Experimental investigation of the effect of an external magnetic field on the thermal conductivity and viscosity of Fe_{3}O_{4}–glycerol
Abstract
Thermophysical properties, such as thermal conductivity and viscosity, of magnetic nanofluids (MNFs) can be enhanced by applying external magnetic fields. Such property enhancement can be beneficial for having a non-contact control of heat transfer rates in many applications such as cooling of electronic devices, heating mediator for targeted cancer treatment, drug delivery, and heat transfer medium in energy conversion systems. In this study, a detailed experimental investigation has been carried out to measure the thermal conductivity and viscosity of a magnetic nanofluid under the influence of a uniform external magnetic field. The MNF (i.e., glycerol–Fe_{3}O_{4}) is prepared by dispersing Fe_{3}O_{4} magnetic nanoparticles in glycerol at different volume fractions of nanoparticles (i.e., φ = 0.5, 1.0, 1.5, 2.0, and 3.0%). The experimental results showed that the viscosity linearly increased with the increase in volume fractions while significantly decreased with the increase in temperature. With respect to the viscosity measurement, the maximum ratio revealed a value of 7.2 for 3.0% volume fraction and 50 °C subjected to 543 [G] magnetic field. Also, a 16.9% thermal conductivity enhancement was achieved when φ = 3.0% at 40 °C under 543 [G] magnetic field. Using the experimental results, a nonlinear model was developed as a function of temperature (T), magnetic field (B), and volume fractions of nanoparticles (φ) to predict the thermal conductivity of glycerol–Fe_{3}O_{4}. The proposed model provided satisfactory performance with an R^{2} value of 0.961, MSE value of 0.00015, and MAE value of 0.00932.
Keywords
Fe_{3}O_{4} nanoparticle Glycerol Magnetic nanofluid Thermal conductivity enhancement Symbolic regressionList of symbols
- B
Magnetic field (G)
- CTAB
Hexadecyltrimethylammonium bromide
- d
Characteristic size of the nanoparticle (nm)
- EG
Ethylene glycol
- ICDD
International Centre for Diffraction Data
- JCPDS
Joint Committee on Powder Diffraction Standards
- k
Thermal conductivity (W m^{−1} K)
- k_{b}
Boltzmann’s constant = 1.38066 × 10^{−23} J K^{−1}
- MAE
Mean absolute error
- MNF
Magnetic nanofluid
- MSE
Mean square error
- PGA
Poly-glutamic acid
- Pr
Prandtl number
- RMSE
Root-mean-square error
- Re
Reynolds number
- SDS
Sodium dodecyl sulfate
- T
Temperature (°C)
Greek symbols
- ρ
Density (g mL^{−1})
- φ
Volume fraction of nanoparticles (%)
- μ
Dynamic viscosity (mPa s)
- ψ
Sphericity of nanoparticles
Subscripts
- eff
Effective
- f
Fluid
- s
Solid
- nf
Nanofluid
Introduction
The effective heat removal in heating/cooling system and thermal management of mechanical/electrical components are key factors of an optimum operation and durability of such systems. To reach this aim, different types of heat transfer fluids (HTF) such as oil, water, and air have been implemented as the working fluid in systems such as heat exchangers [1, 2, 3]. From an economic point of view, it is critical to design highly compact and effective heat exchangers. However, this fact is restricted by the low thermal conductivity of HTFs. To address this issue, various methods such as the implementation of highly conductive metal fins, porous medium, and nanoparticles have been proposed. Recently, nanotechnology, particularly employment of nanofluids, has attracted a great deal of attention of researchers to develop efficient HTFs that can be used as working fluids in many applications especially in heat exchangers for heating and cooling purposes [4]. For instance, nanofluids, being efficient HTFs, are commonly used in condensers and evaporators for heating/cooling purposes to enhance the thermal performance of such systems [5].
Moreover, a combination of a nanofluid and inserts as a passive technique for enhancing the performance of energy conversion systems has been used by many researchers [6].
