0 Introduction

Renewable energy emerges as a superior solution to the challenges of energy depletion, owing to its abundant availability and eco-friendly nature. Notably, solar water heater collectors stand out as a pivotal application of solar energy. These collectors serve the purpose of directly harnessing solar radiation and converting it into usable heat or electricity, finding applications across various industrial sectors. Engineered to harness sunlight's heat-absorbing potential, these collector systems play a crucial role in transforming solar energy into practical forms.

Defined as the component responsible for converting solar energy into diverse usable forms, the solar collector captures electromagnetic radiation across a spectrum, ranging from infrared to long-range ultraviolet (UV), with a visible solar energy component constituting 49%^[1-3]. Enter nanofluids-dispersions of nanomaterials possessing enhanced properties. These nanofluids find extensive utility in diverse manufacturing contexts, including vehicle cooling, solar energy systems, and heat exchangers, thanks to their distinctive thermal attributes.

However, integrating nanoparticles into nanofluids introduces concerns, primarily surrounding nanoparticle stability within the base fluid. The interactions between nanoparticles and the overall stability of the nanofluid warrant thorough examination.

Previous research has explored the use of alumina nanoparticles at concentrations of 1%-3% mixed with water in laminar flow scenarios. Surface temperatures and pressure differentials across the test section were measured, revealing a notable increase in numerical values: 12%, 14%, and 16% enhancement in numbers correlating with nanofluid concentration and Reynolds number, respectively. This suggests that nanofluids have the potential to bolster the efficiency of solar collector systems^[4].

Numerous researchers have delved into enhancing solar thermal efficiency through nanofluid integration. Their findings underscore that incorporating nanofluids into solar collectors leads to a 10% efficiency enhancement when compared to conventional fluids^[5-6]. Further investigations highlight the impact of nanofluids on direct solar energy absorption by nanoparticles suspended in water. Carbon nanotubes increase efficiency by 5%, while copper particles boost it by 8% ^[7-8].

Tian et al.^[1] used Artificial Neural Network (ANN) to analyze the effect of temperature and nanoparticle volume fraction on the thermal conductivity of Graphene oxide-Al2O3/Water-Ethylene glycol hybrid nanofluid. Nanofluids were prepared with varying nanoparticle volume fractions (0.1% to 1.6%) and temperatures (25-55 ℃). The ANN was effectively trained to predict thermal conductivity, yielding an average MSE of 1.67e-6 and a correlation coefficient of 0.999. Results indicated that nanoparticle volume fraction had a more significant impact on thermal conductivity compared to temperature, especially at low concentrations. At high concentrations, increasing temperature led to a further increase in thermal conductivity. For instance, at a volume fraction of 1.6%, increasing temperature from 20 ℃ to 55 ℃ raised thermal conductivity from 0.45 W/mK to 0.54 W/mK. The study underscores the crucial role of nanoparticle volume fraction in enhancing thermal conductivity in hybrid nanofluids. Applying nanofluids within heat exchangers has been shown to optimize system performance, validated through extensive research^[9-12]. Notably, Mohammed et al.^[13] conducted a theoretical exploration of heat transfer improvements facilitated by various nanofluids, including silver, alumina, titanium, and silica. Their study yielded a substantial 15% increase in the performance factor.

