Carbon-coated Fe3O4 core–shell super-paramagnetic nanoparticle-based ferrofluid for heat transfer applications

Herein, we report the investigation of the electrical and thermal conductivity of Fe3O4 and Fe3O4@carbon (Fe3O4@C) core–shell nanoparticle (NP)-based ferrofluids. Different sized Fe3O4 NPs were synthesized via a chemical co-precipitation method followed by carbon coating as a shell over the Fe3O4 NPs via the hydrothermal technique. The average particle size of Fe3O4 NPs and Fe3O4@C core–shell NPs was found to be in the range of ∼5–25 nm and ∼7–28 nm, respectively. The thickness of the carbon shell over the Fe3O4 NPs was found to be in the range of ∼1–3 nm. The magnetic characterization revealed that the as-synthesized small average-sized Fe3O4 NPs (ca. 5 nm) and Fe3O4@C core–shell NPs (ca. 7 nm) were superparamagnetic in nature. The electrical and thermal conductivities of Fe3O4 NPs and Fe3O4@C core–shell NP-based ferrofluids were measured using different concentrations of NPs and with different sized NPs. Exceptional results were obtained, where the electrical conductivity was enhanced up to ∼3222% and ∼2015% for Fe3O4 (ca. 5 nm) and Fe3O4@C core–shell (ca. 7 nm) NP-based ferrofluids compared to the base fluid, respectively. Similarly, an enhancement in the thermal conductivity of ∼153% and ∼116% was recorded for Fe3O4 (ca. 5 nm) and Fe3O4@C core–shell (ca. 7 nm) NPs, respectively. The exceptional enhancement in the thermal conductivity of the bare Fe3O4 NP-based ferrofluid compared to that of the Fe3O4@C core–shell NP-based ferrofluid was due to the more pronounced effect of the chain-like network formation/clustering of bare Fe3O4 NPs in the base fluid. Finally, the experimental thermal conductivity results were compared and validated against the Maxwell effective model. These results were found to be better than results reported till date using either the same or different material systems.


Introduction
The dispersion of nanoparticles (NPs) in various uids enhances their thermal conductivity, which have potential application in heat transfer as coolants in various systems such as automobile radiators, refrigerators, process engineering systems, electronic devices, solar energy heaters, pulsating pipes, and thermosyphons. [1][2][3][4][5] There are several typical base uids used for heat transfer applications such as water, ethylene glycol, ethanol, methanol, dimethyl formamide, poly-alfaolen, and oils. [6][7][8][9][10][11][12][13] Ferrouids or magnetic uids are stable colloidal homogeneous suspensions of magnetic NPs ($10 nm in diameter) in an aqueous or a non-aqueous carrier liquid. 14 The dispersion of NPs in these base uids results in the formation of a nanouid, and if NPs are magnetic in nature, the resulting uid is termed a ferrouid. Generally, NPs show enhanced electrical, thermal, optical and mechanical properties because of their large surface to volume ratio. [15][16][17] Magnetic NPs such as Fe 3 O 4 have attracted great interest from the scientic community because of their unique properties such as biocompatibility, high electrochemical response and thermal stability. 18 Consequently, Fe 3 O 4 NP-based ferrouids exhibit enhanced thermal and electrical conductivities. [19][20][21] However, NPs have high surface energy, which results in their agglomeration or settling at the bottom of the dispersion liquid when used for a long period. Therefore, the coating of inorganic or organic materials over Fe 3 O 4 NPs is necessary for their good dispersion and long-term stability. 18 The oxidation of magnetite (Fe 3 O 4 ) NPs leads to the formation of a stable phase of iron oxide, which is g-Fe 2 O 3 NPs (maghemite), and a more stable form, i.e., a-Fe 2 O 3 (hematite) under particular conditions. 22 Therefore, it is necessary to protect superparamagnetic Fe 3 O 4 NPs from physical and chemical changes by encapsulating them with other materials. Accordingly, capping Fe 3 O 4 NPs with another sub-material (shell) can result in their good dispersion and stability, as reported by Sharma et al. 18 Hence, various coreshell NPs have been reported thus far, especially Fe 3 O 4 @C coreshell NPs, for e.g., Xuan et al. synthesized carbon-encapsulated Fe 3 O 4 core-shell particles via the reduction of glucose. 