Experimental investigation of heat transfer performance and frictional loss of functionalized GNP-based water coolant in a closed conduit flow

Abstract

The convective heat transfer coefficient and friction factor for fully developed turbulent flow of trimethylolpropane tris[poly(propylene glycol), amine terminated] ether-treated graphene nanoplatelet (TMP-treated GNP)-based water coolants are experimentally determined at constant velocity flowing through a horizontal copper tube with uniform heat fluxes. The TMP-treated GNP was first analyzed in terms of structure and morphology to confirm the GNP functionalization with TMP. The colloidal stability of TMP-treated GNP-based water coolant shows the high potential of the coolants for using in heat transfer equipment. Then, the experiments were conducted at a Re range of 3900–11 700 at constant velocity flow (1–3 m s⁻¹) and concentrations of 0.025 wt% to 0.1 wt%. The enhancement in thermal conductivity for TMP-treated GNP-based water coolants was between 20% and 31% compared to the basefluid. The convective heat transfer coefficient for the TMP-treated GNP-based water coolant was found to be up to 107% higher than the basefluid. The Nusselt number increased up to 72% at a heat flux of 23 870 W m⁻². However, the friction factor drop increases simultaneously in the range 4–10%. The results suggest that TMP-treated GNP-based water coolants could function well as working fluids in heat transfer applications and provide good alternatives to conventional working fluids.

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1. Introduction

Nanofluids are suspensions obtained from dispersing different nanoparticles in host fluids to enhance thermal properties.^1–3 They have better thermal properties than conventional heat transfer fluids.^4–13 Over the past two decades, nanofluids have exhibited remarkably improved thermal conductivity, stability, and heat transfer coefficients as well as reduced overall plant consumption and costs. Nanofluids have great application potential in several fields. Nanofluids are increasingly utilized in different heat exchangers to optimize energy consumption.^14–16 Among all nanofluids carbon-alotropes based nanofluids have attracted tremendous attention due to its unique thermal, electrical, and mechanical properties,^17–20 which have very high thermal conductivity with 2-D structure for phonon transport and offer an interface contact area with polymer matrix resulting in the improvement of the various properties of the composite. Graphene is an allotrope of carbon atoms which has drawn attention of researchers recently due to its superior properties, such as high elastic modulus, good electrical conductivity, good thermal conductivity, and self-lubricating behaviour. A favourable thermo-physical property of graphene has made it an excellent candidate for use in nanofluids.²¹ Graphene nanoplatelets (GNPs) are used as filler in epoxy resin, natural rubber and other polymer matrix to enhance their thermal, electrical, and mechanical properties. GNPs are the promising candidate material for the application in thermal management.^22–25

It is evident that nanofluids improve thermo-physical properties, such as the thermal diffusivity and the thermal conductivity, provide excellent stability and convective heat transfer coefficients, and only slightly increase the pressure drop and required pumping power.^26–30 Many studies have been conducted to enhance the thermal properties of heat transfer fluids by adding highly thermally conductive nanoparticles.^31–33 Recently, a significant number of studies have been performed on carbon-based nanostructures, including carbon fiber,³⁴ carbon black,^13,35 carbon nanotubes (CNTs),³⁶ graphite, graphene oxide (GO), graphene, and graphene nanoplatelets.^32,37–41 An experimental investigation of the convective heat transfer coefficient for nanofluids flowing through different types of tubes has been conducted in several studies, and these have considered different types of nanoparticles, including oxides, nitrides, metals, diamond, and carbon-based nanoparticles.^42–46 Early experiments with TiO₂, Al₂O₃, ZnO and SiO₂ nanofluids were undertaken by different researchers to determine the effect of the nanofluid concentration on the thermo-physical properties and the heat transfer coefficient.^47–49 They concluded that the influence of the nanofluid concentration on the heat transfer coefficient is significant in the turbulent region versus the laminar region. However, only limited research has been performed on convective heat transfer when using carbon-based nanofluids as the heat transfer liquid compared with many results for the thermo-physical properties of nanofluids.^50–52

In recent years, researchers have gradually shifted their attention to the use of carbon allotrope based nanofluids.^12,53,54 This is largely due to the ability to address the persisting issues on maintaining the long term stability as well as the exploitation of much effective stabilizing mechanism that uses substances highly benign to the environment, low in molecular weight, as well as requiring low amount in comparison to the conventional approaches.⁵⁵ A large number of scientific research papers have been published investigating the effect of stable carbon based colloidal systems in changing the physicochemical properties of the host fluid as well as its role in improving different mode of heat transfer processes.^6,12,56–61 On this note, it is worthy to highlight that a significant rise in thermal conductivity enhancement was reported with the addition of very low particle loading while incurring minimal penalty to the rheological performances.^11,17,26,27 It was also discovered that substances containing phenolic components served as effective carbon allotrope stabilizer which interact via π–π aromatic stacking between benzene ring structures while abundance of oxygen based groups provide the necessary hydrophilic feature to maintain the solubility of carbon allotropes in aqueous solvent.^12,61 Further, in the light of the π–π interaction, several Polycyclic Aromatic Hydrocarbons (PAH) derivatives have also been reported to be used as stabilizer to effectively isolate CNT and other carbon allotropes in aqueous solution although there were concerns on the prolonged health issues to both environment and humans.^62–65 It was also evident that the flourishing increase in the number of publications related to the study of carbon based nanofluid in physical heat transfer processes (i.e. convection, boiling and radiation) was highly attributed to the above resolved solubility issues.⁶⁶

For instance, synthesizing graphene nanoparticles are relatively easy and cost effective. Small variation of properties of graphene has been reported due to different methods used to manufacture one layer or multi-layer graphene such as, exfoliation of graphene oxide layer, deposition with chemical vapour and mechanical cleavage, etc.^39,67–69 Experimental investigation has revealed that the thermal conductivity and heat transfer properties of one layer graphene are higher than carbon nanotubes (CNT). Two-dimensional honey comb lattice graphene with more than 10 layers called graphene nanoplatelets (GNP). Dispersion of graphene with good stability is one of the big issue, which must be solved. So by using functionalization method (acid treat and amino function), proper ultrasonication and by using solvent it could be able to prepare stable dispersed graphene based nanofluids.^15,70–72

Majority of earlier investigation on nanofluid regarding thermophysical properties and heat transfer coefficient was done on single nanoparticles; based on them, graphene based nanofluids provided the best heat transfer coefficient. Synthesis of nanocomposite and preparation of nanofluid based on nanocomposite are very new and interesting topic for researcher.^15,73–75 Suresh et al.⁷⁶ used hybrid nanofluids of Al₂O₃–Cu and investigated the results experimentally. They reported that about 14% enhancement in Nusselt number for laminar flow was achieved in comparison with pure water. Sunder et al.⁷⁶ synthesized MWCNT–Fe₃O₄ nanocomposite and prepared hybrid nanofluid and achieved 31% improvement in Nusselt number at 0.3% volume concentration and at Reynolds number of 22 000. However, the Nusselt number and heat transfer coefficient of a nanofluid also depends on a number of other factors, such as thermal conductivity and specific heat capacity of the base fluid and nanoparticles, the flow pattern, the viscosity of the nanofluid, the concentration of the suspended nanoparticles, the dimensions and the shape of the particles as well as the flow structure.^44,47 Only a limited investigations have been performed on the dependence of the convective heat transfer of carbon-based nanofluids on relevant thermophysical properties.