In a holistic context, Khodabandeh et al.^[14] conducted a numerical investigation on laminar water nanofluid flow containing GNP-SDBS nanoparticles. The study explored mass fractions of solid nanoparticles from 0 to 0.1% and Reynolds numbers from 50 to 1000 using the finite volume method. They proposed a novel microchannel design where countercurrent flow was employed in upper and lower layers, with enhanced mixing facilitated by cavities, sinusoidal routes, and rectangular ribs on microchannel walls. Results showed a 20% increase in average Nusselt number for each Reynolds number considered, alongside improved heat transfer efficiency and temperature uniformity, especially in the lower layer. The recommended microchannel design is suggested for Reynolds numbers less than 300 to optimize heat transfer. The research conducted by Al-Kouz et al.^[15] explored the performance analysis of an electrically conducting water-Fe₃O₄/CNT hybrid nanofluid within a trapezoidal enclosure with wavy walls. Using computational methods, the study investigated three-dimensional free convection and entropy generation, taking into account a hybrid nanoliquid layer and a permeable medium layer within the enclosure. Various parameters, including the Darcy number, Hartmann number, volume fraction, undulation number of the wavy wall, and Rayleigh number, were considered in the analysis. By employing the Galerkin finite element method through COMSOL multiphysics software, the researchers analyzed the effects of these parameters on streamlines, isotherms, and Bejan number contours. Notably, an increase in Hartmann and Rayleigh numbers was found to significantly reduce the average Bejan number, whereas the average Nusselt number decreased notably only at very high Rayleigh and high Hartmann numbers. The study also observed that increasing the undulation number led to a substantial elevation of the average Nusselt number, particularly at very high Rayleigh numbers. Conversely, an increase in the Darcy number was associated with a significant increase in the average Nusselt number while reducing the average Bejan number. These findings have implications for various applications, including hybrid magnetic nanofluid fuel cells and the processing of electromagnetic nanomaterials in cavities, offering insights into thermal flow characteristics and performance under complex conditions involving magnetic fields, porous media, and thermal buoyancy. The main objective of this research work is to investigate heat exchange in a straight channel using Al₂O₃-water nanofluids across a range of Reynolds numbers (100 to 1800). The study involves both experimental and analytical approaches, including the preparation and analysis of nanofluids with varying volume fractions (1%, 2%, and 3%). The physical properties crucial for assessing thermal and flow characteristics are comprehensively evaluated. Numerical simulations are employed to predict Nusselt number (Nu) and friction factor (f) quantitatively, adds a novel dimension to the investigation.

1 Preparation of Nanofluids

This paper explores the dispersion of Al₂O₃ nanoparticles within a base fluid (water) to create nanofluids. Eq.(1) determines the necessary nanoparticle count to generate nanofluids at three volume fractions: 1%, 2%, and 3%. This methodology stands as the prevailing approach for nanofluid preparation, involving the introduction of nanoparticles into the fluid medium. To ensure even distribution and avert aggregation, an electric mixer is employed. Remarkably, an effective means of enhancing nanofluids' physical properties involves reducing the surface tension of the dissolved warm liquid, as elucidated by Ref. [15].

The nanofluids, comprising Al₂O₃ particles within water, are formulated at distinct concentrations: 1%, 2%, and 3% by volume. Each nanofluid concentration is combined with 10 L of water. Fig. 1 visually portrays nanofluid samples showcasing varying concentrations. Notably, the prepared nanofluids (Al₂O₃/water) exhibit stability across all tests. It is noteworthy that no surfactants, which could potentially alter the nanoparticles' physical properties, were introduced into the nanofluid mixture. The quantity of particles required for nanofluid preparation can be determined using the subsequent relationship^[16]:

$ \phi=\frac{m_p / \rho_p}{m_p / \rho_p+m_f / \rho_f} $

(1)

where ϕ represents the volume fractions of (Al₂O₃/water); m_p represents the mass of the Al₂O₃; ρ_p is the density of Al₂O₃; m_f represents the mass of the water; ρ_f is the density of water. Table 1 provides an overview of the physical properties of both water and nanofluids mixture at different volume fractions.

1.1 Experimental Setup

Fig. 2 shows the apparatuses employed for assessing convection characteristics and pressure drop within a straight channel using nanofluids. Commencing with the lowest flow rate, a state of data stability is initially established. Subsequently, a modest increase in the volume flow rate prompts the system to reattain equilibrium. Maintaining a constant input temperature, the experimental setup necessitates approximately 18 to 25 min to restore stability subsequent to the rise in volume flow rate. Upon achieving the input temperature once more, data collection is reiterated. This procedural iteration persists until the maximum flow rate is attained. In a similar vein, alterations in the volume concentrations of nanofluids are introduced, followed by the replication of the aforementioned actions.

