Nanofluids effect on the overall transfer coefficients change mechanism analysis

The understanding of the enhanced thermal conductivity mechanism in nanofluids remains elusive, underscoring the necessity for investigating their influence on heat conduction. A comparative analysis was carried out on the overall heat transfer coefficients of SiO2, TiO2, MgO, ZrO2, CeO2, Al2O3, and Fe3O4, yielding 346.5, 442.9, 569.2, 465.6, 663.2, 562.4, and 706.2 W/m2 K, respectively. Our investigation further extended to the differential impacts of various nanofluids on heat transfer conduction coefficients, with Fe3O4 nanofluids demonstrating the greatest, and SiO2 the least, heat transfer coefficients. Importantly, these nanofluids play a cooperative role in enhancing heat transfer coefficients. Previous studies have largely concentrated on the effects of individual and mixed nanofluids on overall heat transfer coefficients, neglecting the combined effects of different nanofluids. Moreover, the mechanisms underlying these effects remain vague, with insufficient corresponding characterizations. Our study seeks to address these limitations. We also studied the impact of nanofluid concentration, pH, and temperature on heat conduction. Our results suggest that the overall heat transfer coefficient escalates with increasing nanofluid concentration and temperature. For example, the overall heat transfer coefficients for SiO2 nanofluids surged from 346.5 W/m2 K at 25°C to 369.4 W/m2 K at 35°C, 411.4 W/m2 K at 45°C, and 427.6 W/m2 K at 55°C. A rise in pH also led to an increase in overall heat transfer coefficients up to a certain point, after which they started decreasing. The zeta potentials of the aforementioned nanofluids were −12.1, −24.8, −28.6, −23.2, −35.9, −31.3, and −40.4 mV, respectively, and these potentials dwindled with an increase in pH. The influence of nanofluids on overall heat transfer may have implications for the enhanced oil recovery effect.