In the present research, trimethylolpropane tris[poly(propylene glycol), amine terminated] ether-treated graphene nanoplatelets (TMP-treated GNP) was used. The pristine graphene with high surface area of 750 m² g⁻¹ was used to be functionalized with TMP and surface functionalization was confirmed by Fourier transform infrared (FTIR) spectroscopy, Raman spectroscopy, and transmission electron microscopy (TEM). The objective of this work is to improve understanding of the relation of heat transfer and thermophysical properties for TMP-treated GNP coolants. The thermophysical properties including thermal conductivity and viscosity of the TMP-treated GNP were measured at various concentrations (0.25, 0.05, 0.075, and 0.1 wt%). The variation of convective heat transfer coefficient for TMP-treated GNP nanofluids and friction factor are examined under turbulent flow conditions including Nusselt number, pumping power, efficiency of loop and performance index (velocities ranging from 1 to 3 m s⁻¹) through a horizontal copper tube at a constant heat fluxes of 23 870 W m⁻² and 18 565 W m⁻².

2. Material and methods

2.1 Chemical-assisted functionalization

Pristine GNP (average surface area of 750 m² g⁻¹ and purity over 95%) was purchased from XG Sciences Company. All other chemicals were obtained from Sigma-Aldrich. GNP is first covalently functionalized with carboxyl groups. Pristine GNP is sonicated with a mixture of H₂SO₄–HNO₃ acids in volume ratio of 3 : 1 for 12 h at 60 °C and then followed by string for 36 h at same condition to synthesize carboxylated GNP (GNP-COOH). The suspension is centrifuged at 11 000 rpm with DI water to separate completely and the supernatant reach pH around 3–4 simultaneously. The sample is then placed in the oven for 4 days at 50 °C to dry overnight. Then, in a typical experiment, 1 g GNP-COOH and 100 ml trimethylolpropane tris[poly(propylene glycol), amine terminated] ether are sonicated for 10 min and then ZrCl₄ (52.96 mg) was added. Direct amide is formatted from reaction between unactivated carboxylic acids on GNP surface and primary amines groups on TMP branches.⁷⁷ Then, the mixture sonicated for 8 h and then placed on a magnetic stirrer for 12 h at 70 °C. To increase reaction rate and based on the equilibrium law, the produced water in amidation reaction removed by evaporation of water. Eventually, the suspension resulted is centrifuged at 11 000 rpm with anhydrous THF again and rinsed with ethanol and THF to remove not-reacted materials. The sample is then placed in the oven for 48 h at 60 °C overnight.

2.2 Experimental system

Fig. 1 shows the overall experimental set-up for the present research work which consist of a flow loop, heated section, cooling section, measuring instruments, data acquisition and control unit. The flow loop includes a pump, a magnetic flow meter, a reservoir tank, a differential pressure transmitter, and a test section. This configuration closely resembles heat transfer in most heat exchangers to enable much clear representative of real engineering application. The nanofluids were pumped from a 20 L capacity stainless steel jacketed tank by a Cole-Parmer™ magnetic drive pump at a flow rate of 0–4 l m⁻¹, and the pump flow was controlled by a Hoffman Muller™ inverter. The flow rate and the pressure loss were measured using a N-FLO-25 Electromagnetic flow meter and a Foxboro™ differential pressure transmitter, respectively. Furthermore, for this experimental setup PLC control system was used and WINCC software was used for recording and analysing the data.

Fig. 1 Schematic and pictorial representation of the convection heat transfer experimental set-up along with the major components: (a) flow meter, (b) cooling unit, (c) differential pressure transmitter, (d) auto transformer (Variac), (e) multifunction meter, (f) data acquisition unit and (g) reservoir tank.

A straight seamless copper tube with a length of 1500 mm, 8 ± 0.2 mm outer diameter, and a 4 mm inner diameter was used as the test section. The test section was heated by using an ultra-high-temperature heating flexible tape (Omega, USA) at a maximum power of 900 W, which was linked to PLC system to control the watts and current. Six K type thermocouples (Omega, Singapore) were mounted on the test section by using high temperature epoxy glue at 24 cm equilateral axial distances on the outer surface of the test tube as shown schematically in Fig. S1.† The positioning of the thermocouples was done at outer surface of the cylindrical tube in order to avoid boundary layer interruption originating from the thermocouple probe protruding into the conduit inner surface. As shown in Fig. S2,† there exists a gap between the outer and the inner surface corresponding to the thickness of the conduit. In a pure conduction heat transfer, the inner surface can be described via the classical heat conduction equation. Furthermore, two RTD (PT-100) sensors (Omega, Singapore) were inserted to obtain the bulk temperature at the inlet and outlet of the test section. All thermocouples and RTDs were calibrated via the use of Ametek temperature calibrator (AMETEK Test & Calibration Instruments, Denmark). The thermocouples were connected to the Graphtec (MIDI logger gl220), and the RTDs were connected to the PLC and SCADA system for the continuous monitoring and recording of the temperature data by a WINCC software at a computer. To minimize the heat loss to the surroundings, a thick glass wool wrapping was implemented followed by rubber insulation dressing to provide maximum protection against heat loss to the surrounding. Three type K-thermocouples ware placed on the outermost surface of the insulation to calculate the heat loss. Further, all piping and fittings were covered with rubber insulation to minimize transportation heat loss to achieve steady state temperature at the inlet and outlet of the test section. The comparative assessment between the input and output energy at different Re by using conventional expression (Q = VI = m°C_p(T_in − T_out)) showed the average loss of approximately 6.1%, which is reasonable. It is believed that this low percentage of heat loss would not affect the overall heat transfer calculation process. However, considering the convection and convective heat transfer process occur simultaneously for the present case, further calibration test was needed to determine the exact temperature at the inner surface of the test section. Therefore, a Wilson plot was adopted to accomplish this task which is based on the equating the resistance between different sections of the heat transfer direction and determining the inner surface temperature via mathematical manipulation. The inner diameter (ID) heat flux between different locations of the cross sectional direction was formulated as mentioned in ESI.†

2.3 Stability

Plot of absorbance versus wavelength for highest concentrated colloidal solution in aqueous media was investigated for presenting the specific particle within the binary system (Fig. 2a). Fig. 2b shows the plot of absorbance intensity versus wavelength for the TMP-treated GNP in water taken at specific period of time (34 days). It depicts the noticeably higher dispersibility of TMP-treated GNP in water as the main basefluid. The measurement was carried out at peak wavelength of TMP-treated GNP/water coolants to trace the alteration in the intensity which can be further used to describe the suspension stability at the constant weight fraction of nanoparticles. It can be seen that the colloidal mixture show a gradual downward trend of relative concentration with time, indicating that the level of particle concentration and thus the stability subsided, surprisingly less than 12% sediment. Also, the relative concentration (absorbance intensity) including TMP-treated GNP-based water coolant shows the low amount of sediment (maximum of sediment was 12%). The easily-miscible TMP functionalities in water may explain the higher dispersion of the functionalized GNP flakes.