23 Conversely, Wang et al. synthesized single carbon layer-coated ultra-small Fe 3 O 4 NPs using a one-step hydrothermal technique for surface-enhanced Raman spectroscopy studies, 24 and He et al. used in situ-synthesized carbon-encapsulated Fe 3 O 4 NPs as an anode material for lithium ion batteries. 25 Moreover, Zhao et al. employed the hydrothermal method for the synthesis of interconnected carbon nanospheres covering Fe 3 O 4 NPs. 26 Similarly, Liang et al. synthesized Fe 3 O 4 @Au core-shell NPs for the ultrasensitive detection of carbohydrate-protein interactions. 27 A magnetic metal nanocomposite was coated by carbon to prepare FeNi@C core-shell NPs. 28 Li et al. synthesized Cu@C core-shell NPs via a simple state reduction method and investigated their optical properties. 29 Similarly, Ag@C core-shell NPs were synthesized via the wet chemical route and catalysed under hydrothermal conditions, which exhibited hydrophilic and unique optical properties. 30 Moreover, the reverse micelle method was employed to prepare Fe@Fe-oxide and Fe@Au core-shell nanostructures. 31,32 These core-shell NPs possessed an added advantage over other NPs as their shell can protect their core from physical and chemical changes. Thus, bioincompatible, highly reactive and toxic NPs can be covered with biologically compatible, non-reactive and environmentally friendly materials in the form of shells.
To further explore the unique properties of core-shell NPs, they were introduced in a dispersion liquid to make stable fer-rouids for various applications. Recently, ferrouids were prepared by dispersing Fe 3 O 4 NPs in mineral oil and g-Fe 2 O 3 NPs in various base uids. 19 Core-shell NP-based ferrouids also exhibit good biocompatibility and improved properties. Accordingly, the other applications of core-shell NP-based ferrouids include multimodal imaging, hyperthermia, drug delivery, cytocompatibility tumour targeting, cancer chemotherapy and thermotherapy and other possible biological applications. [36][37][38] Similarly, magnetic NP systems are widely used in the MRI-guided delivery of magneto-electric drug nano-carriers to the brain. 39 Magnetoelectric core-shell NPs exhibit enhanced cell uptake and control drug release under the inuence of an applied and magnetic eld. 40 To manage central nervous system (CNS) diseases, surface-engineered magnetic NPs have been employed as a tool via image-guided therapy and theranostics. 41 Magneto-electric NPs (MENPs) are stimulus-responsive nanosystems for controlled drug release and cell uptake. 42,43 The futuristic application of these magnetic core-shell nanostructures may be projected in the biomedical eld, where previous studies showed the use of magnetic core-shell nanoparticles as an antimicrobial agent. 44 Targeted drug delivery and drug delivery to the brain are limited due to their complicated methods and structural behavior. Thus, to achieve this goal, magnetic coreshells have been suggested as important nanocarriers. 45,46 Although nanouids based on non-magnetic NPs are widely studied, to date, few studies investigating the thermal conductivity of magnetic core-shell NPs for heat transfer applications have been performed. [47][48][49] To the best of our knowledge, the electrical and thermal conductivities of superparamagnetic Fe 3 O 4 @C core-shell NPs have rarely been reported. Therefore, herein, we synthesized Fe 3 O 4 NPs using a chemical coprecipitation method followed by the hydrothermal synthesis technique, which led to the formation of Fe 3 O 4 @C core-shell NPs. Furthermore, these NPs were characterized using various techniques and their electrical and thermal conductivities were measured. The super-paramagnetic Fe 3 O 4 @C core-shell NPs exhibited good thermal and electrical properties, and thus can be exploited for heat transfer applications, such as cooling of electronic devices, fuel cells, and solar cells. 50

Materials and methods
Ferrous sulphate heptahydrate (FeSO 4 $7H 2 O), ferric chloride hexahydrate (FeCl 3 $6H 2 O) and sodium hydroxide (NaOH) were purchased from Sigma Aldrich. Absolute alcohol and hydrochloric (HCl) acid were procured from Chem-Lab (Belgium) and Scharlau (Spain), respectively. All chemicals were of research grade and used without further purication. Similarly, fructose of analytical grade was purchased from Gem-Chem (India) and used as received. Deionized (DI) water obtained from an ultrapure water unit (Puris-Expe water system) was used during the synthesis of the Fe 3 O 4 NPs.

