"Thermal Performance Analysis of a Cross-Flow Automotive Radiator under Variable Air and Coolant Flow"
SanjayMitkar1✉Email
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Department of Mechanical EngineeringG H Raisoni College of Engineering and Managent Pune
Sanjay Mitkar (sgmitkari.nbnscoe@gmail.com)
Department of Mechanical Engineering, G H Raisoni College of Engineering and Managent Pune
Abstract
The study examines the thermal performance of a cross-flow automotive radiator typically used in internal combustion engine vehicles, where 8–30 kW of heat must be dissipated under varying operating conditions. Radiator cooling efficiency primarily depends on air velocity (1–6 m/s) and coolant flow rate (0.05–0.3 kg/s), with air-side management exerting the strongest influence. Experimental analysis showed a maximum coolant-side heat transfer rate of 26.25 kW, with Reynolds numbers between 16,650- 2,800 yielding a convective coefficient of 22.49 kW/m²K. On the air side, Reynolds numbers of 217–1,520 correspond to a heat transfer coefficient of 168 W/m²K and a peak heat flow of 23.8 kW. The overall heat transfer coefficient reached 167 W/m²K. Coolant temperatures decreased significantly along the radiator core, with low flow rates achieving large temperature drops (90°C to ~ 64.3°C), while higher flow rates enhanced total heat removal through increased turbulence. Variable air velocity from 1 m/s to 5 m/s markedly improved convective heat transfer, confirming the dominance of air-side effects. System-level analysis highlights that, since pump flow depends on engine speed, variable-speed fan control provides the primary means of adjusting heat rejection in real time, improving thermal efficiency and reducing energy consumption in modern automotive cooling systems.
Keywords:
Radiator
cross flow heat exchanger
convective heat transfer
coolant
1. Introduction
The radiator is a critical component of automotive thermal management systems, ensuring that engines, batteries, and power electronics operate within safe temperature limits. In conventional internal combustion engine (ICE) vehicles, a small car radiators dissipate 8–15 kW of thermal energy under typical driving and up to 25–30 kW during high-load operation [1].. Similarly, map-controlled thermostats improved temperature regulation (90 ± 2°C), reduced warm-up time by 18%, and cut fuel consumption by 3.5%, demonstrating that control strategies can directly benefit radiator heat balance [2].Efficient radiator design is critical to ensure optimal engine performance, reduced emissions, and long-term component durability by rejecting heat to the ambient air. In electric and hybrid vehicles, although the absence of combustion heat lowers the coolant load from the engine, consequently, radiator design and optimization remain a vital research area for both conventional internal combustion engine (ICE) vehicles and electrified powertrains.
Over the past decades, radiator research has focused on enhancing heat transfer while minimizing pressure drop and pumping power penalties. Various approaches have been investigated, including fin geometry modifications (louvered, wavy, perforated, or composite fins), tube shape optimization (elliptical, teardrop, or multi-port flat tubes), passive flow distribution control, and advanced thermostat or control strategies. Typical improvements reported include 8–15% higher heat transfer coefficients from fin shape modifications and 10–20% performance gains from optimized tube geometries, elliptical tube radiators enhanced heat transfer coefficients by 14% compared to flat-tube designs [3].
Recent studies have also employed computational fluid dynamics (CFD), infrared thermography, and even machine learning techniques to better understand local flow maldistribution, hot-spot formation, and predictive optimization of radiator cores[4,5.]. Despite these advances, key challenges remain. Radiator performance is highly sensitive to operating conditions: coolant flow rate (0.05–0.3 kg/s), air velocity (1–6 m/s), and ambient climate strongly affect heat transfer effectiveness [6]. Furthermore, compact radiator designs must balance thermal enhancement with hydraulic losses, ensuring that pressure drops remain below 5% to avoid excessive pumping power [7]. In practice, the radiator must deliver high heat rejection under peak load while avoiding overcooling at low load, Moreover, modern vehicles demand compact, lightweight, and fault-tolerant radiator systems that can integrate seamlessly with thermal management of multiple subsystems.
In parallel, there is a growing interest in coolant-side enhancement techniques, particularly the use of nanofluids-engine coolants doped with high thermal conductivity nanoparticles such as Al₂O₃, CuO, TiO₂, or graphene. Conventional coolants like water–ethylene glycol mixtures have relatively low thermal conductivity, limiting their ability to cope with rising thermal loads. Studies have shown that nanofluid coolants can enhance thermal conductivity by 20–40% and increase radiator effectiveness by 12–30%, depending on particle concentration and flow conditions. While challenges remain in terms of long-term stability, pumping power requirements, and material compatibility, nanofluids represent a promising path for next-generation high-performance radiators.