Fig. 2 (a) Plot of absorbance versus wavelength for TMP-treated GNP-based water coolant at 0.1 wt% and (b) plot of colloidal stability of TMP-treated GNP in water.

Table 1 lists the particle size distributions and zeta potential for TMP-treated GNP in different solvents. The particle size distribution change is analysed using the dynamic light scattering (DLS) method to check the aggregate size of TMP-treated GNP in different solvents. To measure DLS, the samples were transferred into the folded capillary cell (polycarbonate with gold plated electrodes) for investigation of particle size distribution using Zetasizer Nano (Malvern Instruments Ltd., United Kingdom) at 25 °C. First, TMP-treated GNP-based ethanol, -based methanol and -based di-water show no big aggregation and coagulation in different media. It can be seen that the particle size distribution of TMP-treated GNP-based nanofluids show similar hydrodynamic size in different media, which substantiates the suitable solubility of TMP-treated GNP in different solvents. The above results confirm the critical role of TMP molecules which act as covalent stabilizer to prevent rapid colloidal instability associated with the increase in graphitic domain within the carbon-based structure. Although the difference of zeta-potential is insignificant for different solvents, TMP-treated GNP show an appropriate dispersibility in different media.

Table 1 Zeta potential, average particle size distribution and standard deviation of pristine GNP to DI water, ethanol and methanol media

Solvent	Particles	Average particle size distributions (nm)	% std deviation	Zeta potential (mV)	Standard deviation
Dl water	TMP-GNP	207.3662	3.24	−40.9	6.83
Ethanol	TMP-GNP	118.9029	1.22	−49.67	6.05
Methanol	TMP-GNP	301.989	4.52	−29.7	8.58

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3. Data processing

To study the heat transfer behaviour and energy management of the synthesized TMP-treated GNP coolant in the convective heat transfer was performed. Processing of quantifiable data were conducted following similar protocols as described elsewhere for determining heat transfer and hydrodynamic performance in closed conduit heat transfer analysis. The heat flux, heat transfer coefficient, Nusselt number, friction factor, Reynolds number and Prandtl number are systematically tabulated as shown in Table 2.

Table 2 Parameters for determining heat transfer and hydrodynamic performance in heat transfer analysis

Parameter	Symbol	Formula
Heat flux	q′′
Heat transfer coefficient	h
Nusselt number	Nu
Friction factor	f
Reynolds number	Re
Prandtl number	Pr

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To assess the effectiveness of nanofluids, a performance index (ε) was selected as an appropriate parameter to clarify the range of temperature and velocity that can be used by the TMP-treated GNP coolants:⁴²

R_h is the ratio of the heat transfer enhancement of the new coolant (GNP) to the base-fluid and R_ΔP is the ratio of pressure drop of TMP-treated GNP to the base-fluid. To study the energy saving in the turbulent region, the pumping power can be measured as follow by eqn (2).⁴³where W_nf and W_bf are the pumping power in the presence of nanofluid and basefluid, respectively.

Yu et al.⁷⁸ suggested another type of efficiency (efficiency of loop), which is a combination of the heat transfer coefficient (h) and the pumping power (W). The efficiency was measured by the ratio of the heat transfer coefficient enhancement to the pumping power increase.^78,79 That is,

4. Results and discussion

4.1 Functionalization analysis

The FTIR spectra of the pristine GNP and TMP-treated GNP are shown in Fig. 3. Obviously, in contrast to the pristine GNP, the TMP-treated GNP sample shows clear cues of various functionalities groups. The detailed list of peaks along with their interpretations are listed in Table 3. It can be seen that TMP and TMP-treated GNP show some similar peaks. TMP contains 3 similar branches of propylene glycol and primary amine and due to steric hindrance, one of the branches can attach on the GNP surface and 2 branches remain intact during the reaction. Thus, GNP functionalization with TMP should present same peaks as TMP, which is obvious in Fig. 3. The spectrum of TMP-treated GNP shows peaks at 1637 cm⁻¹ and 1105 cm⁻¹, which could be attributed to the C=O and C–O stretching vibration.⁸⁰ The peak at 1637 cm⁻¹ can be obtained from carboxylation and/or amidation reaction. Further, the appearance of peak at 3430 cm⁻¹ for O–H stretching vibration is attributed to the carboxylation phase. Also, the peaks at 2968 and 2876 cm⁻¹ are in agreement with stretching vibration of C–H groups.⁸¹ In addition, peak centred on 1575 cm⁻¹ is attributable to the N–H bending vibration of primary amines, as a result of the TMP addition to the main structure of GNP. TMP functionalization was further established by the appearance of peaks at 1463 cm⁻¹ and 1375 cm⁻¹ for the CH₂ bending vibration and C–N stretching vibration, respectively.

Fig. 3 Fourier transform infrared spectroscopy (FTIR) spectra of pristine GNP, TMP-treated GNP and pure TMP.

Table 3 Fourier transform infrared interpretation of the functionalized GNP

Peak (cm^−1)	Interpretation
3430	O–H stretching vibration
2968 & 2876	C–H stretching vibration
1637	–C=O stretching vibration (amide band)
1575	N–H bending vibration of primary amines
1463	CH2 bending vibration
1375	C–N stretching vibration
1105	C–O stretching vibration

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Raman spectral analysis of the TMP-treated GNP as well as pristine GNP are shown in Fig. 4. The Raman spectra of the both samples exhibit D and G bands, at around 1362 cm⁻¹ and 1592 cm⁻¹ respectively. The D bands are attributed to the amorphous/disordered carbon (sp³) and G bands to the graphitic carbon (sp²). Increase in the I_D/I_G ratio means that number of sp² hybridized carbons changed to sp³ hybridization carbons because of the covalent functionalization.⁸² However, as could be seen intensity ratio of TMP-treated GNP sample is significantly larger than that of the pristine GNP. Note that TMP-treated GNP and pristine GNP show the I_D/I_G ratios of 0.92 and 0.51, which is in agreement with FTIR results.

Fig. 4 Raman spectra of pristine GNP and TMP-treated GNP.

