Graphite (99.99%, 45 μm) was purchased from Bay Carbon, Inc, USA. All other reagents like sulfuric acid, nitric acid, sodium nitrate, potassium permanganate, hydrogen peroxide, and ethylene glycol were analytical grade. DI water was used throughout the experiment. Graphite oxide (GO) was prepared from graphite using Hummers method 12. Briefly, 2 g of graphite was treated with 46 ml of sulphuric acid in an ice bath. One gram of sodium nitrate was added to the above solution slowly, followed by the addition of 6 g of potassium permanganate. At room temperature, specific quantity of water was added to the above mixture. After 15 min the suspension was further treated with hydrogen peroxide and was filtered. Finally the filter cake was washed with copious quantity of DI water. At last, the suspension was filtered and dried in vacuum oven at 40°C for 8 h. The dried GO was used for synthesizing hydrogen exfoliated graphene (HEG). Exfoliation of GO was done in hydrogen atmosphere at 200°C as reported previously 13. Functionalization of HEG was done by treating as synthesized HEG with conc. H₂SO₄:HNO₃ in the ratio 3:1. The acid-HEG mixture was ultrasonicated for about 3 h at room temperature. After 3 h the sample was washed several times with DI water, filtered and dried in vacuum.

The samples were characterized with different characterization techniques. Powder X-ray diffraction (XRD) studies were carried out using a PANalytical X'PERT Pro X-ray diffractometer with Nickel-filtered Cu K_α radiation as the X-ray source. The pattern was recorded in the 2θ range of 5° to 90° with a step size of 0.016°. The Raman spectra were obtained with a WITEC alpha 300 Confocal Raman spectrometer equipped with Nd:YAG laser (532 nm) as the excitation source. Identification and characterization of functional groups were carried out using PerkinElmer FT-IR spectrometer in the range 500-4000 cm^-1. Digital photograph has been taken with a Canon Power Shot A590 IS 8 Megapixel camera with 4 × optical zooming. Field emission scanning electron microscopy (FESEM) and transmission electron microscopy (TEM) images were obtained using, FEI QUANTA and JEOL TEM-2010F instruments, respectively. Nanofluid was prepared by dispersing a known amount of f-HEG in the base fluid by ultrasonication (30-45 min). Thermal conductivity of the suspension was measured using KD2 pro thermal property analyzer (Decagon, Canada). The probe sensor used for these measurements were of 6 cm in length and 1.3 mm in diameter. In order to study the temperature effect on thermal conductivity of nanofluid a thermostat was used. Electrical conductivity of the nanofluid was measured using ELICO Ltd CM 183, EC-TDS meter.

The convective heat transfer mechanism was studied using an indigenously fabricated setup. The schematic of the setup is shown in Figure 1. It consists of a flow loop, a heat unit, a cooling part, and a measuring and control unit. The flow loop included a pump with flow controlling valve system, a reservoir and a test section. A straight stainless steel tube with 108 cm length and 23 mm inner diameter was used as the test section. The whole test section was heated by a copper coil linked to an adjustable DC power supply. There was a thick thermal isolating layer surrounding the heater to obtain a constant heat flux condition along the test section. Four T-type thermocouples were mounted on the test section at axial positions in mm of 298 (T1), 521 (T2), 748 (T3), and 858 (T4) from the inlet of the test section to measure the wall temperature distribution, and two further T-type thermocouples were inserted into the flow at the inlet and exit of the test section to measure the bulk temperatures of nanofluids. Cooling part is to cool down the nanofluid coming out from the outlet of test section.

The crystallinity of the samples was studied using XRD. Figure 2a shows the X-ray diffractogram of HEG and f-HEG. The characteristic (002) plane in graphite at approximately 26° is shifted to approximately 24° in HEG. This is same in all graphene prepared by different exfoliation techniques 1415. There is not much difference in XRD of f-HEG and HEG except the broadening of the (002) peak. After vigorous acid treatment, the layers might have separated further and that may be the reason for this broadening 16. The functionalization and defects on the carbon based materials can be sought out by Raman spectroscopy 17. Figure 2b shows the Raman spectrum of HEG and f-HEG. In HEG, the peak around 1588 cm^-1 corresponds to the G-band and the peak around 1356 cm^-1 corresponds to D-band. The D- and G-band represent the sp³ and sp² hybridization of carbon atoms present in the sample, respectively. In the case of f-HEG, G-band as well as D-band shifted to higher wave number side and also broadened with respect to HEG peak positions. G-band has a broad peak centered around 1591 cm^-1 and D-band has a peak centered around 1371 cm^-1. The ratio of the D-band intensity to G-band intensity in f-HEG is higher than that of HEG. The increase in the relative intensity of the disordered mode can be attributed to the increased number of structural defects and to the sp³ hybridization of carbon for chemically induced disruption of the hexagonal carbon order after acid treatment. Acid treatment created some functional groups at the edges of the graphene sheets which helped for the proper dispersion of f-HEG on water and EG. The presence of functional groups may be the reason for broadening of the D-band peak.

The effect of acid treatment and attachment of functional groups were further confirmed with FTIR. Figure 3a shows the FTIR spectra of HEG and f-HEG. During the heat treatment in H₂ atmosphere, most of the oxygen containing functional groups has been removed from HEG. So the functional groups are not dominant in FTIR of HEG. After acid treatment, functional groups are formed at the plane and edges of the sheets. The peaks at around 3442 and 1625 cm^-1 are due to OH functional groups. A small doublet peak of CH₂ (2922 and 2860 cm^-1) and CH at 1365 cm^-1 are present both in HEG and f-HEG. The peaks at 1720 and 1380 cm^-1can be assigned to the C = O and C-O stretching vibrations of COOH. These functional groups help graphene sheets to interact with water molecules and disperse properly. Figure 3b shows the digital photograph of f-HEG dispersed DI water and EG based nanofluid after 2 months of the nanofluid preparation. Even after 2 months of preparation no sedimentation was observed.