Additionally, nanofluids have shown considerable potential for other applications including cutting fluids in machining processes, biomedical devices, electronic cooling systems, and oil recovery enhancement [7, 8, 9, 10, 11, 12]. Nanofluids, which were firstly coined by Choi [13], can be produced by dispersing highly conductive nanoparticles such as CuO, ZnO, Al_{2}O_{3}, TiO_{2} (i.e., size of 1–100 nm) into the base fluids including water, oil, kerosene, and glycerol which can lead to an improvement in the thermal conductivity of such fluids. In addition to the thermal conductivity, other thermophysical properties of base fluids such as viscosity (μ) and density (ρ) would be varied by dispersion of nanoparticles at different volume/mass fractions [14]. Moreover, the performance of nanofluids depends on the size of the nanoparticles and their stability, which is their ability to stay suspended. Although having all suitable features of using nanoparticles makes them a proper solution for enhancing the thermal conductivity of a base fluid, several drawbacks remain such as aggregation, sedimentation, and clogging in microchannels which may restrict the potential of using high volume/mass fraction of nanoparticles [15]. Magnetic nanofluid (MNF) is a special type of nanofluid in which the thermophysical properties (e.g., thermal conductivity, viscosity) can be varied in a non-contact way by applying an external magnetic field. MNFs can be produced by dispersing magnetic nanoparticles including but not limited to CO, Fe_{2}O_{3}, and Fe_{3}O_{4} into base fluids such as water, ethylene glycol, kerosene, glycerine, and thermal oils. In MNFs, the application of a magnetic field causes the nanoparticles to aggregate in the carrier fluid, creating highly conductive paths for the heat flow inside the convective heat transfer environment. Therefore, the thermal conductivity and viscosity of MNFs can be tuned by varying the intensity of magnetic field. Such unique behaviors of MNFs in the presence of a magnetic field make it possible to induce and control the heat transfer process as well as fluid flow. A review on the thermophysical properties, heat transfer characteristics, and the practical applications of MNFs is available in Bahiraei and Hangi’s review article [16]. Recently, MNFs have been under considerable investigation for their medical and biological applications. For instance, the ease with which the properties of MNFs can be controlled and their compatibility with human biology provide them with the potential to be used in drug delivery and in hyperthermia method of cancer treatment. A comprehensive review regarding the use of MNFs in hyperthermia applications can be found in [17]. Bio-magnetic fluids are suitable for biomedical applications, since their flow and properties can be tuned using an external magnetic field. Magnetohydrodynamics, which refers to the flow of magnetic nanofluid in presence of magnetic field, is governed by the Navier–Stokes and Maxwell’s equations that can characterize the fluid flow and magnetic field. A review on the mathematical simulation of magnetohydrodynamics is provided in [18].
Summary of experimental studies on glycerol- and EG-based magnetic nanofluids
Author | Nanoparticle | Volume fraction/concentration | Base fluid | Remarks |
---|---|---|---|---|
Abareshi et al. [40] | α-Fe_{2}O_{3} | 0.125–0.75% | Glycerol | Studied rheological properties of nanofluids Viscosity increased by a factor of 1.3 by increasing φ at 40 °C Linear relation between shear stress and shear rate |
Tshimanga et al. [41] | MgO | 0.5–4.0% | Glycerol | Thermal conductivity enhanced by 19% using MgO-glycerol New correlations developed to predict thermal conductivity (R^{2} = 0.99) |
Hemmat Esfe et al. [42] | MgO | 0.25–5.0% | EG | Provided a correlation using ANN successful to predict k_{nf} Maximum improvement ratio was 1.48 at T = 55 °C and d_{p} = 20 nm |
Tsai et al. [43] | Fe_{3}O_{4} | 1.0–2.24% | EG–glycerol | Experimentally showed that k_{cond.} = k_{Maxwell} Brownian motion is a factor to improve thermal conductivity The highest enhancement ratio was observed at 1.08 using φ = 2.0% Fe_{3}O_{4} |
Atashrouz et al. [44] | Fe_{3}O_{4} | 0.0022–0.0055% | Glycol–water | The reason of increase in viscosity is formation of aggregates Proposed two models with less than 5% MARD |
Sundar et al. [45] | Fe_{3}O_{4} | 0–1.0% | EG–water Oleic acid surfactant | 60:40% EG/W + Fe_{3}O_{4} was 2.94 times more viscous than base fluid The effect of surfactant and pH was not studied |
