Performance Assessment of Flat Plate Solar Collector Using Simple and Hybrid Carbon Nanofluids at Low Thermal Capacity

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Abstract

Installation of flat solar collectors (FSCs) has been increasing due to the zero cost of renewable energy. However, the performance of this equipment is limited by the area, the material and the thermophysical properties of the working fluid. To improve the properties of the fluid, metal and metal oxide nanoparticles have mainly been used. This paper presents the performance assessment of the FSCs using simple and hybrid carbon nanofluids of low thermal capacity. Energy and mass balance modeling was performed for this study. A parametric analysis was conducted to examine the impact of key variables on the performance of the solar collectors using simple graphite and fullerene nanofluids, as well as hybrid metal–oxide–carbon nanofluids. From the results of heat transfer in FSCs, using graphite and fullerene nanofluids, it can be concluded that adding these nanoparticles improves the convection coefficient by 40% and 30%, respectively, with 10% nanoparticles. The graphite and fullerene nanoparticles can enhance the efficiency of FSCs by 2% and 1.5% more than base fluid. As the decrease in efficiency using fullerene with magnesium oxide is less than 0.2%, fullerene hybrid nanofluids could still be used in FSCs.

1. Introduction

The deployment of flat solar collectors (FSCs) has been growing steadily thanks to the no-cost nature of renewable energy. Studies such as the one carried out by [1] shows that the efficiency of the solar collector is influenced by the solar radiation and the temperature of the thermal fluid. However, the performance of this equipment is limited by the area, the material and the thermophysical properties of the working fluid. The primary characteristics required for working fluids in solar collectors include a high boiling point, non-corrosiveness, high heat capacity, and high thermal conductivity (TC). Traditionally, water, oil, and ethylene glycol have been the most used fluids in solar collectors. To improve the properties of the fluid, metallic and metal oxide nanoparticles in simple and hybrid nanofluids have mainly been used.

Composed of only one type of particle, simple nanofluids exhibit significantly higher TC than conventional fluids. They have demonstrated notable improvements in heat transfer for applications such as heat exchangers, refrigeration systems, and solar thermal systems. Choi and Eastman [2] defined nanofluids as suspensions of nanometric particles, made of one or more materials, in a base fluid. The concentration of nanoparticles, their shape and size have an impact on the thermophysical characteristics of nanofluids, such as TC, viscosity, heat capacity, as well as on the heat transfer coefficient and optical properties, for example [3]. Colloidal suspensions of nanomaterials (metals, metal oxides, and carbon) provide greater TC, better stability, and less risk of clogging in pipes [4,5]. Larger nanoparticles can cause suspension instability, resistance to flow, clogging of pipes and abrasion problems.

A hybrid nanofluid is a combination of physical and chemical properties, consisting of adding two or more types of nanoparticles to a base fluid. These nanoparticles can be made of different materials such as metal oxides, carbon, polymers and other synthetic materials. The main characteristics of hybrid nanofluids are their high TC, low viscosity, and ability to improve the absorption of solar radiation [6,7]. A literature review of metal oxide and carbon nanofluids used in FSCs is presented below.

1.1. Metal Oxide Nanofluids in FSCs

The TC and heat transfer of a fluid improve with the use of metal oxide nanoparticles, as shown by [8]. The nanofluids used were aluminum oxide (Al₂O₃), magnesium oxide (MgO), cerium oxide (CeO₂), titanium dioxide (TiO₂), zinc oxide (ZnO) and iron oxide (Fe₂O₃). In [9], the thermophysical characteristics of nanofluids, such as viscosity, TC and heat transfer with nanoparticles of (SiO₂), (Al₂O₃), (ZrO₂), (TiO₂), and (CuO) have been experimentally evaluated. The researchers have shown that viscosity increases with decreasing the nanoparticle size, while thermal conductivity increases as the particle size increases. Yousefi et al. [10] carried out an experimental investigation in which they studied the effects of the thermophysical properties of the Al₂O₃/water nanofluid on the efficiency of an FPSC. The authors showed that the efficiency of the solar collector increased by 28.3%. Verma et al. [11] carried out an experimental study of energy and exergy, using MgO-H₂O nanofluid in concentrations of 0.25 to 1.50 vol%. The authors found that at higher concentrations of nanoparticles, when agglomeration occurs, the Brownian movement between the nanoparticles and the molecules of the base fluid decreases, which causes a reduction in the convective heat transfer between the base fluid and the nanoparticles. Sint et al. [12] estimated the thermal efficiency of an FSC using CuOH₂O. Efficiency was improved by 5% with a volume percentage of 2 vol% and a nanoparticle size of 25 nm. The performance is proportional to the volume fraction of the nanoparticles in the base fluid, as described by [13]. Alawi et al. [5] carried out studies with metallic and metal oxide nanoparticles to operate FSCs.