Synthesis of Fe 3 O 4 NPs
Fe 3 O 4 NPs were synthesized via a chemical co-precipitation method. In a typical co-precipitation method, 0.32 mol of ferrous sulphate heptahydrate (FeSO 4 $7H 2 O) and 0.64 mol of ferric chloride were dissolved in 100 mL DI water separately. The Fe 2+ /Fe 3+ ions were mixed properly before dispersing them in an alkali solution. The ion mixture was then transferred to a 100 mL burette. In a 250 mL round-bottom ask, 1.5 M NaOH solution was prepared and the volume was made up to 100 mL. The iron salt ions were then added dropwise to the above alkali solution under vigorous stirring. The pH of the solution was maintained at around 11-12 during the reaction. An additional amount of NaOH solution could be added to the reaction vessel if needed. As soon as the iron salts were added to the alkali solution, precipitation of the salts started, resulting in the formation of a black-colored co-precipitate. The precipitate was then stirred for 30 min at room temperature. Subsequently, the solution was allowed to settle for 30 min and with the help of a strong magnet, the precipitate was separated from the unreacted solution. Finally, the obtained precipitate was washed several times with distilled water. Similarly, by tuning the pouring of aqueous solution of iron salt (drops) into the aqueous solution of alkali and stirring rate, Fe 3 O 4 NPs with three different sizes were obtained including 5 nm, 12 nm and 25 nm.

Synthesis of Fe 3 O 4 @C core-shell NPs
The as-synthesized Fe 3 O 4 NPs of different sizes were dispersed separately in a 5 M aqueous solution of glucose and kept in a tight capped 500 mL bottle, which was half-lled with the solution. To coat a carbon shell over the Fe 3 O 4 NPs, the sample solution was shaken properly and then le in an autoclave for 4-5 h at high pressure and 180 C. The carbonization of glucose occurred at 180 C during the hydrothermal treatment. Aer this reaction, the system was allowed to cool to room temperature. A dark black-colored solution smelling like sugarcane vinegar was obtained, which was decanted with the help of a strong magnet. Subsequently, the sample was washed with distilled water several times. Finally, the black-colored precipitate was collected and dried at 80 C for 4-5 h in an oven. 18,23 Consequently, Fe 3 O 4 @C core-shell NPs with different sizes including 7 nm, 14 nm and 28 nm were obtained using this technique.

Preparation of ferrouids
We introduced ne powders of Fe 3 O 4 and Fe 3 O 4 @C core-shell NPs into DI water in separate beakers. Given that the NPs were highly magnetic in nature, the mixtures were sonicated for 3-4 hours for better dispersion of the NPs. Eventually, we obtained a highly monodispersed NP solution. The prepared ferrouids were found to be stable without any external applied magnetic eld for a long time. Before their application in a heat exchanger, the ferrouids were sonicated again for better heat transfer results. Different concentrations of ferrouids were prepared in a similar way for heat transfer and electrical conductivity measurements.