Fig. 5 illustrates the TEM images of the TMP-treated GNP. TEM images are able to show the surface deterioration and wrinkles of the GNPs that formed as a result of TMP functionalization. Overall, one can see some GNP sheets with large grain size in images. According to the TEM results, the TMP-treated GNP papers preserved their shape. Also, the lines seen in the TEM images are wrinkles on the GNP surface due to the inherent instability of 2D structures. The presence of these lines in TMP-treated GNP can be attributed to the enhancement of wrinkles (waviness) during the sonication procedure, resulting from the flexibility of GNP flakes after treatment. Note that functionalization can increase the wrinkles by increasing the wettability of surface.

Fig. 5 TEM images of TMP-treated GNP.

4.2 Thermo-physical properties

Thermal conductivity of the TMP-treated GNP of all concentrations was measured at temperature range from 25 °C to 50 °C via the use KD₂ pro thermal conductivity meter (Decagon Devices, Inc., Pullman, WA, USA) which was based on transient hot wire method. Fig. 6 shows the thermal conductivity plot of TMP-treated GNP as a function of temperature and concentration. Four different weight concentrations (0.025%, 0.05%, 0.075% and 0.1%) were considered and the variation of thermal conductivity with concentration and temperature are studied. Therefore to prevent from sharp increase in effective viscosity, in this study TMP-treated GNP was considered with low concentrations. The enhancement of thermal conductivity for TMP-treated GNP with surface area of 750 m² g⁻¹ is seen to be 20–31% in weight concentration of 0.1 wt% at temperature range from 25 °C to 50 °C. The increase in thermal conductivity with temperature is more sensible in TMP-treated GNP. Thus, it confirms that the temperature play a key role in increasing the thermal conductivity of TMP-treated GNP coolant. The main mechanism for thermal conductivity enhancement with increase of temperature is attributed to the Brownian motion of the nanoparticles suspended in the basefluid.^27,39 The dynamic viscosities of TMP-treated GNP were measured at the temperature 30 °C. The dynamic viscosity of the TMP-treated GNP is the function of temperature and weight concentration. Similar to other coolants, the rheological behaviour of TMP-treated GNP showed an enhancement of viscosity with increasing concentration of TMP-treated GNP.

Fig. 6 Thermal conductivity of TMP-treated GNP as a function of concentration and temperature.

There is also a rising trend between the density of TMP-treated GNP and weight concentration, thus as the weight concentration increases the density increases. The GNP nanoparticle density is an important parameter for the increased friction factor and pressure drop of the coolants. Since the density of GNP is more than the basefluid, the density of nanofluid increases with concentration. The specific heat capacity of the TMP-treated GNP were measured at bulk temperature of 30 °C (see Table 4).

Table 4 Specific heat, dynamic viscosity and density of the TMP-treated GNP at bulk temperature of 30 °C

GNP concentration	Density (kg m^−3)	Specific heat (J kg^−1 K^−1)	Viscosity (kg m^−3)
0.1	1055.863	2807.352	0.003130
0.075	1040.232	3058.304	0.00235
0.05	1025.058	3358.526	0.001706
0.025	1010.32	3724.108	0.001193

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4.3 Thermal performance studies

Prior to carrying out the set of detailed experiments on the TMP-treated GNP, a set of initial experiments were performed for water as the base-fluid, in order to assess the accuracy and reliability of the experimental set-up. The empirical correlations of Gnielinski, Petukhov and Dittus–Boelter^83,84 were selected as for comparison with the obtained results especially for test of accuracy of the set-up in the turbulent region. The selected correlations respectively, are:

Nu = 0.0236Re^0.8Pr^0.3 (6)

The Gnielinski correlation given by eqn (4), which has range of 3000 < Re < 5 × 106 and 0.5 < Pr < 2000. The Petukhov and Dittus–Boelter correlations are given by eqn (5) and (6). The friction factor, f, is given as (Filonenko⁸⁵):

f = (0.79 ln Re − 1.69)⁻² (7)

Fig. 7 compares the experimentally measured average Nusselt number for the basefluid at a bulk temperature of 30 °C with the empirical correlations. This figure showing a good agreement between the experimental measurements and the Gnielinski correlation at different Reynolds numbers.

Fig. 7 A comparison of the data obtained from the Gnielinski, Petukhov and Dittus–Boelter correlations.

The results highlight relatively small deviation between the current measurement and existing correlations to give a confidence level in further data reduction process. The lowest deviation for an average Nu is shown in Fig. 7 was recorded for comparison with Gnielinski correlation which registered a maximum error of 5.3% and deviation drops with increasing Re numbers. In addition, the correlation of Petukhov and Dittus–Boelter provides an acceptable agreement with the experimental data for the water. In Fig. 7, it can be clearly seen that the expected trend of increase in Nusselt number along with increase in Reynolds number. Likewise, for the friction loss, the experimental results for DW were validated by the Blasius, power law and Petukhov equations. Fig. 8 shows the validation of the friction loss data from the experimental investigation, and the above mentioned equations are seen to exhibit an error rate of less than 7%. The correlations suggesting the reliability of the extracted raw data for conducting further analysis.

Fig. 8 Frictional head loss as a function of Reynolds number for distilled water.

The convective heat transfer coefficient of TMP-treated GNP for different weight concentrations at two different heat fluxes is presented in Fig. 9(a) and (b). It is seen that the augmentations of the convective heat transfer coefficient of TMP-treated GNP significantly exceed those of the thermal conductivity enhancements for different weight concentrations. In all experiments, the convective heat transfer coefficient increases with the fluid velocity, which may indicate an improvement in the heat transfer potential of the TMP-treated GNP coolants compared with distilled water. Similarly, by increasing the velocity and concentration of the TMP-treated GNP, gradual increment was observed in heat transfer coefficient. The enhancement in heat transfer coefficient (HTC) of TMP-treated GNP is attributable to Brownian motion of the nanoparticles, thermal diffusion and thermophoresis.⁸⁶ The heat transfer enhancement is attributed to the thin thermal boundary layer in which higher velocities are present, the improved thermal conductivity and the reduced thermal resistance between the flowing nanofluid and the inner wall surface temperature of the tube. The maximum heat transfer coefficient enhancements for TMP-treated GNP at heat flux 23 870 W m⁻² and 18 565 W m⁻² were, 107% and 72% respectively, for the weight concentration of 0.1 wt% at constant velocity of 3 m s⁻¹. This substantial enhancement was obtained by adding a very small amount of TMP-treated GNP nanoparticles to the distilled water. There was slightly decrement in heat transfer coefficient by decreasing the weight concentration of the TMP-treated GNP. At weight percentage of 0.025 the increment was found at heat flux of 23 870 W m⁻² and 18 565 W m⁻² 75% and 66% respectively. Therefore, at lower weight percentage of GNP the heat transfer coefficient increment was 9% higher at constant heat flux of 23 870 W m⁻² compared to 18 565 W m⁻².

