Thermal Efﬁciency, Heat Transfer, and Friction Factor Analyses of MWCNT + Fe 3 O 4 /Water Hybrid Nanoﬂuids in a Solar Flat Plate Collector under Thermosyphon Condition

: The heat transfer, friction factor, and collector efﬁciency are estimated experimentally for multi-walled carbon nanotubes+Fe 3 O 4 hybrid nanoﬂuid ﬂows in a solar ﬂat plate collector under thermosyphon circulation. The combined technique of in-situ growth and chemical coprecipitation was utilized to synthesize the multi-walled carbon nanotubes+Fe 3 O 4 hybrid nanoparticles. The experiments were carried out at volume ﬂow rates from 0.1 to 0.75 L/min and various concentrations from 0.05% to 0.3%. The viscosity and thermal conductivity of the hybrid nanoﬂuids were experimentally measured at different temperatures and concentrations. Due to the improved thermophysical properties of the hybrid nanoﬂuids, the collector achieved better thermal efﬁciency. Results show that the maximum thermal conductivity and viscosity enhancements are 28.46% and 50.4% at 0.3% volume concentration and 60 ◦ C compared to water data. The Nusselt number, heat transfer coefﬁcient, and friction factor are augmented by 18.68%, 39.22%, and 18.91% at 0.3% volume concentration and 60 ◦ C over water data at the maximum solar radiation. The collector thermal efﬁciency improved by 28.09% at 0.3 vol. % at 13:00 h daytime and a Reynolds number of 1413 over water data. Empirical correlations were developed for friction factor and Nusselt number.