Ishiki et al. [46] | Nanomag-D | N/A | Glycerol and serum | Increasing the glycerol concentration from 0 to 60% increased the viscosity by a factor of 10 Brownian motion, aggregation, and hysteresis played key role in magnetic nanofluids |
Xu et al. [47] | Fe_{3}O_{4} | 2–22 mg | Glycerol | Magnetic solid phase extraction of proteins via Fe_{3}O_{4}NH_{2}GO-DES |
Wan et al. [48] | Fe_{3}O_{4} | 0.28 g | Glycerol | Stable MNF (coated iron oxide particles with PGA or PGMA) was seen in 10% NaCl, 10%CaCl_{2}, or pH range of 2–14 Organic surfactant was added to increase the stability |
Pastoriza-Gallego et al. [49] | α-Fe_{2}O_{3} | Mass fraction up to 25% | EG | Enhanced k_{nf} is temperature independent Enhanced k by 16.8 and 13.4% For Fe_{2}O_{3} and Fe_{3}O_{4}, respectively |
Sonawane and Juwar [50] | Fe_{3}O_{4} | 0.2, 0.5, and 0.8% | EG | Optimized conditions for φ, sonication time, and temperature in MNF Maximum thermal conductivity was measured at 0.694 Wm^{−1} C^{−1} |
Harandi et al. [51] | Fe_{3}O_{4} | 0.1–2.3% | EG | Maximum thermal conductivity ratio was 30% at 50 °C when φ = 2.3% Nonlinear correlation for thermal conductivity with R^{2} = 0.9904 |
Afrand et al. [52] | Fe_{3}O_{4}–Ag | 0.0375–1.2% | EG | Rheological behavior of MNF was examined for range 25–50 °C Non-Newtonian behavior for high values of φ |
Most recently, there has been a notable effort to measure the viscosity of nanofluids, particularly those using glycerol or EG as a base fluid. In much of the relevant literature, many precise correlations and models were proposed to predict the behaviors of MNFs, namely thermal conductivity and dynamic viscosity [53, 54, 55, 56]. To the best of the authors’ knowledge, there has been no experimental investigation on the effect of magnetic field on the thermal conductivity and viscosity of pure glycerol and Fe_{3}O_{4} without surfactant. Pure glycerol is chosen as the base fluid due to its high viscosity which enables the prepared MNF to carry higher volume fractions of nanoparticles without sedimentation. Additionally, in some applications it is necessary to have liquid with low freezing point or higher boiling temperature than water. Thus, the motivation behind this study is to experimentally investigate the effect of magnetic field with various intensities on MNF and establish the thermal conductivity model as a function of volume fraction of nanoparticles (φ), and magnetic field (B) for viscous magnetic nanofluids.
The rest of the paper is organized as follows: Sect. 2 presents the characterization and preparation of magnetic nanofluid. Sections 3 and 4 provide the detailed information on thermal conductivity and viscosity measurements, respectively. Section 5 comprises the results and discussion. Finally, Sect. 6 concludes the paper.
Characterization and preparation of magnetic nanofluid
Preparing homogeneous nanofluid with a long-term stability is a crucial factor for thermal conductivity enhancement. As stated previously, stable nanofluids can be obtained by adding surfactants to base fluids; however, this method has some drawbacks such as undesired increase in viscosity. Since glycerol as a base fluid is highly viscous, the long-term stability and minimum sedimentation can be achieved. In addition, due to the high resistance between layers of glycerol, it can carry higher volume fractions of nanoparticles. In this study, the sonication method was used to disperse the nanosized particles within the glycerol. Magnetic nanofluids (glycerol + Fe_{3}O_{4}) with different volume fractions of nanoparticles (0.5–3%) were prepared in a 50-mL beaker in a room temperature (20–25 °C) without any surfactant. Then the nanofluids were ultrasonicated with a sonicator operated at 40 kHz and 500 W for 1 h to ensure uniform dispersion of nanoparticles within the base fluid.
Thermal conductivity measurement
Viscosity measurement
Range and accuracy of different measuring devices
Device | Measurement range | Resolution/uncertainty |
---|---|---|
Bell 5170 | 1 G–20 kG | ± 1 G from 1 G–20 kG |
SV-10 vibro | 0.3 mPa s–10 Pa s | ±1% of repeatability |
KD2 Pro | 0.1–4.0 (W m^{−1} K) | ± 0.02 W m^{−1} K from 0.1 to 0.2 (W m^{−1} K) ± 5% from 0.2 to 4.0 (W m^{−1} K) |
Results and discussions
The effects of temperature and magnetic field on the viscosity and thermal conductivity of glycerol–Fe_{3}O_{4} are studied, and results followed by discussions are provided in this section.