Fig. 9 The effects of Reynolds number and concentration of TMP-treated GNP on the convective heat transfer coefficient at inlet temperature of 30 °C at input power of (a) 23 870 W m⁻² and (b) 18 565 W m⁻².

Previous studies claimed that the reasons for the heat transfer enhancement of the nanofluids included the mixing effects of the particles near the wall, particle migration, particle shape and rearrangement, the Brownian motion of the particles, the thermal conductivity enhancement, a reduction of the boundary layer thickness, and a delay in the boundary layer development. In addition, the thermal entry length for a fully developed flow in the turbulent region should be expressed as x ≥ 10Dr. According to the experimental findings, there are two reasons for the convective heat transfer enhancement of the nanofluids: delay and disturbance of the thermal boundary layers and the excellent thermal conductivity enhancement of the TMP-treated GNP-water coolant. The chaotic movements created from the Brownian motion and the migration of GNP nanoparticles could affect the development of the thermal boundary layer in the entrance region.⁸⁷ The reason for larger enhancement of the convective heat transfer compared to that of thermal conductivity was introduced by Aravind et al.^39,88 using a simple analogy that the connective heat transfer is proportional to k/δt, where δt is the thickness of thermal boundary layer. Thus, to increase the convective heat transfer coefficient, k can be increased and/or δt can be decreased. According to Ding and Aravind,^39,66 carbon nanomaterials such as CNTs and graphene have a tendency to decrease the thermal boundary layer thickness. Higher thermal conductivity or lower difference between temperatures of bulk fluid and tube wall can be introduced as the main reason for aforementioned enhancement in the convective heat transfer coefficient. More studies, typically flow visualization studies, should be conducted to get a clearer picture of the heat transfer enhancement mechanism.

In order to evaluate the ratio of convective to conductive heat transfer of TMP-treated GNP coolants, the average Nusselt numbers of the TMP-treated GNP coolants as a function of the Reynolds number was measured at different heat fluxes which is presented in Fig. 10(a) and (b). Experimentally, for all cases the average Nusselt number of the TMP-treated GNP coolants showed good increment with increase in Re. The highest Nusselt number was calculated at Re = 11 770, with heat fluxes of 23 870 W m⁻² and 18 565 W m⁻² (at maximum velocity of 3 m s⁻¹ and 0.1 wt%) due to the improved thermal conductivity and the reduced thermal resistance between the flowing nanofluid and the inner wall surface of the tube. The higher Nusselt number for the TMP-treated GNP coolants is attributed to the decrease in circulation temperature by increasing thermal conductivity of working fluid, which decreases the temperature difference between the tube wall and bulk fluid in close conduit. The Nusselt number for TMP-treated GNP showed increment up to 42%, and 72% at the heat fluxes of 18 565 and 23 870 W m⁻², respectively.

Fig. 10 The average Nusselt number of TMP-treated GNP at different concentrations and Reynolds number at input power of (a) 23 870 W m⁻² and (b) 18 565 W m⁻².

The friction factor of TMP-treated GNP coolants flowing through the test section was measured under various conditions at different concentrations and velocities. Fig. 11(a) and (b) shows the measured friction factor for the TMP-treated GNP coolant for all concentrations, as a function of flow velocity. It was observed that, the friction factor increases as the concentration of TMP-treated GNP increases, although there are some fluctuations in measured friction factor at different velocities. At concentration of 0.1 the TMP-treated GNP showed the highest increment in friction factor from 4% to 10.2% at velocities from 1 to 3 m s⁻¹. Consequently, it was observed that as the velocity increases, the dependence of friction factor on the concentration of TMP-treated GNP decreases. At low extent of the Reynolds numbers, Brownian motion can be the main important parameter that influenced on the momentum transfer between the nanoparticles and base-fluid molecules. Thus, as the Brownian motion increase, in the presence of TMP-treated GNP the friction factor increases with higher slope as compared with basefluid.^23,89 However, this mechanism is not dominant when high extent of Re. In summary, the velocity of working fluid can be considered as the most important parameter in increasing the friction factor at the high extent of Re. Overall, the low difference between friction factors of the basefluid and TMP-treated GNP suspensions at different volume flow rates is attributed to the insignificant gap between viscosities of basefluids and TMP-treated GNP. The friction factor change is based on the viscous drag effects of the TMP-treated GNP coolants. Therefore, the nanoparticle density is an important parameter for increasing the friction factor of nanofluids.

Fig. 11 Effect of Reynolds number and concentration of TMP-treated GNP on the friction factor at inlet temperature of 30 °C with input power of (a) 23 870 W m⁻² and (b) 18 565 W m⁻².

The economic performance of the TMP-treated GNP was characteristically evaluated using the performance index (ε), which expressed as the ratio of the heat transfer rate to the pressure drop. Earlier studies (e.g., ref. 90) showed that while the addition of nanoparticles increase the heat transfer rate, it also increase the pressure drop, which is undesirable. Performance index is then introduced to investigate the combined effect of both parameters. The variations of the performance index of the TMP-treated GNP coolants are shown for different Reynolds numbers and various concentrations for a constant bulk temperature of 30 °C in Fig. 12(a) and (b). It was perceived that the performance index of all samples is greater than 1, which indicates the effectiveness of the prepared TMP-treated GNP coolants for convective heat transfer. In addition the Fig. 12(a) and (b) showed the performance index curves for different concentrations reach their peaks at Re 11 700. Therefore, an increase in the performance index was obtained with an increase in the weight fraction of TMP-treated GNP. The highest thermal performance of TMP-treated GNP increased up to 1.87 and 1.55 at constant heat flux of 23 870 W m⁻² and 18 565 W m⁻² at 0.1 wt% and 11 700 Re.

Fig. 12 Performance index of TMP-treated GNP at different concentrations versus Reynolds number at input power of (a) 23 870 W m⁻² and (b) 18 565 W m⁻².

Fig. 12 exhibits a rising trend of performance index with the Reynolds number. In both Fig. 12(a) and (b) it can be seen that performance index of TMP-treated GNP increases along with the increase in Re. A higher performance index indicates greater thermal efficacy of nanofluids. It is also seen that the performance indices of all samples are greater than 1, indicating that TMP-treated GNP coolants has a great heat transfer performance at all Reynolds number. These results also confirm that the positive effects of heat transfer exceeds the negative effects of pressure drop for TMP-treated GNP coolants for a wide range of inlet temperatures, concentrations, and constant velocities; thus, indicating excellent capability of the synthesized TMP-treated GNP coolant for convective heat transfer.

