Prediction of nanofluid convective heat transfer using the dispersion model

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Abstract

The laminar convective heat transfer behavior of nanofluids through a straight tube is numerically investigated in this paper. A new mechanism which is proposed to explain considerable enhancement of nanofluids heat transfer is dispersion that intends to consider the irregular movements of the nanoparticles. Applying this additional mechanism leads to promising results in comparison with the predictions by traditional homogenous model with effective properties. To validate the dispersion model results, the experimental results for three kinds of nanofluids are used. Also the effect of nanoparticle size on nanofluid heat transfer is examined. The obtained results show good agreement between the theoretical and experimental results.

Introduction

The performance of the conventional Heat transfer fluids such as water, minerals oil and ethylene glycol is often limited by their low thermal properties which are the main limitations for industrial process intensification and device miniaturization. Adding high conductivity solid particles to a fluid is one of the known heat transfer enhancement methods. If a suspension of millimeter or micrometer sized particles is used, although showing some enhancement, experienced problems such as poor suspension stability, rapid sedimentation, channel clogging, corrosion, pipeline erosion and great pressure drop which are particularly serious for system performance are accrued. Because of these disadvantages, this method for heat transfer enhancement was not vastly used [1]. To prevent the above disadvantages, the use of nanometer particles was proposed. This new kind of fluids named “Nanofluids” was introduced in 1995 [2]. The term nanofluid is used to describe a solid-liquid mixture which consists of a base liquid with dilute volume fraction of high conductivity solid nanoparticles. The nanofluids have a unique feature which is quite different from those of the conventional solid–liquid mixtures in which millimeter or micrometer sized particles are added [3]. Compared with suspended particles of millimeter or micrometer dimensions, nanofluids show better stability and rheological properties, reported higher thermal conductivities, and no penalty in pressure drop. Because of the excellent potential of nanofluids in heat transfer enhancement, it is expected that the nanofluid will become the next generation of heat transfer fluid for thermal engineering [4].

Nanoparticles can be produced from several processes such as gas condensation, mechanical attrition or chemical precipitation techniques. The preparation of a nanofluid begins by direct mixing of the base fluid with Nanoparticles. Then some methods used for stabilizing the suspensions: 1 – adjusting the pH value of suspensions; 2 – using surface activators or dispersants; 3 – using ultrasonic vibration. These methods can change the surface properties of the suspended particles and can be used to suppress the formation of particle clusters in order to obtain stable suspensions. The use of these techniques depends on the required application of the nanofluid. Selection of suitable activators and dispersants depends mainly upon the properties of the solutions and particles [5], [6].

The enhancement of the local heat transfer coefficient is much more dramatic than the enhancement of the available theoretical predictions. Different reasons such as increasing the nanoparticles surface area compared with micron-sized particles [6], particle migration [1], intensification of turbulence or eddies [4], dispersion of the suspended nanoparticles have been suggested [4], [6], all of them leading to suppression or interruption of the boundary layer.

There are two different approaches to investigate the enhanced heat transfer of the suspensions: the two-phase one and the single-phase one. The first provides the possibility of understanding the functions of both the fluid phase and the solid particle in the heat transfer process, but needs much computation time and computer capacity [6]. By combining Lagrangian statistics and DNS (direct numerical simulation) Sato et al. (1998) applied this approach to analyze the mechanism of two-phase heat and turbulent transport by solid particles (on the micrometer order) suspended in a gas flow [7].

Another two-phase model is mixture model. The mixture model, based on a single fluid two phase approach assumes that the coupling between phases is strong, and particles closely follow the flow. The two phases are assumed to be interpenetrating, meaning that each phase has its own velocity vector field and slip velocity (relative velocity) is defined as the velocity of the nanoparticle phase relative to the velocity of the base fluid phase. Within any control volume there is a volume fraction of primary phase and also a volume fraction of the secondary phase. This model is employed by Behzadmehr et al. (2007) in the simulation of nanofluids [8]. This model prediction is more consistent with the experimental results.

The second approach assumes that both the fluid phase and particles are in a thermal equilibrium condition and flow at the same velocity. This approach which is based on the single phase flow is simpler and takes less computation time. In cases that the main interest is focused on heat transfer calculations, this approach may be more suitable [6].

Homogenous model is one of the nanofluid single phase models. This model differs from conventional pure fluid model only in the effective properties. It means that the continuity, Navier–Stokes and the energy equations are used with the nanofluid effective properties. According to this model, usual correlations of flow and heat transfer feature of a single phase fluid can be generalized to the nanofluid. Maiga et Al (2005) studied nanofluid based on this model [9]; this model is not competent to predict the heat transfer features of nanofluids [4], [10]. Another single phase model uses one more heat transfer mechanism to the common ones, this model is called dispersion model. The present study aims to drive the mathematical model of the dispersion mechanism, and shows that this model has the ability to predict the nanofluid heat transfer more accurately.

Section snippets

Nanofluid properties

The Nanofluid transport and thermal properties are quite different from the base fluid. Effective density and thermal capacity of nanofluids are calculated using some classical formulas as well known for two phase fluids accurately [9].ρnf=(1ϕ)ρf+ϕρp(ρCp)nf=(1ϕ)(ρCp)f+ϕ(ρCp)p

The viscosity of the nanofluids can be estimated with the existing correlations for the two phase mixture [3]. For example, the well known Einstein's formula for evaluating the effective viscosity of a dilute suspension

Dispersion model

The dispersion is a known theory in the porous media subject. Consider saturated flow through a porous medium, and let a portion of the flow domain contain a certain mass of solute. This solute will be referred as a tracer, the tracer which is a labeled portion of the same liquid, may be identified by its density, color, electrical conductivity, etc. Experience shows that as flow takes place the tracer gradually spreads and occupies an ever increasing portion of the flow domain, beyond the

Numerical simulation

For the particular applications under consideration, it is assumed that the nanofluids are continuous, Newtonian and incompressible with constant physical properties. Both the compression work and viscous dissipation are assumed negligible in the energy equation, thermal conductivity is explained by Fourier law. Also, nanoparticles are in thermal equilibrium with the base fluid and there is not any body force and heat source in the problem.

The dispersion model approach has been adopted in order

Nanofluid heat transfer

The dispersion model has been applied for various nanofluids using experimental thermal properties. In order to calibrate the model for a special nanofluid, a base point is selected between the reported experimental data. Some arbitrary values for the dispersion coefficient are selected to evaluate the Nusselt numbers using the developed model and calculated Nusselt numbers are plotted versus the selected dispersion coefficients. Then, using an interpolating procedure, the appropriate value for

Effect of nanoparticle size on nanofluid convective heat transfer

The relationship between the nanoparticle size and the nanofluid heat transfer coefficient has not been studied experimentally. This subject has been investigated using the dispersion model in this section. This study will be carried out using water-Al2O3 nanofluid with 1.0% volume concentration in Re = 1060. The effective conductivity for different nanoparticle size has been derived from Xue & Wen-mei Xu work [16] that is shown in Fig. 7.

The dispersion model has been used for the nanofluids

Conclusion

  • 1.

    The dispersion model was used to investigate the laminar convective heat transfer of nanofluids through a tube. Mathematical expression of the dispersion phenomena in porous media had been published. In this work, a correlation was used for the dispersion in the nanofluid subject. The results obtained from the dispersion model were compared with the existing experimental results for three kinds of nanofluids. Comparisons indicate good agreement between the dispersion model and the experimental

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