Ultrasonic and Thermophysical Studies of Ethylene Glycol Nanofluids Containing Titania Nanoparticles and Their Heat Transfer Enhancements

TiO₂ nanoparticles were successfully synthesised by a simple sol-gel method (37) using Ti[OCH(CH₃)₂]_4, generally referred to as titanium tetra-isopropoxide (TTIP), as a precursor purchased from Sigma-Aldrich Company (USA) with purity of 97%. Titanium(IV) isopropoxide was dropped slowly into the mixed solution of distilled water and ethanol in the ratios of 1:4:1 (TTIP: water: ethanol). The solution was stirred continuously for 1 h at room temperature to obtain a white slurry. HNO₃ was used to adjust pH value in the range 2–3. The white slurry mixture was dried at 120°C for 3 h on a hot plate; the dried powder was sintered at 450°C for 3 h. Finally, we obtained the required TiO₂ nanoparticles. The flow chart of synthesis of TiO₂ nanoparticles is given in Figure 1.

Fig. 1

The synthesised sample of TiO₂ nanoparticles were analysed with XRD pattern using a SmartLab^® X-ray diffractometer (Rigaku Corporation, Japan) (with λ = 1.5406 Å CuK_α radiation) operating at 40 kV, 30 mA and at room temperature. The XRD patterns were used to determine the crystallite size, lattice parameter and phase identification. The structural and morphological analysis of TiO₂ nanoparticles were done by HR-TEM and the selected area electron diffraction (SAED) pattern using the model Tecnai^TM G² F30 field emission gun transmission electron microscope (FEI Company, USA) operating at 200 kV accelerating voltage with resolution point:0.17 Angstrom line:1.24 Å and magnification 1500 LM to 520 kx. Tescan MAIA3 field emission scanning electron microscope (Tescan, Czech Republic) operating at 12.0 kV and magnification 21.4 Kx was used for SEM-EDX analysis of the morphology and average particle size of the TiO₂ nanoparticles. The UV-vis absorption spectrum was recorded using Shimadzu UV-2330 spectrometer (Shimadzu Corporation, Japan) in the range 200–700 nm. The UV-vis spectrum was used to determine direct energy band gap of the TiO₂ nanoparticles.

TiO₂-ethylene glycol nanofluids were prepared at different concentrations, 0.2 wt%, 0.5 wt% and 1.0 wt% of TiO₂ nanoparticles. When TiO₂ nanoparticles are added to the ethylene glycol base fluid, the nanoparticles produce a sediment within a few minutes because they remain in clusters without being dispersed. For the uniform dispersion of nanoparticles in the base fluid, we used an ultrasonic homogeniser VC 505 (Sonics & Materials Inc, USA) working at 20–40 kHz, 500 W.

The crystal phases of the synthesised TiO₂ nanoparticles were determined by XRD patterns as shown in Figure 2. The obtained peaks in the diffraction pattern are identified with the JCPDS Card No. 88-1175. The interplanar spacing has been calculated using Equation (i):

where λ represents the wavelength of CuK_α (1.5406 Å) radiation, θ is the angle between incident beam and the reflection lattice planes and n = 1 is the order of the XRD spectra. The highest peak is observed at 2θ = 25.4° which was indicated to plane (101) and d spacing corresponding to this peak is 3.12 Å. The other peaks in XRD pattern are observed at 2θ = 27.6°, 37.9°, 48.2°, 54.1°, 55.1°, 62.8°, 69°, 70.4°, 75.1° and 82.8° correspond to the (110), (004), (200), (105), (211), (002), (116), (112), (215) and (312) planes of TiO₂ nanoparticles and d spacing are calculated as 2.83 Å, 2.43 Å, 1.88 Å, 1.69 Å, 1.66 Å, 1.47 Å, 1.35 Å, 1.33 Å, 1.26 Å and 1.16 Å, respectively. The intensity of the obtained peaks indicates the well-formed crystalline nature of the sample. The average crystallite size has been computed with Scherrer’s equation (Equation (ii)) (38):

where β_hkl represents the full width at half maxima (FWHM) and K is the Scherrer constant. From this formula, the calculated average crystallite size of the given sample is approximately ~23 nm.