Suresh et al. [6] demonstrated that the use of hybrid nanofluids can enhance TC compared to single nanofluids by preparing a hybrid Al₂O₃-Cu nanofluid using the hydrogen reduction technique in a 90:10 ratio of Al₂O₃-to-CuO nano powder. Measurements on TC and viscosity showed that the increase in viscosity is more pronounced than the conductivity with respect to concentration. The highest conductivity gain was recorded at 12.11% for a 2% volume concentration. Madhesh and Kalaiselvam [4] prepared hybrid nanofluid by mixing surface-modified (crystalline) copper–titanium nanocomposites, with a particle range of 0.1% to 2% (vol.%) and mean nanoparticle size of 55 nm. The results confirm the improvement in surface conductance (hs) from 0.52 to 1%. Hemmat et al. [14] found the increasing effect of nanoparticle concentration on the TC of the Ag-MgO–water nanofluid with the same concentration ratio.

1.2. Carbon Nanofluids in FSCs

The use of carbon nanoparticles is of great interest, mainly due to their reduced weight, greater hardness, high TC, high heat absorption capacity and large surface area. The use of carbon nanoparticles has the additional benefit of having high TC, extreme durability and resistance to corrosion. CNTs made from sheets of graphene that have been rolled up can be found as single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs).

Ahmadi et al. [15] carried out a study in which they dispersed graphene in the base fluid to increase the thermal efficiency of a solar collector. Alawi et al. [16] examined the thermophysical properties of nanofluids composed of carbon nanoparticles and metal oxides. The authors used different nanoparticles such as graphene, CNT, Al₂O₃, and SiO₂. It was found that as more nanoparticles are added to the fluid, the viscosity of the fluid increases. It was observed that the addition of Al₂O₃ and SiO₂ nanoparticles slightly increases the heat capacity of the nanofluids. The findings that the authors showed imply that the most successful nanoparticles for improving the TC of nanofluids are carbon nanotubes and graphene. While the addition of Al₂O₃ and SiO₂ nanoparticles can increase the heat capacity, Tong et al. [17] studied the influence of different types of nanoparticles on the efficiency of an FSC, where they used four types of nanoparticles, MWCNTs, CuO, Fe₃O₄, and Al₂O₃, to evaluate the thermophysical properties, such as their density, viscosity and TC, as well as the efficiency of a solar collector. The findings demonstrated that, compared to the base fluids, the MWCNT nanoparticles increased the efficiency of the solar collector. It was found that as the CuO concentration increased, the efficiency of the solar collector increased. It was found that the addition of Fe₃O₄ increases the efficiency of the solar collector. Although the TC of Fe₃O₄ is high, its low concentration in the nanofluids limited its effect on the efficiency of the solar collector.

Verma et al. [13] evaluated the thermal efficiency of FPSCs using CuO-MWCNT and MgO-MWCNT hybrid nanofluids with water. The efficiency of the FSCs with MgO hybrid nanofluids improved by 25.1% compared to the base fluid and by 16.28% with respect to the MgO/water nanofluid. To the extent that the literature review has been possible,

Table 1. Simple and hybrid nanofluids in FSCs in the literature.

Nanofluids	Metal Oxide	Carbon	Metal–Oxide–Metal	Metal–Oxide–Carbon	Reference
Fe3O4	x				[8,17]
Al2O3	x				[5,8,9,10,16,17,18]
MgO	x				[5,8,11,13]
CuO	x				[5,9,12,17,18]
TiO2	x				[5,8,9,18]
SiO2	x				[5,9,16,18]
ZrO2	x				[5,9]
CeO2	x				[8]
ZnO	x				[8]
MWCNT		x			[5,13,17]
SWCNT		x			[5]
Graphene		x			[15,16]
Al2O3-Cu			x		[6]
CuO-MWCNT				x	[13]
MgO-MWCNT				x	[13]

presents the simple and hybrid metal oxide and carbon nanofluids that have been used in FSCs until now.