Characterization
The phase and crystallinity of the as-synthesized Fe 3 O 4 and Fe 3 O 4 @C powder samples were identied by XRD (D8 AaS Advance X-ray diffractometer using Cu Ka radiation, l ¼ 1.54156 A). Raman analyses were conducted using a Raman spectrometer (Aramis LabRam spectrometer). The microstructure analyses of the as-synthesized powders were carried out using a transmission electron microscope (TEM) (JEOL, JEM2100F) operated at 200 kV. X-ray photoelectron spectroscopy (XPS) was performed for elemental information using an Xray photoelectron spectrometer (Thermo Fisher, USA). Moreover, the functional groups were identied using FT-IR (ATR-FT-IR Nicolet iS 10). The magnetic properties of the as-synthesized powders were analyzed using an ADE 3473-70 Technologies vibrating sample magnetometer (VSM) in the range of À10 kOe to 10 kOe with a magnetization error of AE1%. The zeta potential values of the prepared ferrouids were obtained using a Zetasizer (Nano-ZS; Malvern, UK) operated at room temperature. The electrical conductivities of the ferrouids were measured using an HI 2300 NaCl/TDS/EC meter (HANNA Instruments). For the measurement of the thermal conductivity of the ferro-uids with different concentrations, a WL-373 (GUNT Hamburg, Germany) instrument was used. This unit is particularly suited for the determination of the coefficients of thermal conduction of liquids and gaseous materials. The unit was comprised of a double-walled cylinder with an integrated heater acting as the heat source, and the surrounding cylinder as the heat sink. There was a narrow slot in the unit, which was sufficient to prevent heat by convection, and therefore the heat of transfer in the slot is due to the thermal conduction. Due to the constant width of the slot, thermal conduction occurs in a plane wall. The heat transferred, Q, can be calculated using Fourier's law as follows: where Q a ¼ heat transfer, l ¼ thermal conductivity coefficient, DT ¼ temperature gradient, A ¼ surface area and d ¼ thickness of the slot.  indicating the presence of interstitial water molecules. 18,23,52 The Raman spectrum of the Fe 3 O 4 @C powder sample is shown in Fig. 1e, where the intense D band and G band were observed at around 1352 and 1598 cm À1 , respectively. The D band can be attributed to sp 2 carbon, which indicates a disordered graphitic structure and the G band can be attributed to sp 3 Fig. 2a and b show the low-magnication TEM images of the as-synthesized Fe 3 O 4 and Fe 3 O 4 @C powder samples, and their corresponding size distribution histograms are shown in Fig. 2c and d, respectively. It was observed that the as-synthesized powder samples were comprised of NPs, which were monodispersed on the TEM Cu grid. The average particle size of the Fe 3 O 4 NPs and Fe 3 O 4 @C NPs were found to be around 5 nm and 7 nm, respectively. Similarly, the TEM images of two different sized Fe 3 O 4 NPs (12 nm and 25 nm) and Fe 3 O 4 @C core-shell NPs (14 nm and 28 nm) together with their corresponding size distribution histograms are shown in Fig. S1 (ESI †). Fig. 3a and b show the high-magnication TEM and HRTEM images of the Fe 3 O 4 NPs, respectively. As shown in Fig. 3b, three different types of planes were identied with the d spacings of 0.29, 0.26 and 0.21 nm, which correspond to the (220), (311) and (400) planes of cubic Fe 3 O 4 . 53 The HRTEM results also conrmed the crystalline nature of the as-synthesized Fe 3 O 4 NPs and suggest that they did not transform into another stable form of iron oxide. Similarly, Fig. 3c and d show the high-magnication TEM and HRTEM images of the carbon-encapsulated Fe 3 O 4 (Fe 3 O 4 @C) NPs, respectively. The carbon-shell coating over the Fe 3 O 4 NPs was found to be amorphous in nature, and the thickness of the carbon shell over a random Fe 3 O 4 core NP was found to be approximately in the range of 0.8-1.2 nm. Fig. 4a shows the XPS survey scans of the bare Fe 3 O 4 NPs (red color) and Fe 3 O 4 @C core-shell NPs (black color). Three significant peaks corresponding to the Fe 2p, O 1s and C 1s core levels were obtained for the carbon-coated Fe 3 O 4 NPs, which conrmed the composition of the Fe 3 O 4 @C core-shell NPs, whereas the C 1s core level peak was missing for the bare Fe 3 O 4 NPs. Fig. 4b shows the high-resolution spectrum of Fe 2p core level, i.e., Fe 2p 3/2 and Fe 2p 1/2 , which correspond to the binding energies 710.5 eV and 724.1 eV, respectively. No peak was observed at 719 eV, which corresponds to a-Fe 2 O 3 , indicating that no phase transformation occurred. 