicating limited enhancement in thermal conductivity and heat absorption. As the concentration increases to 0.2%, the contours show a noticeable reduction in temperature, with more uniform gradients along the flow path. This improvement reflects the better thermal transport properties of the nanofluid, which enhances heat removal from the SWC structure. At the highest concentration (0.3%), the temperature distribution becomes even more uniform. It shows a further reduction in overall temperature, especially near the outlet, demonstrating the strong heat-carrying capacity provided by the increased nanoparticle loading. Overall, the figure clearly illustrates that higher Al₂O₃ concentrations improve thermal conductivity, reduce localized hot zones, and promote more efficient, uniform heat transfer within the SWC model.

Figure 14 illustrates the temperature contour distribution within the EWH at a water flow rate of 2.5 L/min. The theoretical analysis indicates that during electric heating, the outlet water temperature increases, and enhanced heat absorption is observed when the twisted-pipe configuration is employed.

4.3. Validation of Numerical Modeling

Figure 15 compares the SWC collector efficiency obtained from numerical simulations and experimental measurements at two flow rates (2.5 L/min and 4.5 L/min) and at different Al₂O₃ nanoparticle volume fractions. Generally, the results show a consistent trend: increasing nanoparticle concentration enhances collector efficiency across both flow rates and numerical and experimental data sets. At each concentration, the higher flow rate of 4.5 L/min yields noticeably better performance than 2.5 L/min, reflecting the combined benefits of improved thermal conductivity from the nanofluid and enhanced convective heat transfer at the higher flow velocity. The percentage differences in thermal efficiency were 5.2% and 7.8% at 2.5 L/min and 4.5 L/min, respectively.

Figure 16 compares the maximum temperature difference of SWC obtained from numerical simulation and experimental measurements at two flow rates (2.5 L/min and 4.5 L/min) and at different Al₂O₃ nanoparticle volume fractions. The results show that increasing nanoparticle concentration increases the temperature difference across both flow rates, as observed in both numerical and experimental data sets. The percentage differences in the maximum temperature difference were 9.7% and 7.5% at 2.5 L/min and 4.5 L/min, respectively.

5. Conclusions

An experimental and numerical analysis is conducted to examine how nano-additives and different flow rates influence the thermal efficiency of a hybrid solar heating system (SWC coupled with EWH). The temperature distribution for different water flow rates and Al₂O₃ additives has been studied. The following conclusions are drawn:

• The lower flow rates consistently yield higher ΔT values because water spends a longer time in the collector, allowing it to absorb more heat. At 2.5 L/min, the system exhibits the highest temperature rise, peaking around 8–8.5 °C. The highest flow rate, 4.5 L/min, produces the lowest ΔT, about 5.5–6 °C at peak conditions. The results highlight the inverse relationship between water flow rate and temperature rise, emphasizing the trade-off between achieving higher outlet temperatures at low flow and maximizing heat extraction at higher flow.
• Results showed that using water only, the collector efficiency increases progressively with flow rate. A significant performance enhancement is observed upon incorporating Al₂O₃ nanoparticles into the fluid, with 0.1% Al₂O₃ volume concentration improving efficiency by ~7.4% over water. At 0.3%, the greatest improvement is recorded, yielding a ~9.3% gain in efficiency compared to the base case.
• The results indicate that the outlet water temperature from the EWH rises, reaching a maximum of approximately 90.6 °C at the lowest flow rate of 2.5 L/min, and in contrast, increasing the flow rate to 3.5 L/min and 4.5 L/min results in a reduction in the outlet temperature to about 75.3 °C and 64.7 °C, respectively. Also, when using Al₂O₃ additives (0.1%, 0.2%, and 0.3%), the outlet temperature increases with all Al₂O₃ concentrations.
• Numerical results illustrate that higher Al₂O₃ concentrations improve thermal conductivity, reduce localized hot zones, and promote more efficient, uniform heat transfer in the SWC and EWH models.