Therefore, a systematic study of radiator cooling performance, considering both geometry-based improvements and coolant-side innovations, is essential for advancing automotive thermal management systems. The study shows how using multiple radiators instead of one improves temperature control under both low (20 kW) and high (40 kW) heat loads, enabling faster warm-up and better handling of peak load while avoiding oversizing and overcooling. [8] The paper describes a compact thermal management system that integrates with HVAC in EVs, showing design trade-offs in packaging size and weight while maintaining sufficient heat rejection and temperature control[9].
2. Literature Review:
Research on radiator cooling performance over the past five years has advanced along multiple directions, ranging from flow distribution control and fin geometry optimization to alternative tube shapes, wet-condition effects, control strategies, and machine-learning-assisted design tools. Collectively, these works establish that even modest geometric or control refinements can yield double-digit heat transfer improvements with minimal hydraulic penalties.
2.1 Automotive Radiator Performance
Salehi et al., tested the system at air velocities 2–6 m/s, coolant flows 3–8 L/min, and coolant inlet 90°C. Combined experiments and CFD to demonstrate that installing passive flow distributors in the radiator plenum reduced flow maldistribution by 18% and boosted effectiveness from 0.63 to 0.71, corresponding to a 12% increase in heat rejection [1]. Feleke et al., varied fin pitch (1.2–1.8 mm), louver angle (25–35°) and edge radius ratio (r/p = 0.01–0.05) at air-side Re no 400–1200 to make cores more compact [3]. The experimental comparison tested flat-tube, circular-tube and elliptical-tube using the ε–NTU method. revealed elliptical tubes provide 14% higher heat transfer coefficients and 11% higher effectiveness than flat tubes [10] many authors further validated elliptical tubes as the most balanced option, The authors present empirical correlations per tube shape and recommend elliptical tubes for compact radiator cores where air-side resistance dominates[1113].
Basir et al. demonstrated that a map-controlled thermostat (MCT) reduced warm-up time by 18%, and achieved 3–4% lower fuel consumption and CO₂ emissions compared to wax thermostats. Confirming that thermostat control strategy significantly affects radiator loading, warm-up, and emissions [2]. Becker et al. showed that active grille shutters combined with staged fan control shortened warm-up time by 22% and prevented frost accumulation in winter conditions, highlighting how radiator control logic directly affects energy efficiency [14]. Recent diagnostic and prediction studies emphasize high-resolution mapping and data-driven modeling. Gan et. al. developed an infrared thermography plus inverse heat conduction method capable of reconstructing core temperature fields with less than 2°C accuracy, detecting hot spots with 12°C gradients enabling real-time monitoring of maldistribution. Machine learning has also entered radiator design [4].
Other works investigate wet operating conditions and non-traditional enhancement structures, confirmed that inlet straighteners and tailored louvers could reduce multi-row maldistribution from 25% to 8%, recovering 10–14% lost capacity [15, 16]. Dika & Dika reported that wavy fins improved Nusselt numbers by 8–12% .while other s found that metal foam inserts deliver 20–35% volumetric heat transfer improvement but often double or triple ΔP, restricting their use to highly space-constrained cores[18, 19]. Habibian & Abolmaali highlighted coolant–fin interaction, showing that wavy fins increased Nusselt number by 9–13% over straight fins but raising EG content from 20% to 50% reduced heat rejection by up to 6%. (due to lower cp) while improving freeze protection[20].