As can be seen in Table 1, the carbon nanoparticles that have been used until now in FSCs are those of graphene in its spherical form and in multi-walled and single-walled carbon nanotubes. However, it has been found that graphite has been used to improve the efficiency of evacuated tube, dish parabolic and linear parabolic solar collectors by [19,20,21], respectively. Likewise, it has been found that fullerene C60 has been used to improve the efficiency in flat photovoltaic/thermal and direct absorption solar collectors by [22,23], respectively.

As shown in this section, several studies have explored the use of simple and hybrid nanofluids in thermal solar collectors. However, there is a notable gap in the literature regarding the application of simple graphite and fullerene C₆₀ nanofluids, as well as hybrid carbon nanofluids. This work aims to develop a mathematical model to simulate the behavior of FSCs using metal oxide and carbon nanoparticles, along with hybrid metal–oxide–carbon nanofluids. The study evaluates the effect of nanoparticle concentration and compares the performance of solar collectors using simple and hybrid nanofluids. A parametric analysis is conducted to examine the impact of key variables on the performance of the solar collectors. The results will assess the potential of hybrid carbon nanofluids in enhancing the efficiency of FSCs. Additionally, this research may serve as a foundation for future studies on the application of nanofluids in other thermal energy systems.

2. Materials and Methods

Mathematical modeling, its validation and the simulation of simple nanofluids and hybrid nanofluids in FSCs are presented in this section.

2.1. Phisical Model

The mathematical modeling was carried out on an FSC; Figure 1a shows the solar collector coupled to a heat exchanger. A pump is also depicted, which helps circulate the working fluid throughout the system. Figure 1b presents a section of the collector, highlighting the main geometric parameters, including the absorber composed of the riser tubes and the absorber plate, the glass cover, and thermal insulation. The specifications are detailed in Section 2.3.

2.2. Mathematicl Modeling

The cross-sectional view of an FSC, as shown in Figure 1b, is presented in Figure 2a. This figure illustrates the main parameters, such as solar radiation, useful heat, and heat losses involved in the heat transfer process of a flat plate solar collector. These parameters are represented in a thermodynamic system, as shown in Figure 2b, which includes geometric, thermodynamic, and fluid flow parameters. These are used to develop the mathematical modeling of an FSC operating with simple and hybrid carbon nanofluids.

2.2.1. Governing Equations

By applying the first law of thermodynamics to the control volume in Figure 2b, we have

$$\dot{Q}-\dot{W}={\sum }_o{\dot{m}}_k{\left(h+gz+{\displaystyle \frac{w^2}{2}}\right)}_k-{\sum }_i{\dot{m}}_k{\left(h+gz+{\displaystyle \frac{w^2}{2}}\right)}_k,$$

(1)

where $\dot{Q}$ and $\dot{W}$ are the heat flux and mechanical power developed by the thermodynamic system, respectively. ${\dot{m}}_o$ and ${\dot{m}}_i$ are the mass flow rates at the system’s outlet and inlet. h, z, and v are the enthalpy, height, and fluid velocity, respectively, and g is gravity.

The energy flow in the thermodynamic system, according to the first law of thermo-dynamics, can be represented as

$$I_c{A}_c{\tau }_s{\alpha }_s=q_u+q_{loss}+{\displaystyle \frac{d{e}_c}{dt}},$$

(2)

where τ and α are the transmittance and absorptance of the transparent cover. $q_u$ and $q_{loss}$ are the useful heat and heat losses of the solar collector. The third term of Equation (2) represents the change in the system’s energy over time.

The useful heat absorbed by the working fluid, $Q_u$, according to [24], is given by

$$Q_u=\dot{m}Cp(T_o-T_i),$$

(3)

where Cp is the specific heat of the fluid, and T_o and T_i are the outlet and inlet temperatures of the system, respectively.

