A review and analysis on influence of temperature and concentration of nanofluids on thermophysical properties, heat transfer and pumping power

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Abstract

The Prandtl number, Reynolds number and Nusselt number are functions of thermophysical properties of nanofluids and these numbers strongly influence the convective heat transfer coefficient. The pressure loss and the required pumping power for a given amount of heat transfer depend on the Reynolds number of flow. The thermophysical properties vary with temperature and volumetric concentration of nanofluids. Therefore, a comprehensive analysis has been performed to evaluate the effects on the performance of nanofluids due to variations of density, specific heat, thermal conductivity and viscosity, which are functions of nanoparticle volume concentration and temperature. Two metallic oxides, aluminum oxide (Al2O3), copper oxide (CuO) and one nonmetallic oxide silicon dioxide (SiO2), dispersed in an ethylene glycol and water mixture (60:40 by weight) as the base fluid have been studied.

Introduction

Nanofluids are prepared by dispersing nanometer-sized particles, generally less than 100 nm, in a base fluid such as water, ethylene glycol, propylene glycol, oil and other conventional heat transfer fluids. Addition of high thermal conductivity metallic nanoparticles (e.g., copper, aluminum, silver) etc. to the base fluid increases the thermal conductivity of such mixtures, thus enhancing their overall heat transfer capability. In the past decade and half, there have been abundant experimental as well as numerical studies to explore the advantages of nanofluids under wide variety of conditions. Several bibliographical references on various aspects of nanofluids research are discussed below.

Choi [1] in 1995 showed from a series of calculations that the thermal conductivity of a fluid can be enhanced by adding nanoparticles. Using the assumption that the Dittus and Boelter [2] correlation (Eq. (1)) also holds for nanofluids, which appears valid for low particle concentrations, he derived that hnf/hbf = (knf/kbf)2/3.Nu=0.023Re0.8Pr0.4Pak and Cho [3] conducted experiments on water based nanofluids containing γ-Al2O3 and TiO2 nanoparticles of mean diameters 13 and 27 nm respectively, and for volumetric concentration ϕ up to 3% to determine their heat transfer and frictional characteristics under turbulent flow conditions. Conducting viscosity measurements up to a high level of 10% volumetric concentration, they found that the viscosity of nanofluids increased substantially with an increase in particle concentration. They presented a Nusselt number correlation for dilute dispersions, which was similar in format to the Dittus–Boelter correlation (Eq. (1)), except the constant multiplier and the power of Prandtl number were 0.021 and 0.5 respectively. Also for these dilute nanofluids concentrations, the friction factor results agreed with the standard correlation available for single-phase fluids. These results in early stages of nanofluids development gave the hope that dilute concentrations of nanofluids can be modeled as a single-phase fluid. Lee et al. [4] measured thermal conductivity of Al2O3 (mean diameter 38 nm) and CuO (mean diameter 23.6 nm) nanofluids in deionized (DI) water and ethylene glycol up to about 4% volumetric concentration, using the transient hot-wire method. Their experimental results showed that for a copper oxide-ethylene glycol nanofluid the thermal conductivity can be enhanced by more than 20% with a particle volumetric concentration of 4%. Comparison between their measured thermal conductivity of CuO nanofluids with that obtained from the model of Hamilton and Crosser [5] did not agree. Therefore, the Hamilton-Crosser model, which was originally developed for microparticles was found to be inadequate to predict the thermal conductivity of nanofluids correctly and new correlations were necessary. From theoretical analysis, Xuan and Roetzel [6] presented a conceptual form of a correlation for the Nusselt number of nanofluids as a function of Reynolds number, Prandtl number, ratio of thermal conductivities of the solid nanoparticles and that of the base fluid, ratio of the volumetric heat capacities (CV = ρCp) of nanoparticles and the base fluid, particle volume fraction, and the particle Peclet number, which is related to the particle size and thermal diffusivity of nanofluids. Eastman et al. [7] used transient hot wire method to measure the thermal conductivity of Cu nanoparticle of mean diameter <10 nm in ethylene glycol. They found that the effective thermal conductivity increased by up to 40% with approximately 0.3% volumetric concentration of Cu nanoparticles over the base fluid. Keblinski et al. [8] studied the mechanism of heat transfer in nanofluids by considering Brownian motion, liquid/particle interface and the effect of nanoparticles clustering. They drew conclusions that Brownian motion was too slow to transport significant amount of heat, so thermal conductivity enhancements was due to a highly conductive layered structure around the particles and also due to cluster of particles separated by liquid layers thin enough to allow rapid heat flow among particles. Xuan and Li [9] conducted an experiment with copper nanoparticles of below 100 nm diameter seeded in DI water, in the Reynolds number range of 10,000 to 25,000 for developing heat transfer coefficient and friction factor correlations for turbulent flow guided by the conceptual correlation of Xuan and Roetzel [6]. They used dilute nanofluid up to 2% volumetric concentration. They presented a Nusselt number correlation under turbulent flow condition as a function of Reynolds number, Prandtl number, particle Peclet number and the particle volumetric concentration. Their friction factor measurements of dilute nanofluid matched with the correlation for the base fluid, water, implying that the single-phase fluid friction correlation can apply to dilute nanofluids. Das et al. [10] presented the temperature dependency of thermal conductivity of nanofluids with water-based CuO and Al2O3 nanoparticles of average particle diameter 28.6 nm and 30.4 nm respectively. Their measured thermal conductivity values of CuO-water nanofluid of 4% volumetric concentration exhibited an increment from 14 to 36% over the base fluid with temperature increasing from 21 °C to 51 °C. They also showed that at temperatures above the room temperature, the Hamilton and Crosser [5] model failed to predict the correct values of thermal conductivities for both Al2O3 and CuO nanofluids, consistently under-predicting the correct values. Putra et al. [11] conducted experimental investigation on natural convection in two types of water-based nanofluids. The average diameters were 87 nm and 131 nm for the CuO and Al2O3 nanoparticles respectively. Under natural convection, they found that the Nusselt number of nanofluid was lower than that of the base fluid for the same Rayleigh number. We notice that this characteristic is different than the general trend under forced convection, where the Nusselt number may generally be higher than that of the base fluid for the same Reynolds number. However, even if the Nusselt number is lower for the nanofluid, the hnf can still be higher, if knf is sufficiently enhanced. Wang et al. [12] presented a model based on the fractal theory for the determination of the effective thermal conductivity of nanofluids. They compared the fractal model prediction to experimental data with 50 nm CuO particles in DI water of less than 0.5% volumetric concentration. They mentioned that beyond this dilute limit, the model needs to be refined by taking into account possible deposition effect. Koo and Kleinstreuer [13] derived a model for the effective thermal conductivity of nanofluids that combines the conventional static part represented by Hamilton-Crosser equation plus a dynamic part due to the Brownian motion. This model includes the effects of particle size, volume concentration, temperature, properties of the base fluid and the nanoparticles and the motion of the surrounding fluid moving with the particles. Using their model of effective thermal conductivity and viscosity, Koo and Kleinstreuer [14] showed through a numerical laminar flow analysis that there was an increase in the heat transfer performance of micro-heat sinks with the addition of CuO nanoparticles of particle diameter 20 nm and particle concentration of up to 4% in the base fluids of both water and ethylene glycol.