Thermal behavior played an important role in the industrial application. 11Zainon and Azmi. 12studied the heat transfer performance of green bioglycol (BG)-based TiO 2 -SiO 2 nanofluids (TiO 2 and SiO 2 hybrid nanofluids in the mixture of water and green BG); the results indicate that different concentrations of TiO 2 -SiO 2 nanofluids enhance heat transfer.The corresponding temperature was 70°C.The research indicated that Al 2 O 3 nanofluids showed higher heat transfer coefficients than the CuO nanofluid. 13Naddaf and Heris studied the oilbased nanofluids effect on thermal conductivity and electrical conductivity. 14uminic and Huminic 15 studied the effect of mixed nanofluids on the heat transfer capability; the results indicated that ND + Ni/water and MWCNT + Fe 3 O 4 mixed nanofluids have a greater effect on heat conduction at all temperatures.Wang et al. 16 studied diathermic oil-based alumina-doped ZnO nanofluids effect on the heat transfer. Nadaf and Heris research showed that all nanofluids thermal conductivity and electrical conductivity would increase, and the temperature, thermal conductivity, and electrical conductivity would increase when the nanofluids concentrations increased.14 Zolfalizadeh et al. studied the impact of graphene nanoplate/water nanofluids effect on the thermal efficiency, and the results indicated that by adding the graphene nanoplate nanoparticles, the corresponding thermal efficiency would be increased.17 The nanofluids could be used for thermal conductivity.4,18,19 The results indicated that the heat transfer coefficients of alumina-doped zinc oxide (AZO) nanofluids increased with the increase in temperature.In addition, the AZO nanofluids had high heat transfer coefficients at high temperatures, and the effect was obvious.Zhang et al. 20 analyzed the nanoparticles effect on the heat transfer coefficients of traditional fluids, and the results indicated that the nanofluids heat transfer coefficients increased with the increase of nanoparticles volume fraction.The SiO 2 -water nanofluids convective heat transfer coefficients increased from 15.1% (0.5 wt%) to 36.8% (2 wt %).The results showed that the Al 2 O 3 nanofluids followed the Maxwell model, but the TiO 2 nanofluids were not followed the corresponding model at high concentrations.The corresponding heat transfer coefficients were similar to the corresponding traditional model of simple fluids. Inaddition, the MWCNTs and titanium dioxide (TiO 2 ) nanoadditive could be used for the tribological and thermophysical attributes of turbine meter oil.23 A simulation of molecular dynamics was conducted to study the effect of nanofluids on heat conduction.24 Zhou et al. 25 studied the nanofluid thermal conductivity using the molecular dynamics simulation method; the results indicate that an increase in Ar atom volume will increase the volume fraction, with the solid-liquid interaction at the interface increased consequently.Chen et al. 26 investigated Cu/Ar nanofluid enhanced heat conduction using a nonequilibrium molecular dynamics simulation.The results indicate that Cu/Ar nanofluids are sensitive to particle size and the volume fraction.The nanofluids adsorb onto the surface.
In recent years, many researchers studied the hybrid nanofluids effect on the heat transfer coefficients. 27Kanti et al. 28 studied the pH effect on the graphene oxide and copper oxide hybrid nanofluids stability and thermal performance.The results indicated that the mono and HNFs show greater stability at the pH value of 9 and 10, respectively.The thermal conductivity of nanofluids increased with temperature and concentration.Other nanofluids thermal conductivity coefficiencies, for instance, the ash nanofluids thermal conductivity and viscosity would increase, but the specific heat would decrease when the volume concentration increased. 29The researcher studied the heat transfer, entropy generation and pressure drop of fly ash-Cu hybrid nanofluid under turbulent flow in a tube, 30 and the results indicated the TPF thermal performance factor values increased with the concentration increasing.
Surfactants were used to enhanced the nanofluids stability. 31But the detailed mechanism of surfactants effect on the nanofluids heat transfer was unclear.Ma et al. 32 affect the Al 2 O 3 -CuO/TiO 2 nanofluids, and the results indicated that the slight of surfactants would enhance the nanofluids heat transfer coefficients, but excess surfactants would decrease the heat transfer coefficients.But other studies hold different opinions. 33owever, there are some limitations to the previous studies. 34Most studies have only focused on the effect of single nanofluids on heat transfer coefficients.The effect of mixed nanofluids has been ignored, as has the effect of temperature, pH, and nanofluid concentration.The details of the mechanism through which nanofluids enhance heat conduction are unclear, with most results only addressing the phenomenon.
The differences between "Thermal conductivity" and "Overall heat transfer coefficient" were as follows.First, the definitions of "Thermal conductivity" and "Overall heat transfer coefficients" were different."Thermal conductivity": This is a fundamental property of nanofluids that determines the rate at which heat energy is conducted through a unit area of the material per unit temperature gradient.The thermal conductivity of the nanofluids tells you how well they conduct heat.For example, metals usually have high thermal conductivities, while nanofluids have low ones."Overall heat transfer coefficient": This is a measure of the overall ability of an assembly (composed of a kind of nanofluids or several kinds of nanofluids) to transfer heat.It depends not only on the properties of the materials involved but also on the nature of the fluid and the conditions on either side of the assembly, such as fluid velocity, temperature, and the type of heat transfer (conduction, convection, or radiation).The units of "Thermal conductivity" and "Overall heat transfer coefficients" were different."Thermal conductivity" was typically denoted by the symbol k or λ.The unit of measurement for "Thermal conductivity" is typically Watts per meter-Kelvin (W/m K) or British Thermal Units per hour-foot-°Fahrenheit (Btu/h ft °F).The unit of measurement for the "Overall heat transfer coefficient" is typically W/m² K or Btu/ h ft² °F.Thermal conductivity is a property of the nanofluids, whereas the overall heat transfer coefficient pertains to a whole assembly or system and involves more complex heat transfer mechanisms.Both are crucial for designing and analyzing systems where heat transfer is significant.
The single and mixed nanofluids effects on the heat transfer conduction coefficients were studied, and the corresponding nanofluids concentration, temperature, pH, and other factors effect the heat transfer coefficients.The detailed mechanism of surfactants effect on the nanofluids heat transfer coefficients was also studied.