2.2 Nanofluid-Based Automotive Radiator Performance
Table-1 shows different types of nano-particles used in a radiator coolant. A nanofluid is a mixture of a base fluid (like water, ethylene glycol) and nanoscale particles (1–100 nanometers in size) that are suspended uniformly in it. Thermal conductivity Increases with nanoparticle addition gives better cooling and higher convective performance. Viscosity Slightly increases and can affect pump power. Specific heat slightly decreases .This requires surfactants or special mixing to avoid settling. These nanoparticles are typically metals, metal oxides, or carbon-based materials like:
Table-1: Types of Nano-particles
 
Nanoparticle
Material Type
1
Al₂O₃ (Aluminum oxide)
Metal oxide
2
Cu (Copper)
Metal
3
CuO (Copper oxide)
Metal oxide
4
TiO₂ (Titanium dioxide)
Metal oxide
5
SiO₂ (Silicon dioxide)
Non-metal
6
CNT (Carbon nanotubes)
Carbon-based
Over the past decade, extensive research has explored the use of nanofluids to enhance automotive radiator cooling performance, primarily focusing on the effects of particle type, concentration, base fluid, flow conditions, and fin/tube geometry. Ramesh Kumar et al., used 3D CFD simulations to analyze a radiator with composite fins and nanoparticle-based coolant at a velocity of 1.61 m/s. Incorporating nanoparticles led to a 12% increase in heat transfer [21]. Sivakumar et al., experimentally investigated hybrid Al₂O₃–Cu/water nanofluids in commercial car radiators at 1.0 vol%, the heat transfer coefficient rose 22% [22]. Sarafraz and Safaei tested a flat-tube automotive radiator operating with TiO₂/water nanofluids at %, the Nusselt number improved 19% and effectiveness increased 14%[23],. Similarly, Al-Rashed and Chamkha simulated graphene–water nanofluids showing 20–27% higher heat transfer. The pumping power requirement increased slightly due to higher viscosity. The study emphasizes graphene’s very high thermal conductivity, showing its superior potential for next-generation radiator coolants compared to oxide-based nanofluids [24]. Sajid et al., tested SiO₂/water nanofluids, finding 15–18% improvement in heat transfer with only 3–4% higher ΔP. SiO₂ nanofluid as a low-cost, effective solution for enhancing radiator cooling performance [25].
Hybrid nanofluids were prepared by dispersing SiO₂ and MWCNT nanoparticles (0.1 vol% total) in different ratios (80:20, 50:50, 20:80) in distilled water. The best composition (20:80 SiO₂:MWCNT) achieved 15.6% Nusselt number increase compared to the base fluid. The results confirmed that mixing oxide particles with MWCNT in proper ratios can significantly enhance radiator air-side heat transfer, even at very low nanoparticle concentrations [26]. Mamat et al.,tested hybrid CuO–TiO₂ (50:50) in 60:40 water–EG ,the overall heat transfer coefficient improved 83% compared to base fluid, demonstrating strong enhancement at optimized loading. Microchannel designs have further amplified nanofluid benefits [27]. The nanofluid increased thermal conductivity by 40% and achieved a heat transfer coefficient of 5366 W/m²K, a 116% improvement over water. Results show that CuO nanofluid microchannels can nearly double cooling capacity, enabling compact radiator designs with superior heat rejection[28, 29].In some Experiments used a 60:40 water–EG base fluid with Al₂SiO₅ nanoparticles at 0.1–0.4 vol% and coolant Reynolds numbers from 500–1500. Also revealed Nusselt number improvements of 174% and 162%, respectively, with convective HTC reaching 37,021 W/m²K, highlighting nanofluid suitability for compact radiator designs[30, 31].Experimental studies also demonstrated that performance scales sharply with concentration. Adhikari et al., reported Al₂O₃–EG/water nanofluids improved HTC by 33.6%, 65.4%, and 83.5% at 0.2%, 0.5%, and 1.0% volume fraction, respectively[32, 33, 34]. Subhedar et al., showed that 0.2–0.6 vol% Al₂O₃–EG/water nanofluids allow frontal area reduction up to 65% without loss of cooling, supporting radiator downsizing for compact vehicles [35]. at 60–80°C produced 28–29% higher HTC, 23–24% higher Nusselt number, and 22.5% higher effectiveness than water, though ΔP increased 24%, highlighting the trade-off between heat transfer enhancement and pumping requirements[36].
In summary, these studies converge on three main findings. First, geometry refinements, tube cross-section, louver edges, and fin design can consistently yield 8–15% higher heat transfer with minimal ΔP penalty. Second, system-level control strategies such as map-controlled thermostats and active shutters improve warm-up, reduce overcooling, and contribute to 3–4% fuel savings. At the same time, nanofluid technology offers substantial potential to enhance automotive radiator efficiency.