Introduction
Energy demand is high all over the world and fossil fuel scarcity is one of the major problems. To meet the energy demand and replacement for fossil fuels, the best source of energy is alternative energy. Sun energy is the best renewable energy, which is available all the days in the year and it is obtainable plenty on the surface of the earth. The best example of solar thermal energy conversion technology is the solar flat plate collector (FPC) which is used for bathing purposes and used in various industrial processes. The convectional fluids are the working fluids in flat plate collectors, because of that, its efficiency is low. To improve the thermal efficiency of the collector, the convectional fluids are replaced with better thermal conductivity nanofluids [1,2].
Some of the literature related to the use of nanofluids in FPCs are mentioned below. Modi et al. [3] enhanced the performance of solar still by 19.40%, 28.53%, and 26.59% utilizing Al 2 O 3 nanoparticles at water depths of 30, 20, and 10 mm. Moreover, the performance improved by 58.25% and 56.31% utilizing CuO nanoparticles at 20 and 10 mm water depth. Hawwash et al. [4] observed enhancement in the collector thermal efficiency by 16.67% utilizing Al 2 O 3 /water nanofluids flow in a FPC. Kiliç et al. [5] have noticed 48.67% enhancement of collector efficiency with 2 wt. % of TiO 2 /water nanofluid. Sundar et al. [6] obtained collector thermal efficiency of 76% with 0.3 vol. % of Al 2 O 3 /water nanofluid at a mass flow rate of 0.083 kg/s. Sharafeldin and Gróf [7] have observed collector efficiency of 10.74% at [(T i -T a )/G T ] value reached to zero at 0.066 vol. % of CeO 2 /water in the collector at 0.019 kg s −1 m −2 mass flux rate. Jouybari et al. [8] obtained a collector efficiency of 73% utilizing 0.6 vol. % of SiO 2 /water nanofluid in a FPC at 1.5 L min −1 volume flow rate. Ziyadanogullari et al. [9] conducted thermal efficiency experiments for TiO 2 /water, CuO/water, and Al 2 O 3 /water nanofluids flow in a FPC at 0.2%, 0.4%, and 0.8% particle concentrations. They obtained improvement in the collector efficiency compared to the base fluid. Rajput et al. [10] have found efficiency of 21.32% at 0.3 vol. % of Al 2 O 3 /water flows in a FPC at 1.3 L min −1 volume flow rate.
Stalin et al. [11] attained thermal efficiency and exergy efficiency augmentation of 28.07% and 5.8% using 0.05% concentration of CeO 2 /water nanofluid flows in a FPC at 3 L min −1 volume flow rate over water data. Choudhary et al. [12] obtained 69.24% collector efficiency utilizing 50:50% water mixture based ZnO nanofluid and ethylene glycol flow in a FPC at 1% concentration and 60 L h −1 volume flow rate.
The use of hybrid nanofluids in various thermal energy systems is a recently advanced topic and growing area. The hybrid nanofluids are prepared with hybrid nanoparticles dispersed in conventional fluids. Osho et al. [18] prepared Al 2 O 3 -ZnO/water hybrid nanofluid and investigated specific heat and viscosity experimentally. The results showed a specific heat decline of 30.1% and viscosity augmentation of 96.4% over the base fluid data. Sundar et al. [19] investigated heat transfer and friction factor for MWCNT-Fe 3 O 4 /water hybrid nanofluid circulates in a tube. Giwa et al. [20] experimentally studied heat transfer using 60:40 weight percentages of Al 2 O 3 :MWCNT/water hybrid nanofluid circulate in a square cavity. The results showed Nusselt number improvement of 16.2%, over the base fluid.
The use of hybrid nanofluids in solar flat plate collectors and direct absorption collectors are given below. Li et al. [21] examined the optical, stability, and thermal performance of SiC-MWCNT/ethylene glycol nanofluid circulate in a solar collector. The maximum thermal efficiency was 97.3% using 1 wt% SiC-MWCNT nanofluid. It was 48.6% greater than that of pure ethylene glycol data. Farajzadeh et al. [22] studied experimentally the efficiency of a FPC using Al 2 O 3 -TiO 2 , TiO 2 , and Al 2 O 3 nanofluids. They obtained collector efficiency improvements of 26%, 21%, and 19% nanofluids at 0.1% weight percentage. Verma et al. [23] examined the performance of a FPC using MgO-MWCNT/water and CuO-MWCNT/water hybrid nanofluids. The results showed 71.54% exergetic efficiency and 70.55% energetic efficiency using MgO-MWCNT/water nanofluid. Okonkwo et al. [24] have noticed collector thermal efficiency improvement of 2.16% at 0.1 vol. % of aluminawater while and it is 1.79% at 0.1 vol. % of alumina-iron/water hybrid nanofluids over water data.
Very few research works are available dealing with the FPC thermal efficiency working with hybrid nanofluids. The studied hybrid nanofluids were alumina-iron, MgO-MWCNT/water, Al 2 O 3 -TiO 2 , and CuO-MWCNT/water nanofluids. The experiments were carried out under forced flow conditions in the FPC. As far as we know, the hybrid nanofluids flow in the solar FPC under natural circulation (thermosyphon phenomenon) and its performance investigation did not present in the literature. Particularly the MWCNT + Fe 3 O 4 /water hybrid nanofluids flow in a FPC and their performance is not presented. The hybrid nanoparticles are considered because of their high magnetic property (Fe 3 O 4 ) and thermal conductivity (MWCNT) and the final MWCNT + Fe 3 O 4 hybrid nanoparticles have magnetic properties.
Accordingly, this study emphases on the experimental estimation of friction factor, heat transfer, and thermal efficiency of MWCNT + Fe 3 O 4 hybrid nanofluids flow in a solar FPC at thermosyphon circulation of nanofluid. The MWCNT + Fe 3 O 4 hybrid nanoparticles were synthesized utilizing the in-situ/chemical co-precipitation method. The hybrid nanofluids water-based with 0.05%, 0.1%, 0.2%, and 0.3% volume concentrations were prepared and utilized in the experiments. The experiments were performed during the daytime, from 09:00 a.m. to 4:00 p.m. The friction factor and Nusselt number correlations were suggested based on the experimental results.