Wen and Ding [15] conducted experiment with the γ-Al2O3 nanoparticle with a size range of 27–56 nm in DI water and presented Nusselt number versus Reynolds number data at the entrance region of a tube under laminar flow condition. They found that the heat transfer enhancement was significantly higher in the entrance region in comparison to the base fluid and decreased along the axial distance. Ding et al. [16] performed experiment on aqueous suspension of multi-walled carbon nanotubes and reported an impressive maximum enhancement of heat transfer coefficient of 3.5 times compared to the basefluid at Reynolds number of 800, with 0.5 weight% carbon nanotubes. Khaled and Vafai [17] showed by numerical analysis that heat transfer enhancement can occur with nanofluids flowing through a channel by controlling the thermal dispersion effect across the channel. Maiga et al. [18], through a numerical analysis under laminar flow condition, proved that the γ-Al2O3 nanoparticles in water and ethylene glycol had enhanced heat transfer coefficients and Nusselt numbers compared to the base fluid for flow inside a tube and also for radial flow between parallel coaxial heated disks. Their computations revealed a new finding that, as the volumetric concentration of nanofluid increased the length of the thermal entry region decreased. Yang et al. [19] measured laminar flow characteristics of graphite non-spherical nanoparticles of aspect ratio L/d  0.02 in automatic transmission oil and synthetic oils. They presented a convective heat transfer correlation of the form Ω = a Reb where Ω is a function of Nu, Pr, L/d and μb/μw and the constants a and b were curve-fit values obtained from their experimental data. Heris et al. [20] investigated experimentally the behavior of CuO and Al2O3 nanofluids of particle size 50-60 nm and 20 nm respectively in water under laminar flow with a constant wall temperature condition and exhibited enhancement of heat transfer coefficient and Nusselt number as volume concentration increased at a fixed Peclet number (Pe = Re Pr). Prasher et al. [21] showed through an order-of-magnitude analysis that the enhancement of thermal conductivity of nanofluids was due to the localized convention caused by the Brownian motion of nanoparticles. They presented a thermal conductivity correlation containing the Maxwell-Garnet model multiplied by functions of Reynolds number, Prandtl number and particle volumetric concentration. Buongiorno [22] evaluated the relative magnitudes of inertia, Brownian diffusion, thermophoresis, diffusiophoresis, Magnus effect, fluid drainage and gravity on convective thermal transport in nanofluids and concluded that Brownian diffusion and thermophoresis were important slip mechanisms in nanofluids. He derived a Nusselt number correlation as a function of Reynolds number, friction factor, Prandtl number and the laminar sub-layer thickness. Liu et al. [23] reported the synthesis of copper nanoparticles in water by a chemical reduction method in which no surfactant was employed to disperse the nanoparticles. They reported a thermal conductivity enhancement of 23.8% with only 0.1 volume percent copper particles. They noticed that the thermal conductivity of their nanofluid exhibited a time dependent behavior, decreasing considerably with time. We believe this decrease may be due to the agglomeration of nanoparticles in the absence of any surfactant. Wang and Mujumdar [24] presented a review of nanofluids research summarizing in a tabular form 16 different correlations proposed by researchers for the effective thermal conductivity of liquid-particle suspensions. They further summarized a list of 11 experiments on the convective heat transfer measurements on different nanofluids. Mansour et al. [25] studied the effect of uncertainties in physical properties of water-γ-Al2O3 nanofluid and observed that the heat transfer and pumping power comparisons of different concentrations of nanofluids and the base fluid are quite sensitive to the these physical properties. Kim et al. [26] applied Cu, CuO and Al2O3 nanoparticles to ammonia-water solution in an absorption refrigeration system. They found that the addition of surfactants and nanoparticles enhanced the absorption performance by 5.32 times over the base fluid. Li et al. [27] compared thermal conductivity measurements of the Al2O3-water nanofluid by transient and steady state methods. They found that at room temperature the results from the steady state and transient methods presented nearly identical values. However, at higher temperatures, natural convection resulted in higher thermal conductivity values with transient method over the steady state method. Jung et al. [28] conducted experiments to study the laminar forced convective heat transfer of nanofluids containing the Al2O3 nanoparticles (dp = 170 nm; ϕ up to 1.8%) in microchannels. They presented a heat transfer correlation Nu = 0.014 ϕ0.095 Re0.4Pr0.6 for water-based nanofluid under laminar flow in microchannels. The Al2O3 nanoparticle of 1.8% volume concentration dispersed in both the base fluids, water and a mixture of water and ethylene glycol, showed an increase in the convective heat transfer coefficient without any major increase in frictional losses. Nguyen et al. [29] experimentally investigated the heat transfer enhancement of Al2O3 nanofluids (dp = 36 nm & 47 nm; ϕ up to 6.8%) with water, in a system used for cooling microprocessors. Their experimental data showed that for the Al2O3 nanofluid of particle diameter 36 nm and for a particle concentration of 6.8%, the heat transfer coefficient increased by 40% when compared to that of the base fluid. They also found that the convective heat transfer coefficient was higher for 36 nm particle than that of 47 nm particles under equal mass flow rate and volume concentration. Fotukian and Esfahany [30], [31] experimentally investigated the turbulent convective heat transfer and pressure loss of the γ-Al2O3-water (dp = 20 nm; ϕ up to 0.14%) and CuO-water (dp = 30–50 nm; ϕ up to 0.236%) nanofluids inside a circular tube. The results showed that for the Al2O3 nanofluid with particle volume concentration of 0.054%, the heat transfer coefficient increased by 48% compared to pure water at a Reynolds number of 10,000. For the CuO nanofluid with particle volume concentration 0.3%, the heat transfer coefficient increased by 25% compared to pure water. The maximum increase in pressure drop was about 20% for the CuO nanofluid of 0.03% volume concentration compared to pure water. For the γ-Al2O3 nanofluid with volume concentration of 0.135% the pressure drop increased by 30% at a Reynolds number of 20,000 compared to pure water.