The useful heat can also be determined as the difference between the useful heat and the heat lost from the solar collector, according to [24]:

$$Q_u=F_R{A}_c\left[G_T\tau \alpha -U_L\left(T_i-T_a\right)\right],$$

(4)

where F_R and U_L are the heat removal factor and the overall loss coefficient, G_T is the irradiance, $\tau \alpha$ is transmittance absorptance and T_a is the ambient temperature.

The instantaneous collector efficiency, η_c, is determined by [25]

$$\eta ={\displaystyle \frac{Q_u}{A_{c}I}}={\displaystyle \frac{\dot{m}Cp(T_o-T_i)}{A_{c}I}},$$

(5)

$$\eta =F_R\tau \alpha -F_R{U}_L{\displaystyle \frac{\left(T_i-T_a\right)}{G_T}},$$

(6)

2.2.2. Heat Removal and Collector Efficiency Factors

The heat removal factor, F_R, is determined as

$$F_R={\displaystyle \frac{\dot{m}Cp}{A_C{U}_L}}\left[1-exp\left({\displaystyle \frac{U_L{F}^{’}{A}_C}{\dot{m}Cp}}\right)\right],$$

(7)

The collector efficiency factor, F’, is calculated by the equation shown by [26]

$$F^{’}={\displaystyle \frac{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$U_L$}\right.}{W\left[\frac{1}{U_L\left[D_o+\left(W-D_o\right)F\right]}+\frac{1}{C_b}+\frac{1}{\pi D_{in}{h}_i}\right]}},$$

(8)

where W, D_in, D_o represent the distance between the fins, the internal and external diameters of the pipes, respectively.

The conductance at the $C_b$ junctions is calculated by the equation:

$$C_b={\displaystyle \frac{k_{b}b}{\gamma }},$$

(9)

where kb and b represent the TC and the length of the junction, while $\gamma$ represents the average thickness of the junction.

The standard fin efficiency, F, is determined by

$$F={\displaystyle \frac{\tanh \left(\frac{m\left(W-D_o\right)}{2}\right)}{\frac{m\left(W-D_o\right)}{2}}},$$

(10)

To calculate m, the following equation is used:

$$m=\sqrt{{\displaystyle \frac{U_L}{k_C{\delta }_C}}},$$

(11)

where k_c and δ_c are, respectively, the TC and the thickness of the absorber.

2.2.3. Convection Heat Transfer Coefficient

The convective heat transfer coefficient h_fi is determined by

$$h_i={\displaystyle \frac{Nuk}{D_i}},$$

(12)

where the Nusselt number is determined, as suggested by [12]:

$$Nu=0.4328(1+11.285{\varphi }^{0.754}{Pe}^{0.218}){Re}^{0.333}{Pr}^{0.4},\mathrm{laminar}\mathrm{flow}$$

(13)

$$Nu=0.0059(1+7.6286{\varphi }^{0.6886}{Pe}^{0.001}){Re}^{0.9238}{Pr}^{0.4},\mathrm{turbulent}\mathrm{flow}$$

(14)

This relationship is valid for (Re ≤ 2300 for laminar flow and Re > 2300 for turbulent flow).

The dimensionless Reynolds and Prandtl numbers were determined as (where N_t is rise tube number)

$$Re={\displaystyle \frac{4\dot{m}}{\pi D\mu N_t}}$$

(15)

$$Pr={\displaystyle \frac{\mu Cp}{k}}$$

(16)

2.2.4. Overall Heat Loss Coefficient

The overall coefficient of losses, U_L, is calculated by

$$U_L=U_t+U_b+U_e,$$

(17)

where U_t, U_b, U_θ are the upper, lower and lateral loss coefficients, respectively. The upper loss coefficient, U_t, is determined as a sample [27]:

$$U_t=\left\{{\displaystyle \frac{\frac{1}{N}}{\frac{C}{T_P{\left[\frac{T_P-T_a}{N+f}\right]}^{0.33}+\frac{1}{h_a}}}}\right\}+\left\{{\displaystyle \frac{\sigma \left(T_P+T_a\right)\left(T_P^2+T_a^2\right)}{{\epsilon }_p+0.5N\left(1-{\epsilon }_p\right)+\frac{2N+f-1}{{\epsilon }_g}}}\right\},$$

(18)

where

$$C=365.9\times \left(1-0.00883\beta +0.0001298\times {\beta }^2\right),$$

(19)

$$f=\left(1+0.04h_a-0.0005h_a^2\right)\times \left(1+0.091N\right),$$

(20)

$$h_a=5.7+3.8V_a,$$

(21)

where V_a is the wind speed, N is the number of covers, ε_p is the emissivity of the plate, ε_g is the emissivity of the roof, and β is the angle of inclination of the collector, respectively.