Acid Treatment on MWCNT
The proposed procedure by Sundar et al. [19] is followed to synthesize the bulk quantity of MWCNT + Fe 3 O 4 nanoparticles. Preparing hybrid nanoparticles with as purchased MWCNT is a little bit difficult because the attachment covenant bond or carboxyl (-COOH) bond is required. The purchased MWCNT does not contain -COOH bonding on the surface. In order to obtain the -COOH bonding, a strong acid treatment technique is used. The MWCNT was dispersed in strong chemicals of 1:3 M of hydrochloric acid and nitric acid up to 3 days under very speed with a magnetic stirrer at 60 • C. After that, the acid-treated, MWCNT was washed with a distilled water several times then dried at 80 • C for 24 h. This method provides the formation of -COOH bond on the surface of MWCNT, through the -COOH layer, the Fe 3 O 4 nanoparticles attached to MWCNT.

Synthesis of MWCNT + Fe 3 O 4 Hybrid Nanoparticles
The method of in-situ growth and chemical coprecipitation was adopted for MWCNT + Fe 3 O 4 hybrid nanoparticles. The synthesis procedure is indicated in Figure 1. The MWCNT-COOH of 0.35 g was diluted in 100 mL of water and then stirred for 1 h, later added 2:1 M ratio of FeCl 3 +/FeCl 2 + iron salts and stirs continuously. Once the iron salts are fully diluted in MWCNT solution, the solution becomes a light orange color, then add water-diluted NaOH slowly and maintain the solution pH to 12. After 10 min, observe the formation of black colored precipitation, which indicates the reaction is completed. During the chemical reaction for the conversion of iron salts to magnetite (Fe 3 O 4 ), the Fe 3 O 4 nanoparticles are attached to the MWCNT through the -COOH layer. This -COOH is very thin and it will no effect the properties and heat transfer characteristics of the fluid, while they dispersed in water. The chloride, sodium, and hydrogen impurities are removed by washing precipitate several times with water. The washed precipitate was dried at 80 • C for 24 h. The pure Fe 3 O 4 nanoparticles were also prepared for comparison purpose based on the same procedure, but without adding the MWCNT to the distilled water.
for comparison purpose based on the same procedure, but without adding the MWCNT to the distilled water.
The MWCNT + Fe3O4 nanocomposite XRD patterns is presented in Figure 2 Sundar et al. [19]. The diffraction peak, 2θ = 34.5° that could be (3 1 1) reflected to magnetite (Fe3O4) nanoparticles. Likewise the diffraction peak, 2θ = 26° that could be (0 0 2) reflected to MWCNT. The analysis indicates that the samples contains two phases of MWCNT and cubic Fe3O4. The other peaks with comparatively high peak intensity can be classified as face-centered cubic Fe3O4. There is no noticeable peaks from other phases. The core peaks of Fe3O4 in the XRD pattern are widened, demonstrating that the crystalline sizes of Fe3O4 nanoparticles are too small. The SEM results for synthesized MWCNT + Fe3O4 nanocomposite are displayed in Figure 3 Sundar et al. [19]. It can be concluded from the figure that the particles are in cubic shape and the Fe3O4 nanoparticles are attached to the MWCNT surface.  The MWCNT + Fe 3 O 4 nanocomposite XRD patterns is presented in Figure 2 Sundar et al. [19]. The diffraction peak, 2θ = 34.5 • that could be (3 1 1)  for comparison purpose based on the same procedure, but without adding the MWCNT to the distilled water.
The MWCNT + Fe3O4 nanocomposite XRD patterns is presented in Figure 2 Sundar et al. [19]. The diffraction peak, 2θ = 34.5° that could be (3 1 1) reflected to magnetite (Fe3O4) nanoparticles. Likewise the diffraction peak, 2θ = 26° that could be (0 0 2) reflected to MWCNT. The analysis indicates that the samples contains two phases of MWCNT and cubic Fe3O4. The other peaks with comparatively high peak intensity can be classified as face-centered cubic Fe3O4. There is no noticeable peaks from other phases. The core peaks of Fe3O4 in the XRD pattern are widened, demonstrating that the crystalline sizes of Fe3O4 nanoparticles are too small. The SEM results for synthesized MWCNT + Fe3O4 nanocomposite are displayed in Figure 3 Sundar et al. [19]. It can be concluded from the figure that the particles are in cubic shape and the Fe3O4 nanoparticles are attached to the MWCNT surface. The SEM results for synthesized MWCNT + Fe 3 O 4 nanocomposite are displayed in Figure 3 Sundar et al. [19]. It can be concluded from the figure that the particles are in cubic shape and the In the existence of the magnetic field, the nonmagnetic particle act as a void, which break the magnetic circuit. This leads to the decrease of magnetization with the growth of void concentration.  The pure Fe3O4 and MWCNT + Fe3O4 nanocomposite magnetic properties were examined by measuring their magnetization-magnetic field (M-H) hysteresis loops with a VSM. The ferromagnetic behavior of the MWCNT-Fe3O4 sample as well as Fe3O4 are shown in Figure 4. The saturation magnetization for Fe3O4 nanoparticles and MWCNT + Fe3O4 nanocomposite is 47, and 34.5 emu/g, respectively. The decrease in the nanocomposite magnetization because of the huge non-magnetic MWCNT in the matrix of MWCNT + Fe3O4. In the existence of the magnetic field, the nonmagnetic particle act as a void, which break the magnetic circuit. This leads to the decrease of magnetization with the growth of void concentration.