Fig. 2

The TEM image of a crystalline sample is shown in Figure 3(a). The average particle size of the TiO₂ nanoparticles ranged from 20–26 nm as shown in the histogram (Figure 3(b)). The SAED pattern in Figure 3(c) shows principally 10 rings which are ascribed to (101), (110), (103), (004), (111), (200), (105), (211), (002) and (116) planes, respectively. These planes are consistent with the XRD results. The d spacings are in agreement with the tetragonal structure of TiO₂ nanoparticles (JCPDS Card No. 88-1175). For the structural analysis TiO₂ nanoparticles were also examined by HR-TEM as shown in Figure 3(d). The crystalline nature of the nanoparticles is visible in the HR-TEM micrograph. The lattice spacing 0.31 nm and 0.28 nm corresponds to (101) and (110) planes respectively. The size and morphology of the TiO₂ nanoparticles were also determined using SEM. Figure 4 shows typical SEM images of TiO₂ nanoparticles. The SEM image shows random distribution of TiO₂ nanoparticles having sizes in the range 18–26 nm. In Figure 4, there is a soft agglomeration of the nanoparticles: isolated particles are connected to each other by attractive physical interactions like Van der Waals force. The agglomeration of nanoparticles in the base fluid probably affects the thermal conductivity performance of the nanofluids. Agglomeration of nanoparticles affects the Brownian motion of the nanoparticles resulting in a decrease in thermal performance of the nanofluids. To remove agglomerations of nanoparticles in the base fluid, a sonication process has been used to break the intermolecular interactions. The EDX spectrum (Figure 5) of the TiO₂ nanoparticles provides information about the constituent components of our sample, which contains titanium and oxygen. The high intensity peaks for titanium and oxygen justifies that the sample contains mainly TiO₂.

Fig. 3

Fig. 4

Fig. 5

The UV-vis absorption spectrum at room temperature of TiO₂ nanoparticles has been recorded in the wavelength range 200–700 nm and is shown in Figure 6(a). It is obvious from the UV-vis absorption spectrum that the peak observed at 315 nm represents a blue shift compared with its bulk counterpart. This indicates that the particle size of the TiO₂ nanoparticles has been reduced (38–40). The optical absorption of the TiO₂ nanoparticles is analysed by Equation (iii):

where E_g represents the optical band gap of nanoparticles, B is a constant, α is the optical absorption coefficient of the nanoparticles. The exponent m depends on the nature of the transition, m = 1/2, 2, 3/2, 3 for allowed direct, allowed indirect, forbidden direct and forbidden indirect transitions respectively. Figure 6(b) shows the Tauc plot of TiO₂ nanoparticles, a satisfactory fit is obtained for (αhν)² vs. hν indicating the presence of a direct band gap. The optical energy gap of the TiO₂ nanoparticles has been determined as 3.28 eV by extrapolating the linear portion of this plot at (αhν)² = 0.

Fig. 6

The thermal conductivity of the nanofluids was measured by using a Hot Disk TPS-500 S thermal constant analyser. The Hot Disk TPS-500 S is the newest transient plane source (TPS) thermal constants analyser. The TPS technique has been used to determine the thermal conductivity of a nanofluid. The temperature dependent thermal conductivity of the TiO₂-ethylene glycol nanofluids is plotted in Figure 7(a) at 0.2 wt%, 0.5 wt% and 1.0 wt%. The results show that the thermal conductivity of TiO₂-ethylene glycol nanofluids increases with concentration of TiO₂ nanoparticles. The thermal conductivity exhibits a slow increase for 0.2 wt% nanofluids while it shows relatively fast increase for 0.5 wt% and 1.0 wt% nanofluid in the temperature range 20–80°C. At 20°C, the value of thermal conductivity of pure ethylene glycol is 0.285 W mK⁻¹ and it has been increased to 0.314 W mK⁻¹ for 1.0 wt% concentration of TiO₂ nanoparticles in ethylene glycol base fluid. The expression of TCE is given by Equation (iv) (41):

where TC_nf and TC_bf are the thermal conductivity of nanofluid and base fluid respectively.

Fig. 7

A number of investigators have developed models for determining the thermal conductivity of nanofluids containing spherical particles. They only consider the effect of volume fraction of the particles. However the thermal conductivity of nanofluids depends on various factors such as size, shape, volume fraction of the suspended particles as well as temperature of suspensions. A few models also propose that the TCE is due to the ordered layering of liquid molecules near the solid particles (42, 43).