The lower loss coefficient, U_b, is determined from

$$U_b={\displaystyle \frac{k_b}{x_b}},$$

(22)

where k_b, x_b are the TC and the thickness of the lower insulation, respectively.

The loss coefficient at the edges is calculated with the following equation:

$$U_e={\displaystyle \frac{A_e}{A_C}},$$

(23)

2.2.5. Simple Nanofluid Properties

The thermophysical properties of nanofluids were determined based on the methods outlined in the relevant studies. The density of the nanofluid is determined as proposed by [3,5]

$${\rho }_{nf}=\left(1-\varnothing \right){\rho }_{bf}+\varnothing {\rho }_{np},$$

(24)

The viscosity of the nanofluid is determined as proposed by [3], and shown in [5] through

$${\mu }_{nf}=\left(1+2.5\varnothing +6.2{\varphi }^2\right){\mu }_{bf}$$

(25)

The specific heat of the nanofluid was determined as suggested by [5] using the equation:

$${Cp}_{nf}={\displaystyle \frac{{Cp}_{bf}{\rho }_{bf}\left(1-\varnothing \right)+{Cp}_{np}{\rho }_{np}\varnothing }{{\rho }_{nf}}},$$

(26)

where Cp, ρ, ∅ are the specific heat, density and volume fraction, respectively. The subscripts nf, np, bf refer to nanofluid, nanoparticle, and base fluid, respectively.

The Brownian movement of nanoparticles was considered by [5,28,29] and here, to estimate the TC of the nanofluid, k_nf, with spherical nanoparticles:

$$k_{nf}=\left[{\displaystyle \frac{k_{np}+2k_{bf}-2\varnothing \left(k_{bf}-k_{np}\right)}{k_{np}+2k_{bf}+\varnothing \left(k_{bf}-k_{np}\right)}}+{\displaystyle \frac{{\rho }_{np}\varphi C{p}_{np}}{2k_{nf}}}\sqrt{{\displaystyle \frac{k_B{T}_m}{3\pi r_c{\mu }_{nf}}}}\right]k_{bf},$$

(27)

For cylindrical nanoparticles, the approach by [18,30,31,32] was considered to estimate the TC of the k_nf, with n = 6:

$$k_{nf}=\left(k_{bf}\right)\left[{\displaystyle \frac{\left(k_{np}+\left(n-1\right)\left(k_{bf}+\varnothing \left(k_{np}-k_{bf}\right)\right)\right)}{{(k}_{np}+\left(n-1\right)\left(k_{bf}\right)-\varnothing \left(k_{np}-k_{bf}\right))}}\right],$$

(28)

2.2.6. Hybrid Nanofluid Properties

The modeling of the FSC with hybrid nanofluids was conducted using the models presented in Section 2.2.1 and Section 2.2.2, incorporating the thermophysical properties of hybrid nanofluids as detailed in this section. These properties were determined as shown by [33], through

$${\rho }_{hnf}={\displaystyle \frac{{\zeta }_1{\rho }_1+{\zeta }_2{\rho }_2}{{\zeta }_1+{\zeta }_2}},$$

(29)

$${Cp}_{hnf}={\displaystyle \frac{{\zeta }_1{Cp}_1+{\zeta }_2{Cp}_2}{{\zeta }_1+{\zeta }_2}},$$

(30)

$$k_{hnf}={\zeta }_1{k}_1+{\zeta }_2{k}_2,$$

(31)

where k_hnf, Cp_hnf and ρ_hnf are the total TC, specific heat and density of the nanocomposite; k₁ and k₂ are the thermal conductivities; Cp₁ and Cp₂ are the specific heats; ρ₁ and ρ₂ are the densities; and ${\zeta }_1$ and ${\zeta }_2$ are the volume concentrations of each of the used nanoparticles.