Physical Properties of MWCNT + Fe3O4 Nanoparticles
According to the total sum rule of composites, the individual weights of MWCNT,   The pure Fe3O4 and MWCNT + Fe3O4 nanocomposite magnetic properties were examined by measuring their magnetization-magnetic field (M-H) hysteresis loops with a VSM. The ferromagnetic behavior of the MWCNT-Fe3O4 sample as well as Fe3O4 are shown in Figure 4. The saturation magnetization for Fe3O4 nanoparticles and MWCNT + Fe3O4 nanocomposite is 47, and 34.5 emu/g, respectively. The decrease in the nanocomposite magnetization because of the huge non-magnetic MWCNT in the matrix of MWCNT + Fe3O4. In the existence of the magnetic field, the nonmagnetic particle act as a void, which break the magnetic circuit. This leads to the decrease of magnetization with the growth of void concentration.

Physical Properties of MWCNT + Fe3O4 Nanoparticles
According to the total sum rule of composites, the individual weights of MWCNT,

Physical Properties of MWCNT + Fe 3 O 4 Nanoparticles
According to the total sum rule of composites, the individual weights of MWCNT, The physical properties such as specific heat, thermal conductivity, and density of MWCNT-Fe 3 O 4 were calculated based on the law of mixtures as follows:
The quantities of 24.2 g, 48.5 g, 97.2 g, and 146 g of hybrid nanoparticles were dispersed in 10 kg of distilled water to prepare 0.05%, 0.1%, 0.2%, and 0.3% volume concentrations. For, φ = 0.05%, 24.2 g of synthesized MWCNT + Fe 3 O 4 is directly dispersed in 10 l of distilled water and then stirred with a mechanical stirrer at low speed for 2 h. The same technique was used for the other nanofluid concentrations.