53 Fe exists in two states, i.e., Fe 2+ and Fe 3+ , in Fe 3 O 4 . The peak at 710.3 eV (pink) is attributed to the Fe 2+ state in Fe 2p 3/2 . The peak observed at 712.7 eV (purple) corresponds to the Fe 3+ state in Fe 2p 3/2 . Similarly, for Fe 2p 1/2 , a peak appeared at 725.7 eV (blue), which correlates to Fe 3+ , and another peak appeared at 723.7 eV (cyan), corresponding to Fe 2+ . The HR O 1s core level spectrum is shown Fig. 4c. The peaks at 531.7 eV (green) and 529.9 eV (wine) are attributed to the Fe-O bond in the Fe 3 O 4 NPs. The other peak observed at 533.1 eV (blue) corresponds to the O-H bond. The HR C 1s core level spectrum is shown in Fig. 4d. The peaks at 28.63 eV (blue) and 285.2 eV (green) correspond to the C-C sp 3 and C]C sp 2 carbon, respectively. The small peaks observed at 287.5 eV (purple) and 289.1 eV (pink) are attributed to C-O and C]O, respectively, which may originate from airborne organic contaminants. Moreover, it was also conrmed that no reaction between the Fe 3 O 4 NPs and carbon coating occurred. Fig. 5 shows the magnetic characterization of the small average-sized Fe 3 O 4 NPs (ca. 5 nm) and Fe 3 O 4 @C core-shell NPs (ca. 7 nm) with respect to different magnetic elds at 300 K. An unusual behavior in magnetic properties was observed in NPs compared to their bulk counterpart. The magnetization was observed to be 60 emu g À1 for Fe 3 O 4 NPs (ca. 5 nm), and it was obvious that there was no coercivity and remanence. Hence, the as-synthesized Fe 3 O 4 NPs (ca. 5 nm) were found to be superparamagnetic in nature. 24 Similarly, the as-synthesized Fe 3 O 4 @C core-shell NPs (ca. 7 nm) also exhibited superparamagnetic behavior, and the magnetization was found to be 30 emu g À1 with no coercivity and remanence. The saturation magnetization was found to be much lower in the case of the core-shell NPs. The low value of the magnetic saturation may be attributed to the carbon coating over the Fe 3 O 4 NPs as carbon materials are diamagnetic in nature. 54 A low coercive eld was also observed in the case of both NPs which indicate their spherical shape. 55 The stabilities of the prepared ferrouids were evaluated in terms of zeta potential and the results are shown in Table 1 and Fig. 6. The zeta potentials were measured  for the different sized Fe 3 O 4 and Fe 3 O 4 @C NP-based ferrouids at 0.7 vol% of NPs. The results suggest coagulation/ agglomeration behavior for the Fe 3 O 4 NP-based ferrouids (zeta potential <AE5), leading to the formation of networks, whereas the Fe 3 O 4 @C NP-based ferrouids showed moderate stability (AE10 < zeta potential < AE30). 56,57 An increase in the stability of NPs or their good dispersibility in the base uid is generally observed for core-shell NPs. 58,59 The electrical conductivities (ECs) of the as-synthesized Fe 3 O 4 NPs (ca. 5 nm) and Fe 3 O 4 @C core-shell NP (ca. 7 nm)based ferrouids with different concentrations and temperature were measured. The EC of the ferrouid was found to increase with an increase in the concentration of both types of NPs, as shown in Fig. 7a and b. Fig. 7a shows the ECs of distilled water (base uid) and the ferrouids with different concentrations of Fe 3 O 4 @C core-shell NPs at various temperatures. The EC of the ferrouids was found to be many times higher than that of the base uid. Similarly, Fig. 7b shows the ECs of Fe 3 O 4 NP-based ferrouids, which followed the same trend as observed in Fig. 7a for the Fe 3 O 4 @C core-shell NP-based fer-rouids. However, the ECs of the bare Fe 3 O 4 NP-based ferro-uids were found to be higher than the core-shell NP-based