In addition to describing the TCE in nanofluids, we consider the effect of three possible mechanisms for heat transfer in nanofluids: (a) translational Brownian motion, (b) the existence of an interparticle potential and (c) convection in the liquid due to the Brownian movement. In the low temperature region, the mean free path due to the collision of nanoparticles increases and leads to TCE due to Brownian particle (K_Brownian) as given as Equation (v):

where ϕ is the volume fraction, C_N is the heat capacity per unit volume of the nanoparticles, l is the mean free path and V_N is root mean square velocity of the particles.

This model explains the individual effect of temperature on the TCE in nanofluids with the help of Brownian motion but does not consider the effect of surface functionality and particle loading of nanoparticles. To overcome the shortcomings of this model, Prasher et al. (44) presents an order-of-magnitude justification to show a local convection effect caused by the Brownian movement of the nanoparticles. Based on the Brownian motion induced convection effect from multiple nanoparticles, the model of Prasher et al. for the TCE ratio of a nanofluid is given in Equation (vi):

where K is the thermal conductivity of nanofluids, K_f is the thermal conductivity of fluids, A and m are the best fit constants, and should be same for different experimental data for a particular fluid. R_e and P_r are Reynolds and Prandtl numbers respectively (Equation (vii)):

where d_N is the particle diameter, R_b is the interfacial resistance (Equation (viii)):

The Reynolds number (R_e) is based on the root-mean-square velocity (ν_N) of a Brownian particle defined as Equation (ix) (45, 46):

where ρ_N is the density of the particles, k_b is the Boltzmann constant and T is the temperature in Kelvin scale.

Figure 7(b) shows the variation of the TCE with temperature ranging from 20–80°C. It is clear from Figure 7(b) that the enhancement in thermal conductivity of TiO₂-ethylene glycol nanofluids is achieved with increasing concentrations of nanoparticles and temperatures. At 20°C, we observed 3.3% to 6.5% and 11.2% TCE on 0.2 wt%, 0.5 wt% and 1.0 wt%, and at 80°C, the TCE becomes 9.9%, 18.3% and 23.8% for 0.2 wt%, 0.5 wt% and 1.0 wt% respectively for TiO₂-ethylene glycol nanofluids. This enhancement is due to better uniformity and stability of suspensions. It has been found that ultrasonication increases the stability and uniformity of the nanofluids. The achieved values of TCE are higher than any of the results reported previously for TiO₂-ethylene glycol or TiO₂-water based nanofluids (13, 14, 30, 31) at such small concentrations. In preparation of the nanofluids, we used very small amounts of nanoparticles, so the fluidic properties of the liquid are almost unaffected, allowing for the easy flow of liquids and better transfer of heat. As the temperature increases, the TCE in the TiO₂-ethylene glycol nanofluids may be attributed to Brownian motion of nanoparticles. It is obvious from Equation (ix) that the root-mean-square velocity (ν_N) of a Brownian particle depends upon particle diameter. If the particle diameter is small, root-mean-square velocity of a Brownian particle is large. Since the synthesised nanoparticles are small in diameter (approximately 22 nm) this results in the increase of Brownian motion, causing convection which in turn increases the thermal conductivity of the nanofluids. The high TCEs are probably due to the small size of nanoparticles because as the particle size decreases, the surface-to-volume ratio of particles increases, which can lead to enhanced thermal conductivity of nanofluids.

The ultrasonic velocity in nanofluids was measured using an ultrasonic interferometer (model nanofluid-10X, Mittal Enterprises, India) at 3 MHz frequency in temperature range 20–80°C. The measured ultrasonic velocity in ethylene glycol matrix and three nanofluids samples containing 0.2 wt%, 0.5 wt% and 1.0 wt% of TiO₂ in temperature range 20–80°C are shown in Figure 8. It is obvious from Figure 8 that the ultrasonic velocity in the nanofluids increases with the temperature. The plot also indicates that the ultrasonic velocity in the nanofluids is larger than that of pure ethylene glycol matrix (1410 m s⁻¹) at 20°C and the velocity increases with the particle concentration (1430 m s⁻¹) for 1.0 wt% loading at the same temperature of 20°C.

Fig. 8

If we consider (ρ_m,ρ_s) and (k_m,k_s) are the density and the compressibility of fluid and suspended particles respectively, B and ϕ are the bulk modulus and the particle volume fraction; then the effective density (ρ_eff) and compressibility (k_eff) of the suspension becomes as Equation (x) (47–49):

The ultrasonic velocity (V) in a medium is given by Equation (xi):

where B, ρ and k represent the bulk modulus, density and compressibility of the medium respectively. λ and μ are the material dependent quantities known as Lamé moduli or Lamé coefficients. The compressibility and density of a fluid medium are changed by the dispersion of nanoparticles and are the function of the particle volume fraction. From Equation (x), it is clear that the evaluation of the effective bulk modulus and compressibility of the suspension is performed with calculation of effective Lamé moduli, which depends on particle volume fraction of suspended particles.