2.3. Model Validation

The validation of the model was carried out with the collector specifications shown in

Table 2. Solar collector specifications.

Parameter	Value
Collector area, Ac, [m2]	1.13
Number of covers, N	1
Number of riser pipes, Nt	6
$\mathrm{Length}\mathrm{of}\mathrm{collector},L_{col}$ [m]	1.13
$\mathrm{Width}\mathrm{of}\mathrm{collector},W_{col}$ [m]	1
$\mathrm{Internal}\mathrm{pipe}\mathrm{diameter},D_{in}$, [m]	0.013
$\mathrm{External}\mathrm{pipe}\mathrm{diameter},D_{out}$, [m]	0.016
$\mathrm{Width}\mathrm{between}\mathrm{pipes},w$ [m]	0.166
Plate thickness, δ [m]	0.0002
$\mathrm{TC}\mathrm{of}\mathrm{the}\mathrm{plate},K_p$$[\mathrm{W}/\mathrm{m}\mathrm{K}$]	384
$\mathrm{Glass}\mathrm{emittance},{\epsilon }_g$	0.84
$\mathrm{Plate}\mathrm{emittance},{\epsilon }_p$	0.05
$\mathrm{TC}\mathrm{of}\mathrm{the}\mathrm{insulation},K_i$ $[\mathrm{W}/\mathrm{m}\mathrm{K}$]	0.038
$\mathrm{Thickness}\mathrm{of}\mathrm{the}\mathrm{insulation},L_{ins}$ [m]	0.0254
Transmittance, Absorbance, τα, taken from [34]	0.84

, and taken from [34] by comparing the results obtained in this work on useful heat and efficiency with those published by [34] and shown in

Table 3. Model validation.

Parameter	[35]	This Work	Error, [%]
Useful heat, W	2055	2010	2.1
Efficiency, %	44.9	45	−0.22

.

The values of radiation, ambient temperature and entrance to the collector were, respectively, 750 W/m², 23 °C and 25 °C. The error of the results with those of the literature is less than 2%, as can be seen in Table 3.

2.4. Simulation

The model was implemented using Engineering Equation Solver software, EES [36]. This software has integrated the thermophysical properties of various substances and can be programmed in a user-friendly environment. The simulation procedure is illustrated in Figure 3. The properties of the base fluid were obtained from the data provided by [37], while the properties of the nanoparticles were assigned as shown in

Table 4. Thermophysical properties of nanoparticles at 20 °C.

Nanoparticles	Density (kg/m3)	Specific Heat (J/kg K)	TC, (W/m K)	Reference
Fe3O4	4950	670	6	[17]
Al2O3	3600	880	30	[24]
CuO	6000	551	33	[24]
MgO	3560	955	45	[38]
MWCNT	1350	650	1500	[17]
SWCNT	2100	600	3500	[1]
Graphite, G	2210	709	1950	[39]
Fullerene, C60	1720	506.7	0.4	[23]

. The various parameters used in the simulation are listed in

Table 5. Varied parameters in simulation.

Parameter	Range
FPSC inclination, β [°] data from [34]	20
Irradiance, GT, W/m2	750
Air velocity, Va, m/s	5
Inlet temperature, Ti [°C]	30, 40 y 50
$\mathrm{Mass}\mathrm{flow}\mathrm{rate},\dot{m}$, [kg/s]	0.01–0.1
Nanoparticle diameter, dp, nm	15
$\mathrm{Volume}\mathrm{fraction},\varphi$	0.001–0.1
$\mathrm{Volume}\mathrm{fraction}\mathrm{of}\mathrm{carbon}\mathrm{nanoparticles},{\zeta }_1$	0.2
$\mathrm{Volume}\mathrm{fraction}\mathrm{of}\mathrm{metal}\mathrm{oxide}\mathrm{nanoparticles},{\zeta }_2$	0.8

.

Assumptions

The assumptions made in the simulation are as follows:

• Fully developed flow and stable conditions.
• The ambient temperature at the top and bottom of the collector are the same.
• Negligible addition to the collector surface by the header.
• In all pipes, the fluid is in uniform flow.