Viscosity analysis
The nanofluid’s viscosity was first measured under no magnetic field, since in highly viscous fluids such as glycerol, the viscosity can vary significantly with temperature. The accuracy of these results was then verified and validated against the following classical models:
Thermal conductivity analysis
Thermal conductivities of magnetic nanofluid (glycerol + Fe_{3}O_{4}) for five different volume fractions of nanoparticles (0.5, 1.0, 1.5, 2.0, and 3.0%) were measured experimentally. Since the thermal conductivity depends strongly on temperature, the samples were kept at a fixed temperature of approximately 300 K during the measurements. The results obtained without the application of a magnetic field were compared to the following classical models:
Summary of measured and calculated thermal conductivity using classical models
Model | 0.5% | 1.0% | 1.5% | 2.0% | 3.0% | MAE | RMSE |
---|---|---|---|---|---|---|---|
Maxwell–Gannet | 0.286152 | 0.287308 | 0.288466 | 0.289628 | 0.291962 | 0.003741 | 0.000039 |
Bruggeman | 0.286153 | 0.287311 | 0.288474 | 0.289641 | 0.291991 | 0.003746 | 0.000039 |
Hamilton–Crosser | 0.286152 | 0.287308 | 0.288466 | 0.289628 | 0.291962 | 0.003741 | 0.000039 |
Rayleigh | 0.285184 | 0.285369 | 0.285553 | 0.285736 | 0.286102 | 0.013244 | 0.000319 |
Jeffery | 0.289277 | 0.293558 | 0.297843 | 0.302133 | 0.310725 | 0.006703 | 0.000050 |
Lu–Lin | 0.288001 | 0.291007 | 0.294017 | 0.297030 | 0.303069 | 0.003645 | 0.000014 |
Experimental | 0.2850 | 0.2882 | 0.2891 | 0.2920 | 0.3055 | – | – |
Proposed correlation for thermal conductivity
Coefficient and accuracy of the proposed model for thermal conductivity
Coefficients | R^{2} (training) | R^{2} (test) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
a _{1} | a _{2} | a _{3} | a _{4} | a _{5} | a _{6} | a _{7} | a _{8} | a _{9} | a _{10} | a _{11} | 0.974 | 0.961 |
12.83 | − 4.588 | 0.06 | 2.338 | − 0.591 | − 2.69 | 1.31 | 6.9e−5 | − 6.8e−6 | − 1.27e−7 | 0.285 |
Performance analysis of the proposed correlation using MAE, MSE, and RMSE
MAE | MSE | RMSE | |||
---|---|---|---|---|---|
Training | Test | Training | Test | Training | Test |
0.00221 | 0.00932 | 8.14e−06 | 0.00015 | 0.00285 | 0.01261 |
Comparison between the proposed model for thermal conductivity and Corcione [70] under no magnetic field at different temperatures
Temp./°C | \(\varphi\) = 1% | \(\varphi\) = 2% | \(\varphi\) = 3% | |||
---|---|---|---|---|---|---|
Proposed model | Corcione [70] | Proposed model | Corcione [70] | Proposed model | Corcione [70] | |
20 | 0.2891688536 | 0.2850001131 | 0.2931524453 | 0.2850001786 | 0.2998622615 | 0.2850002335 |
30 | 0.2991877587 | 0.2890000650 | 0.3072143987 | 0.2890001026 | 0.3207341776 | 0.2890001342 |
40 | 0.3154463438 | 0.2980000299 | 0.3275160321 | 0.2980000475 | 0.3478457738 | 0.2980000618 |
As can be seen in Table 6, both models provided satisfactory results and showed that thermal conductivity is an increasing function of both temperature and volume fraction of nanoparticles. Thus, it can be concluded that the proposed model in this study is a robust and accurate model for thermal conductivity since it includes the magnetic field term alongside temperature and volume fraction of nanoparticles.
Conclusions
In this work, the characterization and preparation of glycerol–Fe_{3}O_{4} was carried out. The viscosity and thermal conductivity were experimentally investigated for five different volume fractions of nanoparticles (0.5, 1.0, 1.5, 2, and 3%) at different temperatures (20–55 °C) under uniform magnetic fields. The results showed that applying magnetic field significantly increased the viscosity and thermal conductivity of MNFs. Also, it was found that the effect of magnetic field was more pronounced on MNFs with high volume fractions of nanoparticles. With respect to the thermal conductivity enhancement, the maximum improvement of 16.9% was observed at 3.0% volume fraction and 40 °C. With respect to the viscosity, the maximum ratio revealed a value of 7.2 for 3.0% volume fraction and 50 °C subjected to 543 [G] magnetic field. Based on the experimental results, a new nonlinear correlation was developed using genetic programming to predict the thermal conductivity of glycerol–Fe_{3}O_{4} as a function of temperature (T), magnetic field intensity (B), and volume fraction of nanoparticles (φ).
Notes
Acknowledgements
The authors would like to thank Dr. Ashutosh Singh for providing laboratory apparatuses for the present experimental study. Also, the first author is grateful to Dr. Amirreza Shirani Bidabadi and Peter J. Krupp for their supports and recommendations.
References
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