| Heat transfer coefficient experiment
Heat conduction coefficients were measured experimentally.The experiment used a transient hot-wire apparatus (KD-2 Thermal Properties Analyzer, Decagon Devices Inc.).The nanofluids were pumped into the experiment instruments and the heat transfer coefficients were measured.The detailed experiment procedures were as follows: (1) The different nanofluids (with or without surfactants) were prepared.(2) Before nanofluids were injected into the pipeline, the nanofluids temperature remained constant.(3) The different nanofluids (with or without surfactants) were injected into the apparatus.(4) The corresponding tests continued for 90 min, so as to make the steady-state condition.After the thermal equilibrium conditions occurred, the flow rate and temperature readings were recorded.(5) The overall heat transfer coefficients were calculated by the corresponding program of the computer.
The detailed experiment device was shown as follows.A system designed to probe the behavior of heat transfer and pressure changes in corrugated channels under varied flow parameters was developed. 35A Plate Heat Exchanger (PHE) made by Alfa Laval India Limited, model M3 FG, was used in these tests.The configuration specifics for the plates and the heat exchanger are made available.The setup primarily consists of two circulating loops for two types of fluids: a nanofluid and distilled water.The hot water system integrates a 25-L insulated tank that houses four immersion heaters, each of 2 kW capacity.The temperature of hot water input to the PHE is governed by a straightforward on-off temperature control mechanism.Hot water circulation through the PHE is ensured by a gasket-sealed water pump.A 15-L container houses the nanofluid which is circulated by a centrifugal pump.The nanofluid is conditioned to a consistent input temperature through cooling before it enters the PHE.For precision, the hot water flow rate is gauged using a rotameter, and the nanofluid flow rate is calculated based on the time required to discharge a specified volume.The setup includes two differential pressure manometers, positioned between the inlet and outlet points of the PHE, to monitor both the hot water and nanofluid streams.Temperatures are tracked using highly precise J-type thermocouples installed at the inlet and outlet points of both the nanofluid and hot water streams.To prevent heat loss, the nanofluid tank, water tank, and associated pipework are thoroughly insulated.Under stable conditions, we monitored the flow rates and final temperatures of the hot water and nanofluid throughout the experiments.The nanofluid flow rate was adjusted within the range of 1-4 liters per minute (lpm), while the input temperature of the cold stream was set between 25°C and 30°C.Simultaneously, the hot stream's flow rate was varied from 1 to 4 lpm, maintaining a stable input hot water temperature of 70°C.Each test session typically lasted around 90 min, allowing the system to attain a steady-state condition.Continual temperature monitoring was carried out to verify the attainment of this state.Once thermal stability was achieved, the respective flow rates and temperatures were logged.The data from each test was then compared against the average results, and potential errors were identified and adjusted.

| Preparation of nanofluids
The two-step method was used to prepare the different nanofluids. 36Weigh 1 g SiO 2 nanoparticles, and then the nanoparticles were dispersed into 1 L deionized water, the ultrasonic dispersion by the Ultrasonic Disperser (Scientz-750F) was conducted for 30 min, and then the Ultrasonic Cell Disruptor (JY92-IIDZ) was used to disperse the nanofluids for 60 min.Then the 0.1 wt% SiO 2 nanofluids were prepared.Other nanofluids TiO 2 , MgO, ZrO 2 , CeO 2 , Al 2 O 3 , and Fe 3 O 4 followed a similar experiment procedure.