3. Results and Discussion

The results obtained through the simulation are presented in this section for FSCs operating with simple and hybrid carbon nanofluids (graphite and fullerene, C₆₀). The ambient temperature and radiation used are 23 °C and 750 W/m², respectively.

In Figure 4, the useful heat and collector efficiency are shown. From the figure, for this range of mass flow, the useful heat obtained was between 450 and 580 W, while for the efficiency, it was between 53% and 69%. These results were similar to those reported by [34,35,40].

3.1. FSCs with Graphite and Fullerene Nanofluids

This section presents the thermophysical properties of nanofluids with respect to volume fraction. The carbon nanofluids evaluated are graphite, G, fullerene, C₆₀, and multi-walled carbon nanotubes (MWCNTs).

Figure 5 shows the change in densities, viscosity and specific heat capacity for graphite and fullerene nanofluids. It is observed that the density and viscosity of nanofluids increases with the volume fraction to 10.81% and 6.76% for the density and 26.62% for the viscosity for the graphite and fullerene, respectively. Specific heat capacities decrease to 16.28% and 13.93% for the graphite and fullerene, respectively, with increasing volume fraction.

According to [41], the improvement in TC depends largely on the volume fraction of solids and, to some extent, on temperature. Figure 6a shows that the TC of graphite nanofluids increases with the volume fraction to 39.16% and 12.25% for the graphite and fullerene, respectively. This is true for nanofluids containing G, which have higher TC levels compared to the base fluid. However, for the fullerene nanofluid, C60, TC tends to increase at a lower rate because C₆₀ nanoparticles have a TC of 0.4 W/mK (see Table 2), which is lower than that of the base fluid, which has a TC of 0.605 W/mK. In Figure 6b, the thermal diffusivity of graphite and fullerene nanofluids is shown to increase with the volume fraction to 44.53% and 19.33% for the graphite and fullerene. At a volume fraction of 0.1, carbon nanofluids such as G have diffusivity greater than 2.000 × 10⁻⁷ m²/s, while for C₆₀, the change in thermal diffusivity is minimal, with a value of 1.503 × 10⁻⁷ m²/s at a volume fraction of 0.1.

Figure 7a presents the Reynolds numbers for the base fluid (water) and nanofluids (graphite and fullerene) as functions of mass flow rate and volume fraction, respectively. The figure demonstrates that the Reynolds number for the base fluid increases from 200 to 2100 as the mass flow rate rises. Conversely, the Reynolds number for carbon-based nanofluids decreases from 1700 to 1300 as the volume fraction increases. This discrepancy arises because the density and viscosity of the nanofluids increase. Figure 7b illustrates the Prandtl number Pr for graphite and fullerene nanofluids as a function of volume fraction. The figure shows that as the volume fraction increases, there is no significant change in the Prandtl number of the fullerene. On the other hand, the Pr of graphite nanofluids decreases. This discrepancy arises because the conductivity of the fullerene decreases.

Figure 8 illustrates the Nusselt number (Nu) and the convection heat transfer coefficient (h) for graphite, fullerene and multiple-walled carbon nanotube nanofluids as a function of volume fraction. The figure shows that as the volume fraction increases, both the Nu and h increase. Notably, the Nu for fullerene is higher compared to graphite and MWCNTs, but the h for fullerene is lower than that of graphite and MWCNTs across the evaluated volume fractions. This discrepancy arises because fullerene has lower TC levels than graphite. From the figure, the use of graphite and fullerene nanofluids improve the convection heat transfer coefficient by up to 40% and 30%, respectively, with 10% nanoparticles.

3.2. FSCs with Simple Metal Oxide and Carbon Nanofluids

This section presents the evaluation of the useful heat and efficiency of an FSC with metal oxide and carbon nanofluids. The metal oxide nanofluids evaluated are those already known, ferrous oxide, Fe₃O₄; aluminum oxide, Al₂O₃; copper oxide, CuO; and magnesium oxide, MgO. Meanwhile, the carbon nanofluids evaluated are graphite, G, and fullerene, C₆₀. The latter are also compared with the results of the already widely studied nanofluids of multi-walled carbon nanotubes, MWCNTs.