Power consumption and pumping characteristics in a loop is a critical parameter in terms of economy as well as energy saving. Pumping power can be considered as an economic performance indicators in a loop system for evaluating the operability of fluid and performance of power plant. Fig. 13(a) and (b) compared the pumping power of TMP-treated GNP coolant at two different heat fluxes and at various concentrations. The both figures shows that there is a slight increase in the pumping power with the TMP-treated GNP loading, and the effect of temperature variation is negligible.⁷⁸

Fig. 13 Pumping power at different concentrations and temperatures at input power of (a) 23 870 W m⁻² and (b) 18 565 W m⁻².

Performance index presented the convective heat transfer efficiency in terms of pressure drop and rate of heat transfer. The increase in needed pumping power is of course undesirable, while the heat transfer coefficient enhancement is highly desirable. To include these conflicting parameters, Yu et al.⁷⁸ suggested another type of efficiency (efficiency of loop), which is a combination of the heat transfer coefficient (h) and the pumping power (W). The efficiency was measured by the ratio of the heat transfer coefficient enhancement to the pumping power increase.

As discussed above, the efficiency of loop should be higher than 1 for being cost-effective in system. It can be seen in Fig. 14(a) and (b) that the efficiency of loop is higher than 1 at all concentrations and Re indicating the promising potential of TMP-treated GNP for being an alternative nanofluid in the convective heat transfer. The effect of the TMP-treated GNP nanoparticles on viscosity is small, and the TMP-treated GNP coolants behave similarly to pure fluid. In addition the benefit of TMP-treated GNP coolant on enhancement of heat transfer is larger than the increase in pumping power and the TMP-treated GNP coolant has the potential for commercial viability.

Fig. 14 Efficiency of loop for the TMP-treated GNP at different concentrations and Reynolds number at input power of (a) 23 870 W m⁻² and (b) 18 565 W m⁻².

5. Conclusions

A novel functionalization approach for preparing highly dispersed trimethylolpropane tris[poly(propylene glycol), amine terminated] ether-treated graphene nanoplatelets (TMP-treated GNP) was developed. Characterization instruments showed a good degree of GNP functionalization with TMP functionality. Also, more than 88% of TMP-treated GNP remain stable after 1 month. TMP-treated GNP coolant showed a significant enhancement in heat transfer characteristics. A series of tests on the physical properties of the TMP-treated GNP were performed and the results were presented in graphical forms. The thermal conductivity, viscosity, specific heat capacity and density of all samples showed reasonable performance for utilization in heat exchangers. The convective heat transfer for the TMP-treated GNP showed significant enhancement compared to the conventional basefluid, indicating that the new fluid can be an effective coolant for heat exchangers in terms of overall thermal properties and energy saving. Also, other characteristics of the TMP-treated GNP such as weak increase in the pressure drop for different concentrations and inlet temperature, low friction factor, lack of corrosive agent, appropriate performance index (ε > 1), and slight increase in the required pumping power are all highly favourable for introducing new fluid for wide industrial applications. The approach is also highly cost-effective and therefore has the potential for mass production and wide application.

The following conclusions were obtained.

(1) Thermal performance enhancement for the TMP-treated GNP was between 20 and 31% in weight concentration of 0.1 wt% at temperature range from 25 °C to 50 °C.

(2) A significant enhancement in the heat transfer coefficient was found at fluxes of 18 565 and 23 870 W m⁻² up to 72% and 107% respectively.

(3) The Nusselt number increased up to 42%, and 72% for the heat fluxes of 18 565 and 23 870 W m⁻², respectively at 0.1 wt%.

(4) The friction factor of the TMP-treated GNP coolant increased by 4–10% compared to the base fluid.

(5) The highest thermal performance of TMP-treated GNP coolant increased up to 1.87 and 1.55 at constant heat flux of 23 870 W m⁻² and 18 565 W m⁻² at 0.1 wt% and Re number of 11 700. All concentrations of TMP-treated GNP coolants provide a good option for the replacement of the conventional working fluids in heat transfer applications.

As a consequence, it is believed that the TMP-treated GNP coolant can be used in many practical engineering applications.

Nomenclature

Cp	Specific heat, J g^−1 K^−1
D	Diameter, m
h	Heat transfer coefficient, W m^−2 K^−1
K	Thermal conductivity, W m^−1 K^−1
L	Tube length, m
m°	Mass flow rate, kg s^−1
Nu	Nusselt number
Pr	Prandtl number
q	Heat flux, W m^−2
Q	Heat transfer rate, W
Re	Reynolds number
T	Temperature, °C
U	Velocity, m s^−1
A	Cross section of the tube (m^2)
f	Friction factor
n	Number of tube passes
G	Mass velocity ([kg m^−2 s^−1)
W	Pumping power

Greek symbols

ρ	Density, kg m^−3
μ	Viscosity, Pa s
ε	Performance index
ΔP	Pressure drop (Pa)
η	Efficiency of loop

Subscripts

bf	Basefluid
nf	Nanofluid
p	Particles
w	Tube wall
in	Inlet
out	outlet
b	Bulkfluid
ID	Inner diameter
Tb	Bulk temperature
OD	Outer diameter

Acknowledgements

This research work has been financially supported by High Impact Research (MOHE-HIR) Grant UM.C/HIR/MOHE/ENG/46 and UMRG-RP012D-13AET and University of Malaya, Malaysia.