3. Coolant used in a Radiator
Automobile radiators use various coolants to absorb and dissipate heat from the engine. Water (Distilled or Deionized) is used in emergency cooling systems.it has good heat capacity, but corrosive and boils/freezes easily therefore not recommended alone and usually mixed with additives. Ethylene Glycol-based coolant is most commonly used coolant.it has excellent heat transfer, anti-freeze, and anti-boil properties, stable over long periods, compatible with additives for corrosion and pH control. Typically mixed with distilled water in 50:50 ratios.
33% EG: Better heat transfer, but limited freeze protection. Suitable for mild winters. 50% EG: Balanced—offers good freeze and boil protection. Standard for most vehicles.70% EG: Extreme freeze protection but reduced thermal performance. Used in very cold regions. Most regions in India do not face extremely low temperatures. A 30% ethylene glycol mixture offers: sufficient freeze protection (–15°C), better heat transfer than a 50% mix. It balances cooling performance and corrosion protection without over-thickening the fluid [37, 38].Table-2 shows thermal properties of nano-particle.
Hybrid Organic Acid Technology (HOAT) is a Mix of organic acids and silicates/phosphates. It has longer life than traditional coolants (up to 5 years or 240,000 km).Compatible with modern aluminium and plastic radiators. Organic Acid Technology (OAT) contains no phosphates or silicates, usually orange, red, or purple in colour. It is Common in modern cars. Inorganic Acid Technology (IAT) is a Traditional coolant with silicates and phosphates. Green in color and requires frequent replacement (every 2–3 years).Still used in older vehicles. Ready-to-Use Premixed Coolants, 50:50 or 60:40 mix of coolant and distilled water. Convenient and prevents incorrect mixing. Available in various types: OAT, HOAT, IAT.
Nanofluid Coolants (Advanced) is Engineered with nanoparticles (like Al₂O₃, CuO, SiO₂).it significantly enhances thermal conductivity of the coolant. Never mix Yellow (Standard) with Blue (Super) coolant, they are chemically different (IAT vs OAT types). Nanoparticles pose challenges in stable dispersion within the base fluid over long periods and under variable temperature and flow conditions in car radiators[39, 40]. This can lead to particle agglomeration, sedimentation, clogging and reduced heat transfer performance. The agglomeration is nanoparticle clustering, sedimentation is nanoparticle settling, and clogging is flow obstruction by these deposits, all of which can degrade the thermal performance and reliability of nanofluid coolants in automotive radiators. The density difference between nanoparticles and base fluid is a principal cause of sedimentation and associated issues, agglomeration induced by surface forces and inadequate dispersion is critical in catalyzing this process. Effective nanofluid stability in automobile radiators depends on balancing these factors through proper particle size, concentration, surface treatment, and fluid preparation techniques.
Table-2: Thermal Properties of nanoparticle
Property
Al2O3 Nanoparticles
Ethylene Glycol-Water Coolant (Typical 50–50 mix)
Water (at 25°C)
Thermal Conductivity W/m⋅K
20 to 35 (solid nanoparticles)
0.3–0.4
0.6
Specific Heat Capacity J/kg⋅KJ
880 (bulk Al2O3)
3500–4000 (mixture)
4182
Density kg/m
3900 to 4000
1050–1100
1000
Viscosity (Pa·s)
Not applicable (solid)
0.002–0.004 (depends on temp and mix ratio)
0.001
Working of Radiator:
Radiator Core:
Coolant tubes carry hot coolant from the engine and densely packed fins that increase surface area and promote heat transfer to air, this setup maximizes cooling efficiency: Flat tubes are used due to more contact area with fins (for better heat transfer), Improved airflow, less resistance than circular tubes.
Thermostat Control
The thermostat is the primary device controlling coolant flow. It is located between the engine and the radiator inlet. Cold engine (below 85°C): thermostat stays closed, coolant bypasses radiator and goes to the engine and warms up quickly. As the engine reaches operating temperature (90°C),thermostat starts opening, coolant flows to radiator and heat is removed. Thermostat fully opens when engine is hot, this ensures the engine doesn’t overcool or overheat.
Water Pump Control
The water pump circulates coolant. Traditional cars use a mechanical pump driven by the engine therefore coolant flow rate depends on engine speed. Modern cars use an electric water pump where flow rate can be varied independently of engine speed. Controlled by the Engine Control Unit (ECU) based on temperature, load, and speed.