Properties of MWCNT + Fe 3 O 4 Hybrid Nanofluids
To estimate the hybrid nanofluids heat transfer coefficient, the properties such as specific heat, viscosity, thermal conductivity, and density are significant. The hybrid nanofluids viscosity and thermal conductivity are experimentally assessed, while the hybrid nanofluids density and specific are assessed based on the mixtures law.
The KD-2 pro thermal properties analyzer (Decagon Devices Inc., Pullman, WA, USA) used to measure the thermal conductivity. The Vibro Viscometer (A&D Vibro Viscometer, SV-10, Tokyo, Japan) used to measure the viscosity. The measured thermal conductivity is presented in Figure 5, along with the base fluid data. Thermal conductivity of hybrid nanofluid increased with the increase of particle volume concentrations and temperatures. With the particle volume loadings of 0.05%, 0.1%, 0.2%, and 0.3% the thermal conductivity enhancement is 5.93%, 11.86%, 12.87%, and 13.88% at 20 • C, however it further enhanced by 10.42%, 20.84%, 24.65%, and 28.46% at 60 • C, respectively, over the base fluid.
The measured viscosity is presented in Figure 6 along with the base fluid data. Hybrid nanofluid viscosity increased with the increase of particle volume concentrations and temperatures. With the particle volume loadings of 0.05%, 0.1%, 0.2%, and 0.3%, the viscosity enhancement is 7.59%, 15.18%, 21.51%, and 27.84% at 20 • C, however it is further enhanced to 15.1%, 29.8%, 40.3%, and 50.4% at 60 • C, respectively, over the base fluid data. temperatures. With the particle volume loadings of 0.05%, 0.1%, 0.2%, and 0.3% the thermal conductivity enhancement is 5.93%, 11.86%, 12.87%, and 13.88% at 20 °C, however it further enhanced by 10.42%, 20.84%, 24.65%, and 28.46% at 60 °C, respectively, over the base fluid. The measured viscosity is presented in Figure 6 along with the base fluid data. Hybrid nanofluid viscosity increased with the increase of particle volume concentrations and temperatures. With the particle volume loadings of 0.05%, 0.1%, 0.2%, and 0.3%, the viscosity enhancement is 7.59%, 15.18%, 21.51%, and 27.84% at 20 °C, however it is further enhanced to 15.1%, 29.8%, 40.3%, and 50.4% at 60 °C, respectively, over the base fluid data. The hybrid nanoparticles specific heat and density were calculated by Equations (4) and (5) and substituted in Equations (7) and (8) to get the hybrid nanofluids specific heat and density.
The MWCNT + Fe3O4 hybrid nanofluids density is calculated by Equation (8). The hybrid nanoparticles specific heat and density were calculated by Equations (4) and (5) and substituted in Equations (7) and (8) to get the hybrid nanofluids specific heat and density.
where, ρ p,hn f is the density of hybrid nanofluid (kg m −3 ), ρ p,water is the density of water   Table 3. Viscosity of hybrid nanofluids.  Table 5. Specific heat of hybrid nanofluids.

Flat Plate Collector
A schematic diagram of the solar FPC is illustrated in Figure 7 and a photo is displayed in Figure 8. The FPC characterizations are presented in Table 6. The core parts are the inlet and outlet headers, insulated tank, and flow meter. Twenty-kilogram hybrid nanofluids or water circulates in the FPC and the collector placed at a tilt of 20 • . The hybrid nanofluids Processes 2021, 9, 180 9 of 19 or water flow rate is measured by a flow meter. The absorber fluid first enters the inlet header of 25.4 mm diameter, and then flows into the riser tubes with 10 mm inner diameter and 12 mm outer diameter. After that enters the insulated tank across 25.4 mm outlet header diameter. The headers and riser tubes are made of copper material. Twelve J-type thermocouples were used to measure the temperatures. Nine thermocouples were utilized for surface temperature measurements (T 1 − T 9 ), one thermocouple (T 10 ) was utilized for the ambient temperature measurement, and two thermocouples were utilized for the inlet and outlet temperatures measurement. The thermocouples needles are connected to a computer across a data logger. An aluminum sheet black-coated was utilized to cover the tubes of the riser and over it a cover glass is used. The fluid flows in the tubes under the buoyancy force. To decrease heat loss, the right, left sides, and the bottom of the collector is insulated with glass wool. Solar radiation was measured by a pyranometer. Yokogawa differential pressure transducer was utilized to measure the pressure drop. The experiments carried out from 09:00 a.m. to 4:00 p.m. in May 2019.  Solar radiation at different intervals of time from 09:00 a.m. to4:00 p.m. is illustrated in Figure 9. It is observed that the solar radiation increased first from 09:00 a.m. to 13:0 p.m. and then decreased from1:00 a.m. to 4:00 p.m., this tendency is divided into tw phases. Phase-1 is from 09:00 a.m. to 1:00 p.m. and Phase-2 is from 1:00 p.m. to 4:00 p.m The heat transfer, friction factor, and efficiency are calculated in the two phases.  Solar radiation at different intervals of time from 09:00 a.m. to4:00 p.m. is illustrate in Figure 9. It is observed that the solar radiation increased first from 09:00 a.m. to 13:0 p.m. and then decreased from1:00 a.m. to 4:00 p.m., this tendency is divided into tw phases. Phase-1 is from 09:00 a.m. to 1:00 p.m. and Phase-2 is from 1:00 p.m. to 4:00 p.m The heat transfer, friction factor, and efficiency are calculated in the two phases.  Solar radiation at different intervals of time from 09:00 a.m. to 4:00 p.m. is illustrated in Figure 9. It is observed that the solar radiation increased first from 09:00 a.m. to 13:00 p.m. and then decreased from 1:00 a.m. to 4:00 p.m., this tendency is divided into two phases. Phase-1 is from 09:00 a.m. to 1:00 p.m. and Phase-2 is from 1:00 p.m. to 4:00 p.m. The heat transfer, friction factor, and efficiency are calculated in the two phases.