References

1. N. Seifvand and E. Kowsari, RSC Adv., 2015, 5, 93706–93716.
2. S. Choi, ASME Fluids Eng. Div. Summer Conf., Proc., 1995, 66, 99–105.
3. S. Chol, ASME Fluids Eng. Div. Summer Conf., Proc., 1995, 231, 99–106.
4. A. Amiri, M. Shanbedi, G. Ahmadi, H. Eshghi, B. T. Chew and S. N. Kazi, Colloids Surf., A, 2015, 487, 131–141.
5. A. Amiri, M. Shanbedi, H. Yarmand, H. K. Arzani, S. Gharehkhani, E. Montazer, R. Sadri, W. Sarsam, B. T. Chew and S. N. Kazi, Energy Convers. Manage., 2015, 105, 355–367.
6. H. K. Arzani, A. Amiri, S. N. Kazi, B. T. Chew and A. Badarudin, Int. Commun. Heat Mass Transfer, 2015, 68, 267–275.
7. S. Zeinali Heris, M. Fallahi, M. Shanbedi and A. Amiri, Heat Mass Transfer, 2015, 1–9,  DOI:10.1007/s00231-00015-01548-00239.
8. S. Kazi, A. Badarudin, M. Zubir, H. Ming, M. Misran, E. Sadeghinezhad, M. Mehrali and N. Syuhada, Nanoscale Res. Lett., 2015, 10, 1–15.
9. S. Rashidi, F. Farzin, A. Amiri, M. Shanbedi, M. Rahimipanah, M. Savari, Z. Taghizadeh-Tabari and S. Z. Heris, J. Dispersion Sci. Technol., 2015 DOI:10.1080/01932691.01932015.01090318.
10. M. Shanbedi, S. Z. Heris, A. Amiri and H. Eshghi, J. Taiwan Inst. Chem. Eng.,  DOI:10.1016/j.jtice.2015.1010.1008.
11. M. Shanbedi, S. Z. Heris, A. Amiri, E. Hosseinipour, H. Eshghi and S. Kazi, Energy Convers. Manage., 2015, 105, 1366–1376.
12. K. H. Solangi, S. N. Kazi, M. R. Luhur, A. Badarudin, A. Amiri, R. Sadri, M. N. M. Zubir, S. Gharehkhani and K. H. Teng, Energy, 2015, 89, 1065–1086.
13. M. N. M. Zubir, A. Badarudin, S. N. Kazi, M. Misran, A. Amiri, R. Sadri and S. Khalid, J. Colloid Interface Sci., 2015, 454, 245–255.
14. T. P. Teng, Y. B. Fang, Y. C. Hsu and L. Lin, J. Nanomater., 2014, 2014, 15.
15. M. Tabandeh-Khorshid, E. Omrani, P. L. Menezes and P. K. Rohatgi, Int. J. Eng. Sci. Tech., 2015 DOI:10.1016/j.jestch.2015.09.005.
16. A. Amiri, S. N. Kazi, M. Shanbedi, M. N. Zubir, H. Yarmand and C. Bee Teng, RSC Adv., 2015, 5, 107222–107236.
17. A. Amiri, R. Sadri, M. Shanbedi, G. Ahmadi, S. Kazi, B. Chew and M. N. M. Zubir, Energy Convers. Manage., 2015, 101, 767–777.
18. M. Shanbedi, S. Z. Heris, A. Amiri, S. Adyani, M. Alizadeh and M. Baniadam, Numer. Heat Transfer, Part A, 2014, 66(8), 947–962.
19. A. Amiri, M. Shanbedi, M. Savari, B. T. Chew and S. N. Kazi, RSC Adv., 2015, 5, 71144–71152.
20. Z. Chen, L. Yang, Y. Hu, D. Wu, J. Yin, G.-A. Yu and S. H. Liu, RSC Adv., 2015, 5, 93757–93764.
21. S. Gharehkhani, S. Farid Seyed Shirazi, S. Pilban-Jahromi, M. Sookhakian, S. Baradaran, H. Yarmand, A. Ataollahi Oshkour, S. Newaz Kazi and W. J. Basirun, RSC Adv., 2015, 5, 40505–40513.
22. Y. Song, J. Yu, L. Yu, F. E. Alam, W. Dai, C. Li and N. Jiang, Mater. Des., 2015, 88, 950–957.
23. M. Shanbedi, A. Amiri, S. Rashidi, S. Z. Heris and M. Baniadam, Heat Transfer Eng., 2015, 36, 315–324.
24. Y. Song, J. Yu, L. Yu, F. E. Alam, W. Dai, C. Li and N. Jiang, Mater. Des., 2015, 88, 950–957.
25. S. F. Seyed Shirazi, S. Gharehkhani, H. Yarmand, A. Badarudin, H. S. Cornelis Metselaar and S. N. Kazi, Mater. Lett., 2015, 152, 192–195.
26. A. Amiri and M. Shanbedi, J. Dispersion Sci. Technol., 2015 DOI:10.1080/01932691.2015.1074588.
27. A. Amiri, R. Sadri, M. Shanbedi, G. Ahmadi, B. Chew, S. Kazi and M. Dahari, Energy Convers. Manage., 2015, 92, 322–330.
28. M. M. Aman, K. H. Solangi, M. S. Hossain, A. Badarudin, G. B. Jasmon, H. Mokhlis, A. H. A. Bakar and S. N. Kazi, Renewable Sustainable Energy Rev., 2015, 41, 1190–1204.
29. Y. Gao, K. Ding, X. Xu, Y. Wang and D. Yu, RSC Adv., 2014, 4, 40898.
30. F. Jafari, S. Khodabakhshi and S. G. Shirazi, RSC Adv., 2014, 4, 64215–64215.
31. K. H. Solangi, M. R. Islam, R. Saidur, N. A. Rahim and H. Fayaz, Renewable Sustainable Energy Rev., 2011, 15, 2149–2163.
32. H. Yarmand, S. Gharehkhani, G. Ahmadi, S. F. S. Shirazi, S. Baradaran, E. Montazer, M. N. M. Zubir, M. S. Alehashem, S. N. Kazi and M. Dahari, Energy Convers. Manage., 2015, 100, 419–428.
33. S. Lee, S.-S. Choi, S. Li and J. Eastman, J. Heat Transfer, 1999, 121, 280–289.
34. K. J. Lee, S. H. Yoon and J. Jang, Small, 2007, 3, 1209–1213.
35. H. Dongxiao, M. Zhaoguo, W. Daxiong, Z. Canying and Z. Haitao, Nanoscale Res. Lett., 2011, 6, 457.
36. A. Nasiri, M. Shariaty-Niasar, A. M. Rashidi and R. Khodafarin, Int. J. Heat Mass Transfer, 2012, 55, 1529–1535.
37. R. Zheng, J. Gao, J. Wang, S.-P. Feng, H. Ohtani, J. Wang and G. Chen, Nano Lett., 2011, 12, 188–192.
38. W. Yu, H. Xie, X. Wang and X. Wang, Phys. Lett. A, 2011, 375, 1323–1328.
39. S. S. J. Aravind, P. Baskar, T. T. Baby, R. K. Sabareesh, S. Das and S. Ramaprabhu, J. Phys. Chem. C, 2011, 115, 16737–16744.
40. S. Girdthep, N. Komrapit, R. Molloy, S. Lumyong, W. Punyodom and P. Worajittiphon, Compos. Sci. Technol., 2015, 119, 115–123.
41. S. A. A. Ghavimi, M. H. Ebrahimzadeh, M. A. Shokrgozar, M. Solati-Hashjina and N. A. Abu Osmana, Polym. Test., 2015, 43, 94–102.
42. P. Naphon, Int. J. Heat Mass Transfer, 2016, 93, 293–300.