Radiator Fan Assistance:
The electric fan is mounted directly behind the radiator, Its purpose is to pull or push air through the radiator fins, increasing airflow over the coolant and improving heat transfer. Fan switches ON/OFF or varies speed (in variable fan setups) based on coolant temperature and vehicle speed. When the vehicle is moving at a decent speed (say 40–50 km/h or higher), air naturally passes through the radiator due to vehicle motion. This “ram air effect” can cool the coolant even if the fan is OFF. In this case, the fan may not need to run, saving battery power. The fan becomes important when vehicle is idling, as there is no natural airflow. In low-speed driving airflow through radiator is insufficient. In case of high engine load or AC operation an extra cooling is needed. Airflow is controlled passively by vehicle motion and actively by electric or clutch fans.
4.1 Heating and cooling circuit
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Once the engine reaches its normal operating temperature, usually around 82C, the thermostat opens gradually and allows coolant partially to flow through the radiator circuit. When it reaches to 90–95°C, thermostat opens fully now the water pump pushes all the hot coolant from the engine into the radiator. The temperature sensor constantly monitors the coolant and signals the ECU to control the fan as needed, ensuring stable temperature. The radiator cap keeps the system pressurized, raising the boiling point of the coolant, and directs excess coolant (1.1bar) into the reservoir when expansion occurs. Once the engine cools down, this coolant is drawn back into the system, maintaining a closed and balanced loop. This process keeps the engine within a safe operating range, typically between 90 and 105°C, preventing overheating and ensuring efficient performance.
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Fig-1: Cooling and Heating circuit
4. Calculations
A typical automotive radiator is a compact cross flow heat exchanger, where coolant circulates through tube–fin assemblies while ambient air extracts heat under both forced and natural convection. However, with growing power densities, stricter emission norms, and the trend toward compact lightweight vehicles, conventional radiator designs are under increasing pressure to deliver higher heat rejection within limited packaging space.
Here’s a 3D model of a typical radiator core, 0.5m ×0.4 m× 0.03m. Face area: Just the visible front surface 0.2 m². Extended surface area: Due to fins and multiple tube rows, the effective heat transfer area increases drastically up to 3.91 m² which is typical for small cars, tube height is 2mm and width 10mm gives hydraulic diameter as 3.33mm.The air side hydraulic diameter 3.6mm.Table-3 shows radiator and material specifications.
Table-3: Radiator and material specifications
Property
Value
Coolant density
1050 kg/m³
Dynamic viscosity
0.0025 Pa·s
Specific heat
3400 J/kg·K
Boiling point
197.3°C
Freezing point
−12.9°C (pure); lower when mixed with water
Thermal conductivity
0.37 W/m·K
Tube hydraulic diameter (approx)
3 mm = 0.003 m
Tube shape
Flat-oval (oblong), not round
Tube cross-section
10 mm × 2 mm
Number of tubes
40 tubes in a row
Rows
1 to 2 (depending on core thickness)
Tube length
500 mm Matches core Length
Fin thickness
0.15 mm = 0.00015 m
Fin pitch
2.0 mm = 0.002 m
Fin Material
Aluminum
Pump Type
Centrifugal, belt-driven
Pump Power Source
Engine crankshaft (via serpentine belt or timing belt)
Dittus Boelter equation gives
For air side developing or transitional flow correlation
6. Result:
On coolant side maximum heat transfer rate from coolant is 26.25kW, Re no 2,800 to 16,650, Pr no 30 and Nu no 214 gives heat transfer coefficient on coolant side obtained as 22.49 kw/m2k., On air side Re no 217 to 1520 ie laminar to transitional flow regime, Pr no 0.7 and Nu no 23 gives heat transfer coefficient on air side as 168 W/m2k. The maximum air side heat flow rate is 23.8 kW. The overall heat transfr coefficient U = 167 W/m2k.
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Fig-2: Coolant outlet temperature Vs Radiator Length
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The coolant temperature decreases along the length primarily due to heat loss through the tube walls and fins to air as shown in Fig. 2. High coolant Re induces turbulence, enhancing heat transfer, causing a sharper temperature drop at higher flows. Low flow rate means the coolant moves more slowly through the radiator. This longer residence time allows more heat to transfer from coolant to air. Consequently, the coolant temperature drops significantly. Lower flow rates provide better cooling per unit of coolant but may struggle to remove total heat if flow is too low. Higher flow rates remove more heat overall but have less temperature difference. Thus, the observed coolant temperature drop from 90°C to about 64.3°C at low flow rate illustrates efficient heat transfer given longer fluid residence time, while higher flow rates trade-off temperature drop for flow volume to maintain adequate heat removal.