Nusselt Number
The absorbed heat rate by water or hybrid nanofluids is calculated by Equation (9). 1 where, .
Q is the absorbed heat rate (W), C p is the specific heat (J kg −1 K −1 ), . m is the mass flow rate, U o is the outside overall heat transfer coefficient (W m −2 K −1 ), h i is tube-side convective heat transfer coefficient (W m −2 K −1 ), k is the thermal conductivity (W m −1 K −1 ), D o and D i are the tube outside and inside diameters (m), respectively, A i and A o are the tubes inside and outside areas (m 2 ), respectively, L is the tube length (m); T s and T m are surface and mean fluid temperatures (K), respectively.
Equations (9) and (10) are used to estimate the heat transfer coefficient (h i ). While Equations (11) and (12) are utilized to evaluate the Nusselt number and Prandtl number of water and hybrid nanofluids.

Friction Factor
The friction factor (f) is calculated by Equation (13).
where, ∆P is the pressure drop, v is the fluid velocity in the riser tube, and D i is the riser tube inner diameter.
where . Q is the heat gain (W), A c is the solar collector surface area (m 2 ), F R is the heat removal factor, τα is the absorptance-transmittance product, G T is the global solar radiation (W m −2 ), U L is the solar collector overall loss coefficient, T i is the inlet temperature (K), and T a is the ambient temperature (K).
Equation (15) is used to estimate the collector thermal efficiency (η i ).
By substituting the values from Equation (15) into Equation (16), the F R τα (heat removal factor and absorptance-transmittance) and F R U L (heat removal factor and overall loss coefficient) values are evaluated. A graph is drawn between instantaneous efficiency (η i ) verses T i − T a /G T , the F R U L term is the curve slope and F R τα term is constant.

Nusselt Number of Hybrid Nanofluids
Equation (11) is utilized to estimate the Nusselt number. The data for both Phase-1 and Phase-2 are shown in Figure 10a,b along with the data from Sieder and Tate equation [28] calculated by Equation (17). It is observed from the figure that the deviation between the present results and literature data is within ±2.5%.
The next correlations were developed for Nusselt number.

Friction Factor of Hybrid Nanofluids
The friction factor of each riser tube over the length was estimated depending on the pressure difference between the differential pressure transducer. The friction factor in the

Friction Factor of Hybrid Nanofluids
The friction factor of each riser tube over the length was estimated depending on the pressure difference between the differential pressure transducer. The friction factor in the case of water is calculated with Equation (20) Hagen-Poiseuille law [29] for the two phases.
Hagen-Poiseuille law, f = 64 Re (20) The experimental friction factor in the case of water versus the calculated values by Equation (20) for Phase-1 and Phase-2 is displayed in Figure 14a,b. The deviations between the experimental and calculated values are within ±2.5%.