Sharma et al. [32] conducted experiments on the Al2O3-water nanofluid (dp = 47 nm; ϕ up to 0.1%) to evaluate the heat transfer coefficient and friction factor in a circular tube with twisted tape inserts in the transition flow regime. Their results showed that at Reynolds numbers of 3000 and 9000, the heat transfer enhancement in circular tube with 0.1% particle volume concentration are 13.77% and 23.69% respectively when compared to water. Furthermore, for the same particle volume concentration of 0.1%, the heat transfer enhancement with twisted tape insert inside a circular tube were 36.96% and 44.71% at Reynolds numbers of 3000 and 9000 respectively, when compared to flow of nanofluid in a plain tube. They presented new correlations for Nusselt number and friction factor for nanofluid flow with twisted tape inserts as a function of the twist ratio. Noie et al. [33] experimentally analyzed the heat transfer enhancement in a two-phase closed thermosyphon using the Al2O3-water nanofluid (dp = 20 nm; ϕ up to 3%). Their study showed that with the use of nanofluids the efficiency of the thermosyphon increased by up to 14.7%. Farajollahi et al. [34] carried out experiments to evaluate the heat transfer characteristics of γ-Al2O3-water (dp = 25 nm; ϕ up to 2%) and TiO2-water (dp = 10 nm; ϕ up to 0.75%) nanofluids in a shell and tube heat exchanger under turbulent flow condition. From their experimental data they proposed that, there existed two different optimum nanoparticle volumetric concentrations for the two different nanofluids used, beyond which the convective heat transfer coefficient decreased with an increase in the particle volumetric concentration, at a constant Peclet number. They presented that the convective heat transfer coefficients for 0.3, 0.5, 0.75,1 and 2% of the γ-Al2O3-water nanofluids were about 46, 56, 46, 38 and 19% higher than those of water respectively. Similarly, the convective heat transfer coefficients for 0.15, 0.3, 0.5 and 0.75% of the TiO2-water nanofluids were about 20, 56, 33 and 18% higher than those of water respectively. This finding is new and additional research is warranted to confirm this characteristic. Ferrouillat et al. [35] conducted experimental study on the convective heat transfer and frictional losses using the SiO2-water nanofluids (dp = 22 nm; 5–34 weight%, equivalent to ϕ = 2.31–18.79 vol%) in a horizontal tube with constant wall temperature boundary condition. They performed the measurements at three different conditions (isothermal, heating and cooling) as well as at different inlet temperatures of 20, 50, 70 °C with various Reynolds numbers ranging from 200 to 10,000. They concluded that for all the measurements for Reynolds number higher than 1000, a significant heat transfer enhancement of about 50% was observed with the nanofluid volume concentration of 18.79%. To our knowledge, a nanofluid of this volume concentration is the highest measured thus far. They used Performance Evaluation Criterion (PEC) defined as the ratio of heat transferred to the required pumping power in the test section showing that PEC decreases with an increase in the nanoparticle concentration. We believe due to the lower density and viscosity of the SiO2 nanofluid compared to other nanofluids the pumping power may not be prohibitively high. Lee et al. [36] experimentally measured the effective convection coefficient, viscosity and the thermal conductivity in microtubes for the oxide nanoparticles (Al2O3, CuO and ZnO) and carbon nanotubes suspended in DI water. They measured particle sizes in the nanofluids using dynamic light scattering technique and reported that their measured particle sizes were at least four times larger than the nominal particle size claimed by the vendor. This was due to the agglomeration of nanoparticles. They reported an effective convective coefficient increase of 5% for the Al2O3 nanofluid of volume concentration 3%, 13.3% for the CuO nanofluid of volume concentration 4% and 11.6% for the carbon nanotube of volume concentration 0.2%. From their measurements they proposed an useful conclusion, that nanofluid is effective as long as the increase in the thermal conductivity of the nanofluid is higher than the one third power of the viscosity increase. Xie et al. [37] experimentally showed an increase in the convective heat transfer coefficient of nanofluids in laminar flow inside a circular copper tube with constant wall temperature. They conducted experiments using four different nanoparticles, MgO, Al2O3, TiO2 and ZnO suspended in 55% distilled water and 45% ethylene glycol by volume as the base fluid. They reported an increase in the heat transfer coefficient of about 252, 40, 18 and 10% for the MgO, Al2O3, ZnO and TiO2 nanofluids of 0.01% volume concentration respectively, when compared with the base fluid at a Reynolds number of 1000. This highest convective heat transfer enhancement of 252% for the MgO nanofluid is quite intriguing. Further research should be performed on the MgO nanofluid to confirm this finding. If the pressure loss penalty of this nanofluid is not too severe, this may be an excellent candidate. Sarah et al. [38] conducted experiments on mass transfer to a rotating disk electrode with the CuO nanoparticles (30-50 nm) in distilled water. They presented a new correlation for the Sherwood number as a function of volume concentration, Reynolds number and Schmidt number. From their measurements they concluded that an increase in mass transfer up to 50% can be attained by adding a small amount of nanoparticles of the order of ϕ = 1.94%. Kalteh et al. [39] presented a two-phase numerical simulation of Cu-water nanofluid under laminar flow in a microchannel. The conservation equations of the liquid and the solid phases were solved simultaneously. They used microparticle correlations for nanoparticles as new correlations are not available yet. Their analyses showed that the Nusselt number predicted by the two-phase model was much higher than that predicted by a homogeneous single–phase model. Peng et al. [40] measured pressure loss of R113 refrigerant containing the CuO nanoparticles under flow boiling inside a tube for mass fractions of nanoparticle up to 0.5 weight%. Using their experimental data, they presented a nanoparticle impact factor correlation, which can be used for frictional pressure loss calculation for refrigerant based nanofluid.