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Fig-3: Heat Transfer Rate Vs Air velocity
Fig. 3
shows that by increasing air velocity from 1 m/s to 5 m/s consistently lowers the coolant outlet temperature, indicating more effective cooling at higher air speeds. At a given air velocity, raising the coolant flow rate (from 0.1 to 0.3 kg/s) results in a smaller temperature drop occurs per unit mass due to the larger coolant mass flow. Most pronounced reductions in outlet temperature are observed at low flow rates and high air velocities. Increasing air velocity increases both the coolant temperatures drop (ΔT) and the total heat transfer rate (Q). Increasing coolant flow rate decreases the temperature drop (ΔT) across the radiator, since more coolant passes through per second and each "unit" of coolant has less time to cool down, but the overall heat transfer rate (Q) actually increases.
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Fig-4 : Pump ,Overall HTC Vs Air velocity Fig-5 : Fan power, Overall HTC Vs Air velocity
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In most vehicles, the mechanical coolant pump is driven by the engine, so its flow rate (and therefore cooling effect) depends on engine speed, not on real-time cooling demand. This means that under low engine RPMs, coolant flow is relatively low, and at higher RPMs, coolant flow increases—even if the cooling demand doesn't always match these conditions. Air velocity dominates HT rate in radiators; coolant flow is less critical after a certain point as shown in Fig. 4 and Fig. 5.
The fan is the main device you can directly control to regulate radiator cooling performance as cooling demand changes. Modern vehicles often use electric fans or variable-speed fan clutches with electronic control. By sensing coolant temperature, engine load, ambient temperature, and A/C usage, the fan control system can precisely adjust fan speed (and thus air velocity) to provide just enough cooling, rather than running at full speed all the time. During idle or stop-and-go traffic, the engine speed—and thus pump flow—may be low, but heat rejection needs are high. Here, the fan compensates by increasing air velocity to maintain correct engine temperature. On highways, natural airflow through the radiator increases with vehicle speed, so fan speed can be reduced or the fan even shut off, saving energy.
7. Conclusion
The mechanical pump flow is tied to engine speed; it cannot be modulated to match real-time cooling demand. Therefore variable fan speed is the key tool for optimising radiator performance and energy use. Efficient fan control keeps engine temperature stable, reduces unnecessary noise and energy use, and supports reliable engine operation across varying driving and environmental conditions. Therefore optimal heat rejection, focus on controlling the fan side—whether through electronic, hydraulic, or clutch-based variable speed systems—since fan speed can be adjusted to meet real cooling needs while the mechanical pump remains tied to engine RPM.
In automobile radiators, Al2O3 added in low volume concentrations (e.g., 0.1% to 1%) as coolant additives to enhance heat transfer performance, enabling more efficient engine cooling and potential downsizing of the radiator system. Ultrasonication is a process that uses high-frequency ultrasonic waves to disperse and break apart nanoparticle agglomerates in liquids. These forces cause nanoparticles to collide and break into smaller, more uniformly dispersed particles, preventing clustering or agglomeration. This improved dispersion through ultrasonication leads to greater nanoparticle stability in the base fluid, enhances thermal conductivity, and reduces viscosity by maintaining small particle sizes evenly spread throughout the fluid. However, the prepared nanofluid’s stability can degrade over time due to re-agglomeration or sedimentation, which can be managed by proper formulation techniques, surfactants, or periodic maintenance. Stable nanofluids show little or no increase in nanoparticle size or cluster formation over time, indicating low agglomeration. Zeta potential is the electric potential at the nanoparticle surface that indicates repulsion forces among particles. A high absolute value (such as greater than ± 30 mV) suggests strong repulsion between particles, preventing agglomeration, thus indicating stable suspension.
Data availability statement:
No new data were created or analyzed in this study. Therefore, data sharing is not applicable.
Declarations
The authors declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article."
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Funding:
There is no funding received.
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Author Contribution
The study was conceptualized and designed by myself. Experimental setup, data collection, and analysis were performed . Theoretical modeling, numerical calculations, and validation of experimental results were undertaken to ensure data accuracy and consistency.The manuscript draft was prepared by myself.
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Total words in MS: 3844
Total words in Title: 14
Total words in Abstract: 198
Total Keyword count: 4
Total Images in MS: 7
Total Tables in MS: 3
Total Reference count: 40