Friction Factor of Hybrid Nanofluids
The friction factor of each riser tube over the length was estimated depending on the pressure difference between the differential pressure transducer. The friction factor in the case of water is calculated with Equation (20) Hagen-Poiseuille law [29] for the two phases.
Hagen-Poiseuille law, f = The experimental friction factor in the case of water versus the calculated values by Equation (20) for Phase-1 and Phase-2 is displayed in Figure 14a,b. The deviations between the experimental and calculated values are within ±2.5%. The friction factor of hybrid nanofluids at different Reynolds number in Phase-1 is illustrated in Figure 15a. The friction factor is increased with the increase of Re and volume concentration. The friction factor increases by 5.11%, 7.51%, 9.91%, and 11.51% at 0.05%, 0.1%, 0.2%, and 0.3% volume concentrations and Re of 248, 242, 238, and 235, respectively compared to water data. The friction factor is further increases by 7.65%, 11.8%, 14.46%, and 18.91% at 0.05%, 0.1%, 0.2%, and 0.3% volume concentrations and Re of 1774, 1674, 1528, and 1413, respectively, over water data. The friction factor of hybrid nanofluids at different Reynolds number in Phase-1 is illustrated in Figure 15a. The friction factor is increased with the increase of Re and volume concentration. The friction factor increases by 5.11%, 7.51%, 9.91%, and 11.51% at 0.05%, 0.1%, 0.2%, and 0.3% volume concentrations and Re of 248, 242, 238, and 235, respectively compared to water data. The friction factor is further increases by 7.65%, 11.8%, 14.46%, and 18.91% at 0.05%, 0.1%, 0.2%, and 0.3% volume concentrations and Re of 1774, 1674, 1528, and 1413, respectively, over water data.  Figure 15b represents the friction factor of hybrid nanofluids at different Re in Phase-2. The friction factor is increased with the decrease of Re and the increase of volume concentration. The friction factor is increased by 5.91%, 9.99%, 12.62%, and 17% at 0.05%, 0.1%, 0.2%, and 0.3% volume concentrations and Re of 1867, 1750, 1652, and 1395, respectively compared to water data. The friction factor is further increased by 3.75%, 5.51%, 7.27%, and 9.03% at 0.05%, 0.1%, 0.2%, and 0.3% volume concentrations and Re of 562, 544, 506, 476, and 435, respectively over water data.
The next correlations were established for the friction factor.  Figure 15b represents the friction factor of hybrid nanofluids at different Re in Phase-2. The friction factor is increased with the decrease of Re and the increase of volume concentration. The friction factor is increased by 5.91%, 9.99%, 12.62%, and 17% at 0.05%, 0.1%, 0.2%, and 0.3% volume concentrations and Re of 1867, 1750, 1652, and 1395, respectively compared to water data. The friction factor is further increased by 3.75%, 5.51%, 7.27%, and 9.03% at 0.05%, 0.1%, 0.2%, and 0.3% volume concentrations and Re of 562, 544, 506, 476, and 435, respectively over water data.
The next correlations were established for the friction factor.
The next correlations were established for the friction factor.
384 < Re < 206; 0 < < 0.3% The experimental friction factor in the case of hybrid nanofluids along with water data in comparison with the calculated values by Equations (21) and (22) for Phase-1 and Phase-2 are exhibited in Figure 16a,b. The deviations between the experimental and calculated values are within ±1.5%.
The collector thermal efficiency versus (T i − T a /G T ) parameter at different hybrid nanofluids concentrations is displayed in Figure 18. At midday (13:00 h), the collector efficiency is high for all working fluids compared to those at 09:00 a.m. and 4:00 p.m., hence the graph is drawn by considering the data from 09:00 a.m. to 1:00 p.m. The collector thermal efficiency is 49.81%, 52.17%, 54.84%, 60.24%, and 63.85% for water, 0.05%, 0.1%, 0.2%, and 0.3 vol. % of nanofluids and Re values of 1892, 1774, 1674, 1528, 1413, respectively. At the fixed solar radiation and collector area, the heat gain by MWCNT + Fe 3 O 4 hybrid nanofluids in the riser tubes is higher than those absorbed by water, resulting in elevated collector efficiencies.    The collector thermal efficiency versus (T − T G ⁄ ) parameter at differen nanofluids concentrations is displayed in Figure 18. At midday (13:00 h), the col ficiency is high for all working fluids compared to those at 09:00 a.m. and 4:00 p.m the graph is drawn by considering the data from 09:00 a.   The data in Figure 18 are fitted linearly to obtain the slope (F R U L ) and the intersection point (F R τα). These two parameters have a significant effect on the collector efficiency. The fitted data of F R τα, F R U L , and their coefficients of determination (R 2 ) at each measurement condition of water and hybrid nanofluids MWCNT + Fe 3 O 4 are presented in Table 7. The efficiency enhancement for 0.05%, 0.1%, 0.2%, and 0.3 vol. % of nanofluid, when the reduced temperature (T i − T a /G T ) reached 0.0029, is about 4.61%, 9.96%, 20.79%, and 28.09% at Re of 1774, 1674, 1528, 1413, respectively over water data. The slope (F R U L ) is found to be 2.26, 2.72, 3.42, 3.30, and 3.71 for water, 0.05%, 0.1%, 0.2%, and 0.3 vol. % of nanofluid.