It is obvious from Equations (x) and (xi) that the bulk modulus and change in density of the nanoparticles suspension as a function of volume fraction causes an enhancement in the ultrasonic velocity. An increase in the wave velocity with increase in the particle concentration of given nanofluids indicates that there is positive change in the bulk modulus and density of the nanofluids. It may be predicted that the comparative change in the density with respect to bulk modulus is small. As the particle concentration in nanofluids increases, the compressibility of the given matrix decreases. A strong cohesive interaction occurs among the molecules after dispersion of TiO₂ nanoparticles in the ethylene glycol matrix. Thus for the TiO₂ nanofluids, the ultrasonic velocities are larger in comparison to the ethylene glycol matrix and increase with the nanoparticle concentration.

In the low frequency region, the velocity in nanofluids is independent of particle size (49, 50). Here all the nanofluids have been prepared with nanoparticles fabricated at low evaporation rate and velocity of the ultrasonic wave is measured at different temperatures and low frequency (3 MHz). Thus it was concluded that the temperature dependent velocity at low frequency in the nanofluids depends only on the particle concentration. At low frequency, the ultrasonic velocity in a nanofluid is a quadratic function of temperature (Equation (xii) (51):

where V₀ is the ultrasonic velocity at 0°C, V₁ and V₂ are the absolute temperature coefficients of velocity and T is the temperature difference between experimental and initial temperature (0°C). The first and second terms in Equation (xii) are in good agreement for a simple liquid system, but the third nonlinear term is caused by non-linear change in bulk modulus and density of the nanofluid system with temperature.

The acoustic particle sizer APS-100 (Matec Applied Sciences, USA) was used to examine the PSD in the nanofluids. The APS-100 works on Epstein and Carhart theory (52) and is mainly based on the ultrasonic spectroscopic method. The APS-100 computes the sound attenuation (dB) per unit length (cm) over the 1–100 MHz frequency range in particle-liquid suspensions with high precision. This attenuation spectrum can be converted to PSD data. According to Epstein and Carhart theory (52), the attenuation of the ultrasonic wave in a nanofluid can be understood with the understanding of the thermal wave length (; K_S, ρ_S and C_S: thermal conductivity, density and specific heat of the dispersed particle: ω ; frequency of the wave) and the viscous wave length (; η: viscosity of the matrix). When the viscous wave length is comparable to particle radius (r), the viscous loss is a prominent cause behind the ultrasonic attenuation; while the viscous drag, scattering and thermal losses are effective when the thermal wave length λ_T ≈ r. The expressions for the ordinary viscous dissipation (α_V), the viscous drag loss (α_VD) (47, 50) of the sound waves are given as Equation (xiii) and Equation (xiv):

where η_d and η_V represent the dynamic and the volume viscosities of the nanofluid, k̅ is the wave number, . Biwa (53) calculated the change in the ultrasonic attenuation with respect to volume fraction caused by scattering at microscale in low frequency limit. The expression to compute the ultrasonic attenuation is given as Equation (xv) (53):

where γ^sca represents the scattering cross-section which depends on the frequency of the ultrasonic wave, particle size, bulk modulus and density of the base/carrier fluid and suspended particles. The thermal attenuation is caused by temperature variation produced by propagation of the sound waves in different components of suspension. The thermal loss mainly depends on the frequency and particle size. The particle size has been obtained by APS-100 in range of 19 nm to 24 nm as visualised in Figure 9. It has been confirmed from Figures 3(a) and 9 that the PSD obtained by APS-100 is in good agreement with that obtained by the TEM micrograph. Ultrasonic spectroscopy is sensitive to particles with radius between about 10 nm to 1000 mm. The maximum particle concentration which can be analysed varies between about 1 wt% to 50 wt% depending on the nature of the system. On the other hand, the technique is unsuitable for analysing dilute suspensions i.e., particle concentrations below about 1 wt%. In the present study (Figure 9) the weight percentage of TiO₂ is 1 wt%. Systems with different weight percentages of TiO₂ show the same PSD because nanoparticles are dispersed in base fluid with the same technique and the same ultrasonication time.

Fig. 9