1.2 Empirical Method and Theoretical Evaluation

The empirical configuration of the present study is elucidated in Fig. 2. The setup primarily comprises essential components such as thermocouples, a flow meter, a manometer, a pump, and the test section. To propel the nanofluid through the test section, a 370 W pump exerts force, drawing the fluid from a 10 L reservoir. The upper and lower walls of the rig are subjected to solar irradiation and are effectively insulated. Ensuring minimal heat exchange with the environment, the test section is enveloped by 5 cm thick layers of fiberglass insulation. Within the fluid circulation path, a flow meter is integrated, positioned between the circulation pump and the entry point of the development section. This flow meter boasts the capacity to accurately gauge flow rates ranging from 10 to 110 cm³/min.

1.3 Correlation of Data

The quantification of heat absorbed by the nanofluids from the test area can be determined employing the following formula^[17-19]:

$ Q_u=\dot{m} \mathrm{Cp}_w\left(T_{\mathrm{ws} . \mathrm{co}}-T_{\mathrm{ws} . \mathrm{cin}}\right) $

(2)

where $\dot{m}$ is fluid mass flow rate, Cp_w is fluid specific heat, T_ws.cin and T_ws.co are fluid inlet to the solar collector and fluid outlet from the solar collector.

To delineate the average heat transfer coefficient, one can utilize the following expression^[18]:

$ h_{\mathrm{nf}}=\frac{\mathrm{Cp}_{\mathrm{nf}} \cdot \rho_{\mathrm{nf}} \cdot U \cdot A\left(T_{\mathrm{out}}-T_{\mathrm{in}}\right)}{\pi \cdot D \cdot L\left(T_{\mathrm{s}}-T_{\mathrm{b}}\right)} $

(3)

where h_nf represents the convective heat transfer coefficient of a nanofluid flowing inside a tube, Cp_nf is the specific heat capacity of the nanofluid, ρ_nf is the density of the nanofluid, U is the average velocity of the nanofluid flow, A is the cross-sectional area of the tube, T_out and T_in are the outlet and inlet temperatures of the nanofluid, respectively, D is the inner diameter of the tube, L is the length of the tube in meters. Finally, T_s represents the surface temperature of the tube wall, and T_b is the bulk mean temperature of the nanofluid. The formula for computing the average Nusselt number is presented as follows^[18]:

$ N u_{\mathrm{nf}}=\frac{h_{\mathrm{nf}} \times D_{\mathrm{h}}}{k_{\mathrm{nf}}} $

(4)

where k_nf represents the fluid's ability to conduct heat and D_h stands for the hydraulic diameter of a straight channel which is described as follows^[18]:

$ D_{\mathrm{h}}=\frac{4 A_c}{P_m} $

(5)

where P_m is the wetted perimeter, defined as the total length of all sides in contact with the fluid for a non-circular conduit. The expression for the frication factor (f)^[20] is as follows:

$ f=\frac{\frac{2 \times \Delta P}{L / D \times \rho \times U_{\mathrm{in}}^2}}{4} $

(6)

where △P is the pressure drop across the length of the pipe, U_in represents the average inlet velocity of the fluid. The Nusselt number, serving as an indicator of the heat transfer coefficient, quantifies the heat transferred within a system.The Nusselt number, serving as an indicator of the heat transfer coefficient, quantifies the heat transferred within a system. In the context of laminar flow, the Shah-London equation is employed to characterize this phenomenon^[21].

$ \mathrm{Nu}_{\mathrm{av}}=1.953\left(\operatorname{Re} \cdot D_h P_r \frac{D_h}{L}\right)^{\frac{1}{3}} $

(7)

where Re and P_r are the Reynolds number and Prandtl number, respectively.

2 Mathematical Formulation 2.1 Problem Description

As illustrated in Fig. 3, the current investigation employs straight channels as the software setup. These channels are characterized by walls on both the upper and lower surfaces, uniformly subjected to heat flux conditions. The assumptions governing this study encompass a steady and developed flow, characterized by two-dimensional movement and incompressibility. Additionally, the nanofluid mixture (Water/Al₂O₃) is presumed to be in a state of thermal equilibrium and experiences consistent flow velocity. Furthermore, the mixture is assumed to exhibit Newtonian fluid behavior.