Figure 9 and Figure 10 present the useful heat output and the efficiency, respectively, of the FSCs with respect to the volume fraction of the nanofluids. Both parameters increase with the addition of nanoparticles for all the nanofluids studied. For instance, at ϕ = 0.1, aluminum and magnesium metal oxide nanofluids provide approximately 1% more useful heat than ferrous and copper metal oxide nanofluids. Additionally, both the useful heat generated by the fullerene nanofluid, and the efficiency, exceed that of ferrous oxide and cuprous oxide nanofluids. Graphite demonstrates the highest useful heat output among all evaluated nanofluids. This and fullerene nanoparticles can enhance the efficiency of FSCs by 2% and 1.5%. The superior values observed of the carbon nanofluids, in addition to the diameter of the nanoparticles, is primarily attributed to their thermal diffusivity (α = k/ρCp), which counteracts the storage effect and compensates for the low specific heat, high density, and viscosity values, as well as the low conductivity of fullerene.

3.3. FSCs with Hybrid Carbon Nanofluids

As shown in Section 3.2, the simple carbon nanofluids evaluated in this study per-form similarly to the simple metal oxide nanofluids of aluminum (Al₂O₃) and magnesium (MgO). Consequently, to visualize the improvement in the performance of FSCs using combinations of metal oxide nanoparticles with the carbon nanoparticles evaluated here, this section presents results from the evaluation of hybrid nanofluids based on graphite and fullerene combined with Al₂O₃ and MgO nanoparticles.

Figure 11 and Figure 12 show the useful heat and the efficiency, respectively, of the FSCs using carbon hybrid nanofluids with respect to volume fraction. From these figures, it can be seen that both parameters increase when the volume fraction increases in all cases. However, when metal oxide nanoparticles are added to carbon nanoparticles, at the volume fraction of 0.1, both the useful heat and the efficiency decrease to 0.85% for G-Al₂O₃–water and G-Al₃O₂–water hybrid nanofluids. While the C₆₀-Al₃O₂–water and C₆₀-MgO–water hybrid nanofluids decrease to 0.48% and 0.56%, respectively. This behavior has also been observed by authors such as Verma et al. [13], where the addition of magnesium and copper nanoparticles reduced the efficiency of the collector with carbon nanotubes. This may be due to the pressure drop and irreversibilities, as the authors have noted.

From the evaluation of FSCs using hybrid carbon nanofluids presented here, it can be concluded that while the performance of the solar collector is not significantly improved, the density of the nanofluid decreases, which reduces the pressure drop in fluid flow. As the decrease in efficiency using fullerene with magnesium oxide is less than 0.85%, fullerene hybrid nanofluids could still be used in FSCs.

4. Conclusions

The density and viscosity of nanofluids increase with volume fraction. Graphite nanofluids showing a greater increase in density compared to fullerene nanofluids. Specific heat capacities decrease as the volume fraction increases, with the base fluid (H₂O) exhibiting a higher specific heat capacity at zero volume fraction compared to the corresponding nanofluids with graphite and fullerene nanoparticles. TC generally increases with volume fraction; however, for the fullerene nanofluid (C₆₀), TC decreases due to the lower TC of C₆₀ nanoparticles (0.4 W/mK) compared to the base fluid (0.605 W/mK). Thermal diffusivity of both graphite and fullerene nanofluids increases with volume fraction. Additionally, as volume fraction increases, both the Nusselt number and the convection coefficient increase. Notably, the Nusselt number for fullerene is higher compared to graphite, but the convection coefficient for fullerene is lower than that of graphite across the evaluated volume fractions. This discrepancy is attributed to the lower TC of fullerene compared to graphite. From the evaluation of heat transfer in FSCs, using graphite and fullerene nanofluids, it can be concluded that adding these nanoparticles improves the convection coefficient by 40% and 30%, respectively, with 10% nanoparticles.

From the performance results of the FSCs, it can be concluded that graphite and fullerene nanoparticles can enhance the efficiency of FSCs by 2% and 1.5% more than base fluid. From the evaluation of FSCs using hybrid carbon nanofluids presented here, it can be concluded that while the performance of the solar collector is not significantly improved, the density of the nanofluid decreases, which reduces the pressure drop in fluid flow. As the decrease in efficiency using fullerene with magnesium oxide is less than 0.85%, fullerene hybrid nanofluids could still be used in FSCs.