43. M. Shanbedi, S. Z. Heris, M. Baniadam, A. Amiri and M. Maghrebi, Ind. Eng. Chem. Res., 2012, 51, 1423–1428.
44. M. Memari, A. Golmakani and A. M. Dehkordi, Ind. Eng. Chem. Res., 2011, 50, 9403–9414.
45. A. Ijam, R. Saidur, P. Ganesan and A. Moradi Golsheikh, Int. J. Heat Mass Transfer, 2015, 87, 92–103.
46. J. Z. Liang, J. Z. Wang, G. C. P. Tsui and C. Y. Tang, Polym. Test., 2015, 48, 97–103.
47. W. Azmi, K. Sharma, P. Sarma, R. Mamat and S. Anuar, Int. J. Therm. Sci., 2014, 81, 84–93.
48. L.-W. Fan, X. Fang, X. Wang, Y. Zeng, Y.-Q. Xiao, Z.-T. Yu, X. Xu, Y.-C. Hu and K.-F. Cen, Appl. Energy, 2013, 110, 163–172.
49. G. Żyła, Int. J. Heat Mass Transfer, 2016, 92, 751–756.
50. M. N. Mohd Zubir, A. Badarudin, S. N. Kazi, N. M. Huang, M. Misran, E. Sadeghinezhad, M. Mehrali and N. Yusoff, Int. J. Heat Mass Transfer, 2015, 87, 284–294.
51. R. Moriche, S. G. Prolongo, M. Sánchez, A. Jiménez-Suárez, M. J. Sayagués and A. Ureña, Composites, Part B, 2015, 72, 199–205.
52. B. Román-Manso, E. Domingues, F. M. Figueiredo, M. Belmonte and P. Miranzo, J. Eur. Ceram. Soc., 2015, 35, 2723–2731.
53. M. Shanbedi, D. Jafari, A. Amiri, S.Z. Heris and M. Baniadam, Heat Mass Transfer, 2013, 49, 65–73.
54. S. A. Angayarkanni and J. Philip, Adv. Colloid Interface Sci., 2015, 225, 146–176.
55. Y. Liu, W. Q. Loh, A. Ananthanarayanan, C. Yang, P. Chen and C. Xu, RSC Adv., 2014, 4, 44151.
56. K. J. Lee, S. H. Yoon and J. Jang, Small, 2007, 3, 1209–1213.
57. D. Han, Z. Meng, D. Wu, C. Zhang and H. Zhu, Nanoscale Res. Lett., 2011, 6, 1–7.
58. A. Nasiri, M. Shariaty-Niasar, A. Rashidi and R. Khodafarin, Int. J. Heat Mass Transfer, 2012, 55, 1529–1535.
59. S. W. Lee, K. M. Kim and I. C. Bang, Int. J. Heat Mass Transfer, 2013, 65, 348–356.
60. S. S. Gupta, V. M. Siva, S. Krishnan, T. Sreeprasad, P. K. Singh, T. Pradeep and S. K. Das, J. Appl. Phys., 2011, 110, 084302.
61. R. Zheng, J. Gao, J. Wang, S.-P. Feng, H. Ohtani, J. Wang and G. Chen, Nano Lett., 2011, 12, 188–192.
62. N. Nakashima, Y. Tomonari and H. Murakami, Chem. Lett., 2002, 31, 638–639.
63. H. Murakami and N. Nakashima, J. Nanosci. Nanotechnol., 2006, 6, 16–27.
64. C. P. Firme III and P. R. Bandaru, Nanomedicine: Nanotechnology, Biology and Medicine, 2010, 6, 245–256.
65. M. Zhou, H. Bi, T. Lin, X. Lü, D. Wan, F. Huang and J. Lin, Carbon, 2014, 75, 314–321.
66. Y. Ding, H. Alias, D. Wen and R. A. Williams, Int. J. Heat Mass Transfer, 2006, 49, 240–250.
67. W. Yu, D. M. France, D. Singh, E. V. Timofeeva, D. S. Smith and J. L. Routbort, J. Nanosci. Nanotechnol., 2010, 10, 4824–4849.
68. J. E. Park, G.-H. Lee, H.-W. Shim, D. W. Kim, Y. Kang and D.-W. Kim, Electrochem. Commun., 2015, 57, 39–42.
69. B. Ou, R. Huang, W. Wang, H. Zhou and C. He, RSC Adv., 2014, 4, 52950.
70. W. Zhang, W. He and X. Jing, J. Phys. Chem. B, 2010, 114, 10368–10373.
71. B. Ahmadi-Moghadam and F. Taheri, Eng. Fract. Mech., 2015, 143, 97–107.
72. M. R. Tokala, B. Padya, P. K. Jain and C. H. Shilpa Chakra, Superlattices Microstruct., 2015, 82, 287–292.
73. A. Amiri, M. Shanbedi, H. Eshghi, S. Z. Heris and M. Baniadam, J. Phys. Chem. C, 2012, 116, 3369–3375.
74. T. T. Baby and R. Sundara, J. Phys. Chem. C, 2011, 115, 8527–8533.
75. N. Jha and S. Ramaprabhu, J. Phys. Chem. C, 2008, 112, 9315–9319.
76. S. Suresh, K.P. Venkitaraj, P. Selvakumar and M. Chandrasekar, Exp. Therm. Fluid Sci., 2012, 38, 54–60.
77. C. L. Allen, A. R. Chhatwal and J. M. J. Williams, Chem. Commun., 2012, 48, 666–668.
78. W. Yu, D. M. France, E. V. Timofeeva, D. Singh and J. L. Routbort, Int. J. Heat Mass Transfer, 2012, 55, 5380–5396.
79. W. Yu, D. M. France, D. S. Smith, D. Singh, E. V. Timofeeva and J. L. Routbort, Int. J. Heat Mass Transfer, 2009, 52, 3606–3612.
80. B. Ghiadi, M. Baniadam, M. Maghrebi and A. Amiri, Russ. J. Phys. Chem. A, 2013, 87, 649–653.
81. A. Amiri, R. Sadri, G. Ahmadi, B. Chew, S. Kazi, M. Shanbedi and M. S. Alehashem, RSC Adv., 2015, 5, 35425–35434.
82. A. Amiri, G. Ahmadi, M. Shanbedi, M. Savari, S. N. Kazi and B. T. Chew, Sci. Rep., 2015, 5, 17503.
83. F. W. Dittus and L. M. K. Boelter, Int. Commun. Heat Mass Transfer, 1985, 12, 3–22.
84. S. Z. Heris, M. Shokrgozar, S. Poorpharhang, M. Shanbedi and S. H. Noie, J. Dispersion Sci. Technol., 2013, 35, 677–684.
85. G. K. Filonenko, Teploenergetika, 1954, 1, 40–44.
86. Z. Liang, L. Jizu, B. Minli and G. Detian, Heat Transfer Eng., 2015, 36, 452–461.
87. E. B. Haghighi, M. Saleemi, N. Nikkam, R. Khodabandeh, M. S. Toprak, M. Muhammed and B. Palm, Int. Commun. Heat Mass Transfer, 2014, 52, 1–7.
88. S. S. J. Aravind and S. Ramaprabhu, RSC Adv., 2013, 3, 4199–4206.
89. A. Amiri, M. Maghrebi, M. Baniadam and S. Z. Heris, Appl. Surf. Sci., 2011, 257, 10261–10266.
90. P. Samira, Z. Saeed, S. Motahare and K. Mostafa, Korean J. Chem. Eng., 2014, 1–8.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra23998b

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