2.2 Management Equations

The non-dimensional governing equations for a nanoparticle-based fluid mixture that has laminar flow, are non-compressible, homogeneous and stable in two dimensions^[19]:

Continuity equation:

$ \frac{\partial U}{\partial X}+\frac{\partial U}{\partial Y}=0 $

(8)

U-momentum equation:

$ \left(U \frac{\partial U}{\partial X}+V \frac{\partial V}{\partial Y}\right)=-\frac{\mathrm{d} p}{\mathrm{~d} X}+\frac{1}{\operatorname{Re}}\left(\frac{\partial^2 U}{\partial X^2}+\frac{\partial^2 U}{\partial Y^2}\right) $

(9)

V-momentum equation:

$ \left(U \frac{\partial V}{\partial X}+V \frac{\partial V}{\partial Y}\right)=-\frac{\mathrm{d} p}{\mathrm{~d} Y}+\frac{1}{\operatorname{Re}}\left(\frac{\partial^2 V}{\partial X^2}+\frac{\partial^2 V}{\partial Y^2}\right) $

(10)

Energy equation:

$ \left(U \frac{\partial \theta}{\partial X}+V \frac{\partial \theta}{\partial Y}\right)=\frac{1}{\operatorname{Re} \cdot P_r}\left(\frac{\partial^2 \theta}{\partial X^2}+\frac{\partial^2 \theta}{\partial Y^2}\right) $

(11)

2.3 Grid Independent Test

In a broader sense, the credibility of numerical calculations hinges on the grid independence test, which determines the requisite grid size for the present investigation. This test was executed across four distinct grid dimensions (9.6×23, 23×26, 15×47, 20×100). Utilizing these grid sizes, the Nusselt number(Nu) and the distribution of the friction factor (f) were computed along the walls of a straight channel containing AL₂O₃-nanofluids. This calculation encompassed three different volume fractions, with Reynolds numbers ranging from 100 to 1800, and maintained a consistent length (25 cm) and width (2.5 cm) of the channel.

2.3.1 Geometrical model

The geometry was implemented based on the current Flat Plate Solar Collector (FPSC) prototype using OpenFOAM toolbox advanced design software, including the absorber plate, tubes, cover the glass, the air space between the glass and the absorber plate. The cross section details are explained in Fig. 3.

2.3.2 Mesh generation

Conducting grid-independent tests aids in striking a balance between accuracy and computational efficiency. The number of elements directly impacts the computational time required. In this model, the output entails 1.5 million cells. Fig. 4 illustrates the condition of the mesh, highlighting the identified exposed zones.

The sizing reached a maximum of 0.14962 m, alongside high smoothing settings. A total of 330910 statistics nodes and 1416020 elements were employed, with five layers of inflation featuring smooth transitions. The change ratio stood at 0.272, while the growth rate was 1.2. The setup incorporated physical properties pertaining to glass, aluminum, copper, air, and established boundary conditions for the flat solar collector. Positions and flow rates for the collectors were determined. To theoretically compute the glazing absorption plate's temperature, the solver employed continuity, momentum, and energy conservation equations. Boundary conditions were specified for particles smaller than 20 nm, assuming a spherical shape, density of 3510 kg/m³, conductivity of 1000 W/(m·K), and specific heat of 497.26 J/(kg·K). Nanofluid thermophysical properties were automatically updated by the solver. Its primary objective was to assess the thermal performance of the FPSC. Results from the software's post-processing are depicted in Fig. 5.

The Nusselt number appears to increase slightly with a significant rise in Reynolds numbers across various grid dimensions, as shown in Fig. 6(a). The friction factor exhibits a decreasing trend with increasing Reynolds numbers across various grid dimensions. This implies that, for different grid sizes, the friction factor tends to decrease as the Reynolds number increases, as shown in Fig. 6(b).