Thermoeconomic Analysis
The thermoeconomic analysis is conducted based on the procedure given by Lucia and Grisolia [30] and Grisolia et al. [31]. From the experimental results, it is noticed that the thermal efficiency of the collector is maximum when the daytime reached 13:00 h compared to the daytime at 09:00 a.m. and 4:00 p.m., respectively. Hence, the thermoeconomic analysis was performed at the mid-daytime of 1:00 p.m., because of the maximum collector efficiency. Hence, the increased thermal efficiency is converted into useful cost and area saving of the collector. The collector thermal efficiency is 49.81%, 52.17%, 54.84%, 60.24%, and 63.85% for water, 0.05%, 0.1%, 0.2%, and 0.3 vol. % of nanofluid, respectively at the midday of 13:00 h. The purchased FPC area is 3 m 2 and its cost is $223.88. For water and water-based hybrid nanofluids, the same FPC is used. The collector area is decreased to 2.86, 2.72, 2.48, 2.34 m 2 for 0.05%, 0.1%, 0.2%, and 0.3 vol. % of nanofluid, respectively. With the use of hybrid nanofluids in the collector, the collector cost is decreased to 213.75, 203.35, 185.12, and 174.65$ for 0.05%, 0.1%, 0.2%, and 0.3 vol. % of nanofluid, respectively, whereas it is $223.88 using water in the collector.
The uncertainties of various instruments used in the present study are calculated from the procedure of Coleman and Steel [32]. Table 8 indicates the measured parameters, their maximum values, and the uncertainty of the measurements. The calculated uncertainty values are presented in Table 9.

Conclusions
Water and water based MWCNT + Fe 3 O 4 hybrid nanofluids are used as working fluids in a flat plate solar collector, and the thermal efficiency, heat transfer, and friction factor characteristics are experimentally investigated. The fluids circulate naturally (thermosyphon) in the collector. The viscosity and thermal conductivity of hybrid nanofluids MWCNT + Fe 3 O 4 are augmented as the particle concentrations and temperatures increase.
The maximum obtained viscosity and thermal conductivity improvements are 50.4% and 28.46%, respectively at 0.3 vol. % of nanofluid and at a temperature of 60 • C. The Nusselt number was enhanced with the increase of particle volume concentrations. At daytime 13:00 h, the Nusselt number and friction factor are increased by 18.68% and 18.91% at 0.3 vol. % and Reynolds number of 1413 over water data. The collector thermal efficiency is boosted by 28.09% with the utilization of 0.3% volume concentration of MWCNT + Fe 3 O 4 hybrid nanofluids and Reynolds number of 1413 over water data.
Finally, it was confirmed that the utilization of MWCNT + Fe 3 O 4 hybrid nanofluids in the solar flat plate collector leads to improve collector heat transfer and thermal efficiency compared to water data. Due to the enhanced hybrid nanofluids thermal conductivity, its heat-absorbing capacity is higher than that of water. Consequently, the hybrid nanofluids are advantageous in the solar flat plate collector under thermosyphon conditions.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.