Figure 4a shows the FESEM image of as-synthesized HEG taken by putting a small amount of powder sample on carbon tape. The image shows a large area of transparent graphene sheet with rough and soft wrinkled surface morphology. Transmission electron microscopy is also a powerful technique used extensively to provide definitive identification of graphene materials. The sample preparation was done by depositing a drop of ethanol dissolved HEG on Cu grid. Figure 4b clearly shows the wrinkles on the surface and folding at the edges of HEG sheets.

The proper functionalization helped to make well-dispersed HEG nanofluid. Figure 5a shows the normalized thermal conductivity (K_n/K_f) of f-HEG dispersed DI water based nanofluid as a function of temperature for different f-HEG volume fractions. All the measurements were carried out for low volume fractions so as to keep the viscosity of the fluid at a minimum level. For DI water based f-HEG nanofluids, the range of volume fractions used was from 0.005 to 0.05%. The percentage enhancement in thermal conductivity was calculated using the relation ((K_n - K_f) × 100)/K_f, where 'K_f' was the thermal conductivity of base fluid and 'K_n' was that of nanofluid. For 0.05% volume fraction, the enhancement in thermal conductivity is about 16% at 25°C and about 75% at 50°C. The enhancement is less than 10% for 0.005% volume fraction. It is clear from the graph that the thermal conductivity increases with increasing temperature and volume fractions. According to Das et al. 4, in nanofluid the main mechanism of thermal conductivity enhancement can be thought as the stochastic motion of the nanoparticles. This Brownian-like motion will be dependent on fluid temperature and so the huge enhancement in thermal conductivity with temperature is quite explicable. At low temperature this motion was less significant giving the characteristics of normal slurries which rapidly changed at elevated temperature bringing more nanoeffect in the conducting behavior of the fluid. The error bar is shown only for low and high volume fractions.

Figure 5b shows the normalized thermal conductivity of f-HEG dispersed EG based nanofluids with varying temperatures and volume fractions. The thermal conductivity of EG based nanofluids did not show much enhancement for low volume fractions. Till around 0.05% volume fraction there was no enhancement in thermal conductivity. Thermal conductivity started increasing from 0.05% volume fraction onwards. For 0.08% the enhancement was about 1% at 25°C and about 5% at 50°C. This low enhancement in thermal conductivity may be due to the high viscosity of EG. Even though the enhancement in thermal conductivity of EG based nanofluids with f-HEG is low, it is slightly higher than that of CNT dispersed EG 18.

The conventional theoretical models on thermal conductivity of nanoparticles suspended fluids does not consider particle size, shape, the distribution, and the motion of dispersed particles, while only thermal conductivities of base fluid and particles, and volume fraction of article. Maxwell was the man who first investigated the thermal conductivity of liquid suspensions analytically 19. Later, Hamilton and Crossser modified Maxwell's model by taking in to consideration of geometry of particles 20. In 1987 Hasselman and Johnson 21 modified Maxwell's model by including the interfacial thermal resistance (Kapitza resistance, R_bd). The resulting theoretical prediction for the effective thermal conductivity (K) enhancement of the particle-in-liquid colloidal suspensions is given by,

where α = 2 R_bdK_f /d, d is the average particle diameter, R_bd is the interfacial thermal resistance, K_f and K_p are the thermal conductivity of base fluid and particles, respectively. This is also called Maxwell-Garnett type effective medium approximation (MG-EMA). In the absence of thermal boundary resistance (R_bd = 0), the above equation reduces to Maxwell's model. The results are shown in Figure 6a,b for DI water and EG, respectively. The thermal conductivity is correlated with lower and upper bounds of R_bd. The lower and upper bound MG-EMA correlation is almost matching for the DI water based nanofluid at 25°C. When the temperature increases the thermal conductivity is going away from the correlated values. But in the case of EG based nanofluids the calculated value is very much less than the correlated value. This suggests that there are other mechanisms contribute to the thermal conductivity of EG based f-HEG dispersed nanofluids.

Finally electrical conductivity was also measured for some volume fractions of f-HEG dispersed nanofluid. Figure 7a shows the normalized electrical conductivity (σ_n/σ_f) for three different volume fractions at varying temperature in DI water based nanofluid. 'σ_n' represents the electrical conductivity of nanofluid and 'σ_f' that of base fluid. The graph suggests that like thermal conductivity, electrical conductivity also increased with increase in volume fraction and increase in temperature. Similar trend was observed for f-HEG dispersed EG nanofluids also. Figure 7b shows the normalized electrical conductivity of f-HEG dispersed EG based nanofluid for three different volume fractions at varying temperature. The experiments were repeated several times and the error in measurements was less than 4%.

The heat transfer coefficient, (h) is a macroscopic parameter describing heat transfer when a fluid is flowing across a solid surface of different temperature. It is not a material property. The convective heat transfer coefficient is defined as

where x represents axial distance from the entrance of the test section, q is the heat flux, T_s is the measured wall temperature, and T_f is the fluid temperature decided by the following energy balance:

where c_p is the heat capacity, M is the mass flow rate, and E(x) is the energy at position x. Equation 3 is based on an assumption of zero heat loss through the insulation layer.

And mass flow rate can be calculated using the relation,

where u is the velocity of flow, A is the area of cross-section, and ρ is the density of fluid. Reynolds number is defined as Re = ρuD/μ and the Prandtl number is defined as Pr = ν/α, where μ is the fluid dynamic viscosity, ν is the fluid kinematic viscosity, and α is the fluid thermal diffusivity.