ferrouids. This may be attributed to the amorphous nature of the carbon coating, which resulted in a decrease in the EC. Fig. 7c shows a comparison of the ECs of the Fe 3 O 4 and Fe 3 O 4 @C core-shell NP-based ferrouids at 50 C. It was quite obvious that the Fe 3 O 4 NP-based ferrouid at a particular concentration of Fe 3 O 4 NPs exhibited a higher EC compared to the core-shell NP-based ferrouid. Fig. 7d demonstrates the percentage enhancement in the EC compared to that of the base uid. It was found that the Fe 3 O 4 NP-based ferrouid exhibited the highest value of EC, i.e., 205 mS cm À1 for 0.7 vol% of NPs at 50 C. Conversely, the EC value of 130 mS cm À1 was recorded for the Fe 3 O 4 @C core-shell NP-based ferrouid at the same concentration and temperature. The percentage enhancement was calculated using the following equation:

Results and discussion
where s 0 ¼ EC of DIW and s ¼ EC of the ferrouid. The maximum enhancement in the EC of the Fe 3 O 4 NP-and Fe 3 O 4 @C core-shell NP-based ferrouids was obtained as $3222% and $2015%, respectively, for 0.7 vol% of NPs at 50 C. There are many factors that affect the EC of a nanouid or  a ferrouid such as volume fraction, temperature, structure of NPs, types of NPs, and types of uids. 60 The EC of a nanouid/ ferrouid generally increases with an increase in the volume fraction of the nanouid/ferrouid and with temperature. The ions on the surface of the colloidal NPs are attracted to the oppositely charged ions, which results in the formation of a layer. Another layer of ions is also formed, where the ions from the suspension become attached to the rst layer by Coulomb force, which electrically screens the rst layer. The ions in the second layer are loosely associated and move due to the electric force of attraction and thermal motion. Hence, as the temperature increases, the free ions move rapidly into the suspension of the ferrouid, which results in a high EC. An increase in the concentration of NPs also enhanced the EC as more solid NPs suspended into the uid were available to expose their surfaces toward the ions and formed an electrical double layer. However, a relatively low EC in the case of the Similarly, the thermal conductivities of the Fe 3 O 4 NP-and Fe 3 O 4 @C core-shell NP-based ferrouids were measured. Fig. 8a and b show the graphs of the coefficient of thermal conductivity versus temperature gradient for the Fe 3 O 4 @C coreshell NP (7 nm)-and Fe 3 O 4 NP (5 nm)-based ferrouids, respectively. For both types of NPs, with concentrations in the range of 0.1 vol% to 0.7 vol%, it was observed that the coefficient of thermal conductivity (l) increased consistently. The average thermal conductivity coefficients for water was found to be 0.71 W m À1 K À1 , and for the ferrouids at different concentrations of Fe 3 O 4 @C core-shell NPs, i.e., 0.1, 0.2, 0.3, 0.4, 0.5, 0.6 and 0.7 vol% they were found to be 0.82, 0.90, 0.99, 1.19, 1.22, 1.46 and 1.54 W m À1 K À1 , respectively, as shown in Fig. 8a. A similar trend was observed for the Fe 3 O 4 NP-based ferrouids, and the values of the coefficient of thermal conductivity for various concentrations, i.e., 0.1, 0.2, 0.3, 0.4, 0.5, 0.6 and 0.7 vol% were obtained as 0.84, 0.92, 1.02, 1.16, 1.21, 1.48 and 1.80 W m À1 K À1 , respectively, as shown in Fig. 8b. The comparison of thermal conductivities and percentage enhancement of Fe 3 O 4 NP-and Fe 3 O 4 @C core-shell NP-based ferrouids are shown in Fig. 8c and d, respectively. Fig. 8d depicts the increase in percentage enhancement with respect to DI water from 16% to 116% as the concentration of Fe 3 O 4 @C core-shell NPs varied from 0.1 vol% to 0.7 vol%. Similarly, a 17% to 153% enhancement with respect to DI water was The maximum enhancement was observed for 0.7 vol% of Fe 3 O 4 NPs. This may be attributed to the clustering effect of the NPs as their surface energies were quite high owing to their high surface to volume ratio and the formation of a chain-like network of small-sized NPs, which increased the effective volume fraction of heat conductive phases in the ferrouid.