| Influencing factors analysis
The effect of single nanofluids and mixed nanofluids on overall heat transfer coefficients was analyzed.The effect of single nanofluids (SiO 2 , TiO 2 , MgO, ZrO 2 , CeO 2 , Al 2 O 3 , and Fe 3 O 4 ) on the heat transfer coefficient was measured.The mixed nanofluids (SiO 2 , TiO 2 , MgO, ZrO 2 , CeO 2 , Al 2 O 3 , and Fe 3 O 4 ) were mixed in pairs at a ratio of 1:1.Temperature has an effect on the heat conduction coefficient. 37The effect of different temperatures on the heat conduction coefficient was studied.The temperature range was from 25°C to 55°C.The effect of nanofluid concentration on the heat conduction coefficient was studied.The nanofluid concentrations were in the range of 0.1-0.6 wt%.The effect of differing pH on the heat conduction coefficient was studied.The pH range was from 4 to 11.The pH was adjusted by NaOH and HCl.

| Zeta potential measurement
Zeta potential is an electrostatic potential that exists very near the surface of particles suspended in liquids. 38Zeta potential measurements were conducted to measure the charges of the nanofluids and nanofluids stability. 39The zeta potentials of the nanofluids at different pHs were measured using a Zetasizer Nano ZS.The detailed measurement procedures were as follows: (1) following Section 2.3, prepare different 0.4 wt% nanofluids, and the nanofluids pH was adjusted to different pH values (from 4 to 11); (2) the nanofluids solutions were poured into the Zeta potential cell by pipette; (3) measure the zeta potentials of the different nanofluids.

| Nanoparticles properties analysis
Figure 1 shows the SEM analysis of the SiO 2 , TiO 2 , MgO, ZrO 2 , CeO 2 , Al 2 O 3 , and Fe 3 O 4 nanoparticles.The SEM figures showed that different nanoparticles showed some aggregates.The different nanoparticles sizes were among 20-50 nm, and it was difficult to accurately the nanoparticles sizes.Table 1 shows the specific surface area of different nanoparticles.The results showed that the specific surface areas of SiO 2 , TiO 2 , MgO, ZrO 2 , CeO 2 , Al 2 O 3 , and Fe 3 O 4 nanoparticles were 24.6, 36.8, 32.9, 28.4,45.6, 40.6, and 48.2 m 2 /g, respectively.But it was not absolutely certain, the heat transfer coefficients were related to the nanofluids charges and nanoparticles properties.

| Effect of single nanofluids
Figure 2 shows the effect of single nanofluids on the overall heat transfer coefficient (W/m 2 K).The different nanofluids showed different heat transfer coefficients.The overall heat transfer coefficients for SiO 2 , TiO 2 , MgO, ZrO 2 , CeO 2 , Al 2 O 3 , and Fe 3 O 4 were 346.5, 442.9, 569.2, 465.6, 663.2, 562.4,and 706.2 W/m 2 K, respectively.The differences were due to the fact that different nanoparticles have different surface areas and charges. 40,41igure 3 shows the hydrodynamic diameter of different nanofluids.As was shown in Figure 3, the different nanofluids showed different hydrodynamic diameters.For instance, the hydrodynamic diameters of SiO 2 , TiO 2 , MgO, ZrO 2 , CeO 2 , Al 2 O 3 , and Fe 3 O 4 nanofluids were 24.5, 36.1, 50.6, 46.5, 66.9, 43.7, and 60.7 nm, respectively.Most nanofluids hydrodynamics diameters followed the rule that the less the hydrodynamic diameter was, the higher the overall heat transfer coefficients were.Some nanofluids did not follow this rule.
Nanofluids viscosities were the basic properties for nanofluids physicochemical properties. 42The viscosity of different nanofluids is shown in Figure 4.As was shown in Figure 4, the different nanofluids showed different viscosities, and the SiO 2 , TiO  the heat conduction coefficient.For other nanofluids, different nanoparticles showed obvious synergistic effects on the overall heat transfer coefficient (Figure 5B-D).