All these literatures discussed in the preceding paragraphs, support the notion that nanofluids are good candidates for future generation of heat transfer fluids. Reviewing the literatures carefully, we observe that the fluid dynamic and thermal performances of nanofluids are strongly dependent upon their thermophysical properties. And the thermophysical properties of nanofluids are strongly dependent upon temperature, the volumetric concentration and the properties of the dispersed particles. However, no concentrated investigation has appeared in the literature thus far, studying how changes in thermophysical properties due to temperature and concentration variation would affect the heat transfer coefficient and pumping power requirement of nanofluids. In the present paper, our objective is to present such a comprehensive analyses. First we developed correlations of thermophysical properties from measurements of three nanofluids (CuO, Al2O3, SiO2 in 60:40 EG/W). Using those correlations, we studied in detail how variation of nanofluids’ properties with concentration and temperature, affect the Prandtl number, Reynolds number, Nusselt number, Muromtseff number, thermal diffusivity etc. Subsequently we analyze their influence on the heat transfer coefficient, the friction factor and the pumping power. Our study is focused on a base fluid of ethylene glycol and water mixture, because in cold regions of the world, this is the fluid of choice for heat transfer. We have selected a 60:40 EG/W mass ratio because this ratio provides protection against freezing down to the lowest level of -48.3 °C as specified in the ASHRAE handbook. Long period of building heating consumes about 40-60% of total energy use in cold regions like Alaska. This study will be useful for applications in cold regions where nanofluids may be successful, in building heating systems, automobile radiators and outdoor heat exchangers in industrial plants.

