A simple model to estimate thermal conductivity of fluid with acicular nanoparticles
Introduction
Enhancing heat transfer for operation and maintenance of equipment has been the focus of researches in many fields. In some cases, particles have been added to fluids in order to improve thermal conductivity. Many predictive equations have been proposed to estimate the increase in thermal conductivity due to the addition of particles. Nevertheless, previous models were developed on the basis of the solid/liquid suspension concept [1]. Great discrepancies between values estimated by equation and those obtained from experiments arise when the added particles are of nanoscale, thus undermining the predictive accuracy of the equation. According to Xuan and Li [2], as well as Eastman et al. [3], the thermal conductivity of nanofluids depends strongly on the volume fraction and properties of the added nanoparticles.
To understand why such discrepancy occurs, so that the equation can be modified to ensure better prediction accuracy, factors such as size, surface area and shape of the added particles [4], [5], [6], [7], [8], [9] as well as interfacial shell [10] have been studied. Besides, some researchers used the concept of the n-point probability function Sn(rn) to discuss macroscopic properties of two-phase random heterogeneous media, and to extend the sphere system into the spheroid system by utilizing the arbitrary aspect ratio [11]. Garboczi and Douglas proposed the concept of intrinsic conductivity to solve the problem of effects of shapes and sizes of particles on thermal conductivity [12].
Nanoparticles in fluids are engaged in Brownian motion, causing random collision between solid particles and liquid molecules. As a result, these particles remain steadily suspended in the fluid and deposition rarely occurs. The effect of particle motion on thermal conductivity should be taken into consideration when modifying conventional prediction equations. In this literature, the conventional prediction equations for thermal conductivity are modified into the simple prediction equations for thermal conductivity of nanofluids containing CuO acicular nanoparticles by considering the factors of perturbation motion and shape of added particles. The results calculated by these simple prediction equations are compared with those of the corresponding experiments in order to verify the accuracy of theoretical estimation of the proposed prediction equations.
Section snippets
Maxwell equation
Among conventional models of effective thermal conductivity of solid/liquid suspensions, Maxwell theory predicts that spherical particles can enhance heat-transfer performance [1]. The equation proposed by Maxwell for estimating thermal conductivity is as follows:where kp represents the thermal conductivity of the solid particles added, kl the thermal conductivity of the bulk liquid, and ϕ is the volume fraction, vol%. Since the Maxwell equation
Effect of nanoparticle rotation
Brownian motion causes the particles to be engaged in random motion, both translational and rotational. In Maxwell equations, the particles are assumed to be spherical and hence their rotation will have no influence on the volume covered. However, the situation will be different when the particles added to the nanofluid are acicular in shape (Fig. 1). The sample nanofluids used in this study were prepared by the submerged arc nanoparticle synthesis system (SANSS) [13]. When the applied
Results and discussion
Fig. 3 shows the increasing ratio of the thermal conductivity (keff = knanofluids/kl) of the fluids containing CuO nanoparticles in experiment compared to, predictions of Maxwell's equations, and those of the modified equations. For the fluids of the highest concentration 0.4 vol%, the experimental thermal conductivity increases about 9.6%. In this figure, it can be found that thermal conductivities predicted by Maxwell's equations are obviously underestimated. With the standard based on the
Conclusions
The Maxwell equation has been in use for many years and considers only spherical particles added to solid/liquid suspensions. Subsequent researches have made modifications to the equation taking into account other factors such as shape and layer adsorption. This study explores the effect of rotation of acicular particles on the changes in volume concentration. Experimental results and analyses reveal that rotation has significant influence on the volume concentration and the shape of the
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