| Effect of mixed nanofluids
When the different nanofluids were mixed together, the heat transfer coefficients were higher.

| Overall heat transfer coefficient impact factors
Figure 6 shows the effect of nanofluid concentration on the overall heat coefficient.The results indicate that the heat coefficients increased with the increase in nanofluid concentration.When the nanofluid concentration increased to 0.4 wt%, the overall heat transfer coefficients became stable and would not change, as this nanofluid concentration was equilibrium.In other words, there exists an adsorption equilibrium during the nanoparticle adsorption process; once the adsorption equilibrium is reached, the overall heat transfer coefficient is stable.For different nanofluids, the heat transfer coefficients (HTE) followed the rule 2 .The nanofluids stability and thermophysical properties would influence the heat transfer property. 29,30,43,44igure 7 shows the effect of temperature on the overall heat transfer coefficients.The results show that heat transfer coefficients increase with increasing temperature.In the previous studies, the stability and thermophysical properties of Al 2 O 3 -graphene oxide hybrid nanofluids were studied. 27For instance, the overall heat transfer coefficient for SiO 2 nanofluids increased from 346.5 W/m 2 K (25°C) to 369.4 W/m 2 K (35°C), 411.4 W/ m 2 K (45°C), and 427.6 W/m 2 K (55°C).These results are in accordance with the relevant literature. 45,46he pH value would have effect on the nanofluids stability and heat transfer coefficients. 28Figure 8 shows the effect of pH on the overall heat transfer coefficients.The results show that the heat transfer coefficients increased with the increase of pH to a certain point, after which the heat transfer coefficients decreased.Different nanofluids showed different maximum overall heat transfer coefficients.Fe 3 O 4 nanofluid showed the highest overall heat transfer coefficient, while SiO 2 nanofluid showed the lowest overall heat transfer coefficient.K, respectively.In addition, the single surfactants could make the overall heat transfer coefficients lower than the nanoparticles alone.Therefore, the surfactants effect on the nanoparticles alone effect onto the overall heat transfer coefficients.

| Effect of surfactants
Figure 10 shows the enhancing effect of SDS, CTAB, and TX-100 on nanofluid overall heat transfer coefficients.8][49] The results indicate that different surfactants enhance the overall heat conduction of nanofluids.In addition, different surfactants had varying effects.As shown in Figure 10A, SDS enhanced the different nanofluids at different concentrations.However, Figure 10B shows that the SiO 2 and TiO 2 nanofluid heat conduction coefficients were enhanced with different DTAB concentrations (0-300 ppm).For the MgO, ZrO 2 , and Al 2 O 3 nanofluids, the overall heat conduction coefficient was enhanced with DTAB (dodecyltrimethyl ammonium bromide) concentrations from 0 to 200 ppm, but was decreased with DTAB concentrations from 200 to 300 ppm.In addition, for CeO 2 nanofluids and Fe 3 O 4 nanofluids, the overall heat conduction coefficients increased with DTAB concentrations from 0 to 100 ppm, but decreased with concentrations from 100 to 300 ppm. Figure 10C shows that the TX-100 deceased the heat conduction coefficients of most nanofluids (SiO 2 , TiO 2 , ZrO 2 , Al 2 O 3 , and Fe 3 O 4 ).However, TX-100 surfactants increased the heat conduction coefficients of MgO and CeO 2 nanofluids from 0 to 100 ppm, but decreased them from 100 to 300 ppm.indicate that different nanofluids hold different charges, which would influence their heat conduction coefficients.When the nanofluids' zeta potentials were lower than −30 mV, the nanofluids became more stable. 50,51igure 12 shows the effect of pH on the zeta potential of different nanofluids.3][54] As shown in Figure 12, the SiO 2 nanofluids showed the highest zeta potential at different pHs, while the Fe 3 O 4 nanofluids showed the lowest zeta potential.For other nanofluids, the zeta potential procedure was different.