2.4 Validation of Numerical Methods

To validate and to affirm the accuracy of both numerical analysis and empirical findings, several metrics were scrutinized: the Nusselt number, friction factor, relative thermal conductivity, and relative viscosity. These metrics were juxtaposed with the simulation results derived from earlier studies. Notably, the average Nusselt number concerning the laminar flow of nanofluids between parallel plates was calculated and contrasted against outcomes from prior numerical investigations^[22-25].

The trends that emerged from this comparison were intriguing. Fig. 7(a) visually underscores the Nusselt number's correlation with Reynolds number, revealing that an increase in the latter corresponds to a rise in the former. Meanwhile, the simulation outcomes of the friction factor were aligned with those reported in other relevant literatures^[26-33]. This alignment led to the deduction that the friction factor escalates as the size of nanoparticles decreases, as visually depicted in Fig. 7(b).

3 Results and Discussions 3.1 Nusselt Number

The interplay between the Nusselt number and velocity is depicted in Fig. 8, considering nanofluids at varying velocities (6-15 mm/s) and nanoparticle diameters (30 nm). In the experimental examination of a straight channel, it becomes evident that the Nusselt number increases in direct proportion to the velocity surge, attributed to the concurrent escalation of Reynolds number. This correlation is observable.

Interestingly, when nanoparticles' size is amplified, an observable elevation in the Nusselt number occurs for a given Reynolds number. This trend aligns with expectations and demonstrates the impact of particle size on heat transfer dynamics. Additionally, the modest increase in thermal conductivity for the liquid contributes to a corresponding rise in the rate of heat transfer, aligning with predictions made by other researchers^[31].

It is worth noting that among the considered fluids, pure water (∅=0%) exhibits the lowest Nusselt number. This disparity can be attributed to its comparably lower thermal conductivity compared to nanofluids, further emphasizing the beneficial effects of nanoparticle dispersion on heat transfer efficiency.

3.2 Friction Factor

The friction factor, as illustrated in Fig. 9, is plotted over a velocity range from 7 mm/s to 15 mm/s, highlighting the significant influence of velocity on the friction factor for different nanoparticle concentrations. Notably, as the velocity of nanofluid particles increases, there is a distinct reduction in the friction factor. In contrast, a noticeable upward trend in the friction factor becomes apparent with escalating volume concentrations of substances.

These trends are deeply influenced by the viscosity characteristics of the nanofluids. This viscosity influence leads to heightened friction factors within the channel, a phenomenon intriguingly aligned with the observations of previous researchers who faced challenges in conclusively establishing this relationship^[32]. This harmony in findings reinforces the paramount importance of comprehending the intricate connection between nanofluid viscosity and the behavior of the friction factor within the channel.

4 Conclusions

In the realm of nanotechnology, the fabrication of nanoparticles has reached remarkable heights in contemporary times. Among their diverse applications, nanofluids hold a crucial role in enhancing heat transfer processes. These fluids introduce a new dimension by infusing conventional water with nanoparticles, thereby yielding a novel medium for effective heat transfer. This article provides an encompassing overview of recent strides in harnessing nanostructures to investigate heat transfer dynamics in solar collectors.

Nanofluids, comprising minute nanoparticle quantities, exhibit significantly heightened thermal conductivity compared with regular water. Essential factors, including particle size, nanoparticle composition, and the underlying material, intricately influence the heat transmission capacity of these fluids. The presence of these exceptional nanoparticles tangibly augments the heat transfer efficiency of the fluid involved in convection processes.

The impact of nanofluids' additives on overall solar system efficiency has been systematically evaluated. During experimental trials, the concentration of nanofluids proved to significantly influence the efficiency of solar collectors. This influence extended to parameters such as friction coefficient and Nusselt number, which were meticulously correlated through adept correlation equations. Moreover, input coefficients, including Reynolds number and nanoparticle size concentrations, were explored under flux conditions. Intriguing findings emerged from these computations. The authors substantiated that as the Reynolds number decreases, the coefficient of friction factor increases. Simultaneously, the coefficient of heat transmission exhibits an increment as both Reynolds number and particle size increase. This interplay underscores the intricate relationship between fluid dynamics, nanoparticle characteristics, and heat transfer efficiencies.