Section snippets

Convective heat transfer theory of nanofluids

Heat transfer coefficient of any fluid is directly proportional to the Nusselt number via the relation h = (Nu·k)/d. Pak and Cho [3] were possibly the first to propose an experimentally derived correlation for the Nusselt number for nanofluids, very similar to the well-known correlation due to Dittus-Boelter [2] for single-phase fluids. Pak and Cho proposedNunf=0.021Renf0.8Prnf0.5Xuan and Li [9], [41] presented two equations for the Nusselt number of copper-water nanofluids which included the

Viscosity

Namburu et al. [45] conducted measurements of viscosity of copper oxide nanoparticles dispersed in 60:40 EG/W using the LV DV-II+ Brookfield viscometer [44] with a Julabo computer controlled temperature bath to set the nanofluid’s temperature at different values. They presented the following correlation for the viscosity of CuO nanofluid as a function of concentration and temperature.logμnf=C1e(-C2T)where C1 = 1.8375(ϕ)2  29.643(ϕ) + 165.56 with R2 = 0.9873 and C2 = 4 × 10−6(ϕ)2  0.001(ϕ) + 0.0186 with R2 = 

Effect on the Prandtl number

The Prandtl number is dependent on fluid properties, μ, Cp and k, which in turn are dependent on T and ϕ. Fig. 4(a) shows how adding different volumes of nanoparticles affect the Prandtl number of nanofluids at the room temperature. As the volume concentration of particles increases, the Prandtl number increases more rapidly for the CuO nanofluid. As typical numbers, by adding nanoparticles of 6% volume, the Prandtl number can be enhanced by 124%, 50%, 29% for CuO, Al2O3 and SiO2 nanofluids

Conclusions

Addition of nanoparticles to a liquid increases the viscosity significantly and the thermal conductivity moderately, however the specific heat and density change modestly. For example, the viscosity of the Al2O3 nanofluid of 6% volumetric concentration increases by 91% in comparison to the base fluid of 60:40 EG/W at the room temperature of 293 K. Under the same conditions the thermal conductivity of the same nanofluid increases by 22.4%, the density by 13.9% and the specific heat decreases by

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