| Economics evaluation
The previous study showed that the Fe 3 O 4 nanofluids showed the highest overall heat transfer coefficients, and Fe 3 O 4 nanoparticles were recyclable due to the magnetic.The surfactant usage was low.So the nanofluidssurfactants methods to enhance the heat transfer were economically viable, especially for the Fe 3 O 4 nanofluids.

| CONCLUSIONS
This study addressed the effect of different nanofluids on overall heat conduction.Previously, most studies focused only on the effect of single and mixed nanofluids on overall heat transfer coefficients; studies on the synergistic effects of different nanofluids on overall heat transfer coefficients are few.In addition, in the previous study, the zeta potentials measurement of the nanofluids effect on the heat transfer coefficients study was few.The detailed conclusions are as follows: In addition, the surfactants would alter the physical properties of nanofluids, so the heat transfer coefficients would be altered.In total, the heat conduction transfer would increase when the nanoparticles specific surface area increased.

Figure 11
Figure 11 shows the overall heat transfer coefficients of different nanofluids with a pH of 4. The results show that different nanofluids have different zeta potentials.The zeta potentials of SiO 2 , TiO 2 , MgO, ZrO 2 , CeO 2 , Al 2 O 3 , and Fe 3 O 4 nanofluids were −12.1, −24.8, −28.6, −23.2, −35.9, −31.3, and −40.4 mV, respectively.The resultsindicate that different nanofluids hold different charges, which would influence their heat conduction coefficients.When the nanofluids' zeta potentials were lower than −30 mV, the nanofluids became more stable.50,51Figure12shows the effect of pH on the zeta potential of different nanofluids.The results indicate that the zeta potentials of different nanofluids decreased with increasing pH values, which is in accordance with most research on the effect of pH on zeta potential.[52][53][54]As shown in Figure12, the SiO 2 nanofluids showed the highest zeta potential at different pHs, while the Fe 3 O 4 nanofluids showed the lowest zeta potential.For other nanofluids, the zeta potential procedure was different.

F
I G U R E 8 Effect of pH on overall heat transfer coefficients.F I G U R E 9 Surfactant effect on the overall heat transfer coefficients.CTAB; cetyl trimethyl ammonium bromide; SDS, sodiumdodecyl sulfate; TX-100, Triton X-100.F I G U R E 10 Effect of (A) SDS, (B) CTAB, and (C) TX-100 on the overall heat transfer coefficients of nanofluids.CTAB; cetyl trimethyl ammonium bromide; DTAB, dodecyltrimethylammonium bromide; SDS, sodiumdodecyl sulfate; TX-100, Triton X-100.F I G U R E 11 pH values of different nanofluids at a pH of 4. F I G U R E 12 Effect of pH on the zeta potential of different nanofluids.

( 1 )
Different nanofluids have different heat transfer coefficients.SiO 2 nanofluid showed the lowest overall heat transfer coefficient, while Fe 3 O 4 nanofluid showed the highest.Compared with single nanofluids, mixed nanofluids can increase heat transfer coefficients.(2) Overall heat transfer coefficients increase with the increase of temperature and nanofluid concentration.Heat transfer coefficients increased with the increase of pH up to a certain point, but decreased beyond it.(3) Different surfactants have different effects on the overall heat coefficients of nanofluids.(4) Different nanoparticles have different physical properties, for instance, surface area and surface charge.
Zainon and Azmi 12 studied the green boglycolbased TiO 2 -SiO 2 nanofluids heat transfer performance, and the results indicated that the different TiO 2 -SiO 2 concentrations would cause the different heat transfer coefficients, and the highest overall transfer coefficients were at 70°C.Sun and Wang 21 studied the nanofluids effect on the heat transfer and flow behaviors in nanochannels by molecular dynamic simulations.Utomo et al. 22 studied the thermal conductivity, viscosity, and heat transfer coefficient of Al 2 O 3 and TiO 2 nanofluids.