Moreover, the dispersed NPs in the water-based ferrouid executed Brownian motion, which led to collisions between the NPs and with the molecules of the water. 61,62 Conversely, in the case of the Fe 3 O 4 @C core-shell NPs, the thermal capacity of the carbon coating and percolation pathways for heat conduction were responsible for the thermal conductivity enhancement. 61,62 It should be noted that at only 0.7 vol%, the thermal conductivity of the Fe 3 O 4 @C core-shell NP-based ferrouid was  signicantly less than that of the Fe 3 O 4 NP-based ferrouid. Moreover, the effects of different NPs sizes on the enhancement of the electrical and thermal conductivities were also studied, as shown in Fig. 9a and b (Fig. S2 and S3, ESI †), respectively. Fig. 9a shows the variation in the electrical conductivity enhancement of the Fe 3 O 4 NP-and Fe 3 O 4 @C NP-based ferro-uids with NP size. The EC was found to be enhanced with a decrease in the size of the NPs for both types of ferrouids. The increase in EC with a decrease in the NP size is attributed to the increase in surface area and electrophoretic mobility of the NPs. 63,64 A similar trend was observed for the thermal conductivity enhancement, which increased with a decrease in NP size for both types of ferrouids, as shown in Fig. 9b. The exceptional enhancement in the thermal conductivity especially in the case of the bare Fe 3 O 4 NP (5 nm)-based ferrouid compared to the larger-size Fe 3 O 4 NP (12 nm and 25 nm)-based ferrouids is due to the more pronounced effect of chain-like network formation/clustering of the NPs, as inferred from the zeta potential values (Table 1 and Fig. 6). However, owing to the carbon coating over the bare Fe 3 O 4 NPs, relatively better dispersion and less agglomeration of the different sized Fe 3 O 4 @C NPs (as inferred from their more negative zeta potential values, Table 1 and Fig. 6) in the base uid (water) resulted in a lower enhancement in thermal conductivity for the Fe 3 O 4 @C NP-based ferrouids compared to the Fe 3 O 4 NP-based ferrouids.
To theoretically validate the obtained results, the experimental values of the thermal conductivities of the Fe 3 O 4 NP (ca. 5 nm)-and Fe 3 O 4 @C NP (ca. 7 nm)-based ferrouids were tted with the existing Maxwell model, 65 as shown in Fig. 10. Based on the effective medium theory, the effective thermal conductivity of the Fe 3 O 4 NPs coated with carbon was calculated using the following equation: 66 where k ep is the equivalent thermal conductivity of the Fe 3 O 4 @C NPs, k p is the thermal conductivity of the Fe 3 O 4 NPs, g is the ratio of coated nanolayer thermal conductivity to the particle thermal conductivity, and b is the ratio of coated layer thickness to that of the particle radius. The thermal conductivity of the ferrouids based on Fe 3 O 4 NPs and Fe 3 O 4 @C NPs was calculated using the Maxwell equation as follows: where k ff , k bf and k np are thermal conductivities of the ferro-uid, base uid and NP (k ep was used instead of k np in the case of the carbon-coated Fe 3 O 4 NPs), respectively, and ⌀ np is the concentration of NPs (vol%) in the base uid. It can be seen in Fig. 10 that the values predicted by the Maxwell model are higher at low concentrations for the Fe 3 O 4 NP (ca. 5 nm)-based ferrouids. In contrast, for the Fe 3 O 4 @C (ca. 7 nm) NP-based ferrouid, the predicted values of thermal conductivity closely t the experimental data. The slight deviation in the thermal conductivity values of the Fe 3 O 4 NP-based ferrouids is attributed to the clustering or aggregation of the NPs, as inferred from the zeta potential values (Table 1 and Fig. 6). 67 Therefore, the Maxwell model validated the experimental results for the Fe 3 O 4 @C NP-based ferrouid. These obtained results were compared with the results reported in the literature, as presented in Table 2.

Conclusion
In conclusion,

Conflicts of interest
The authors declare no competing nancial interest.