Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids

Abstract

Heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids is investigated for various pertinent parameters. A model is developed to analyze heat transfer performance of nanofluids inside an enclosure taking into account the solid particle dispersion. The transport equations are solved numerically using the finite-volume approach along with the alternating direct implicit procedure. Comparisons with previously published work on the basis of special cases are performed and found to be in excellent agreement. The effect of suspended ultrafine metallic nanoparticles on the fluid flow and heat transfer processes within the enclosure is analyzed and effective thermal conductivity enhancement maps are developed for various controlling parameters. In addition, an analysis of variants based on the thermophysical properties of nanofluid is developed and presented. It is shown that the variances within different models have substantial effects on the results. Finally, a heat transfer correlation of the average Nusselt number for various Grashof numbers and volume fractions is presented.

Introduction

Nanotechnology is considered by many to be one of the significant forces that drive the next major industrial revolution of this century. It represents the most relevant technological cutting edge currently being explored. It aims at manipulating the structure of the matter at the molecular level with the goal for innovation in virtually every industry and public endeavor including biological sciences, physical sciences, electronics cooling, transportation, the environment and national security.

Low thermal conductivity of conventional heat transfer fluids such as water, oil, and ethylene glycol mixture is a primary limitation in enhancing the performance and the compactness of many engineering electronic devices. To overcome this drawback, there is a strong motivation to develop advanced heat transfer fluids with substantially higher conductivities to enhance thermal characteristics. Small particles (nanoparticles) stay suspended much longer than larger particles. If particles settle rapidly (microparticles), more particles need to be added to replace the settled particles, resulting in extra cost and degradation in the heat transfer enhancement. As such an innovative way in improving thermal conductivities of a fluid is to suspend metallic nanoparticles within it. The resulting mixture referred to as a nanofluid possesses a substantially larger thermal conductivity compared to that of traditional fluids [1].

The presence of the nanoparticles in the fluids increases appreciably the effective thermal conductivity of the fluid and consequently enhances the heat transfer characteristics. Nanofluids have a distinctive characteristic, which is quite different from those of traditional solid–liquid mixtures in which millimeter and/or micrometer-sized particles are involved. Such particles can clot equipment and can increase pressure drop due to settling effects. Moreover, they settle rapidly, creating substantial additional pressure drop. However, nanofluids exhibit little or no penalty in pressure drop when flowing through the passages. Moreover, they flow smoothly through microchannels without clogging them. Thus, nanofluids are best for applications in which fluid flows through small passages because nanoparticles are small enough to behave similar to liquid molecules. Nanofluids show promise in significantly increasing heat transfer rates in a variety of applications, with minimum pressure drop. Enhancements were recently reported for copper Cu nanofluids, where just a 0.3% volume fraction of 10 nm diameter copper Cu nanoparticles led to an increase of up to 40% in the thermal conductivity of ethylene glycol [2]. This can be attributed to several factors such as nanoparticle clustering [3], ballistic phonon transport [3], layering at the solid/liquid interface [3], the interaction and collision among particles and surface area enhancement. In addition, the suspended particles increase the surface area and the heat capacity of the fluid. That is, a significant improvement in the effective thermal conductivity is achieved as a result of decreasing the size of the suspended particles (nano-sized particle) rather than using larger particles (micro-sized particle). Since heat transfer occurs on the surface of a solid, this feature greatly enhances the fluid’s heat conduction contribution. Wang et al. [4] studied the thermal conductivity of nano-sized SiC suspensions using a transient hot-wire method. Their experimental results showed that the thermal conductivities of the studied suspensions were increased and the enhancement was proportional to the volume fraction of the solid phase. The dependence of the thermal conductivity of nanoparticle–fluid mixture on the base fluid was analyzed by Xie et al. [5].

When simulating heat transfer enhancement using nanofluids, modeling of the effective thermal conductivity possesses a challenge. This can be attributed to several factors such as gravity, Brownian motion, friction force between the fluid and the ultrafine solid particles, sedimentation, layering at the solid/liquid interface, ballistic phonon transport through the particles and the clustering of nanoparticles. This implies that the slip velocity between the fluid phase and the nanoparticles is not zero, although the particles are ultrafine. A body of theoretical work in the literature [6], [7], [8] is available on the effective thermal conductivity of two-phase mixtures that contain powders with particle diameters in the order of millimeters or even micrometers since the first published theoretical work by Maxwell [9]. Maxwell’s model predicted that the effective thermal conductivity of suspensions containing spherical particles increases with an increase in the volume fraction of the solid particles. Hamilton and Crosser [10] investigated the possibility of increasing particle surface area by controlling particle shapes to be non-spherical. Approximately, an order of magnitude improvement in surface area per particle volume was achieved experimentally using this approach alone. The authors developed an expression for the effective thermal conductivity of two-component mixtures as a function of liquid and solid particle thermal conductivities, particle volume fraction, and an empirical scaling factor that takes into account the effect of different particle shapes on the effective thermal conventional solid particles suffer from significant clogging problems due to their significant size conductivity. An alternative expression for calculating the effective thermal conductivity of solid–liquid mixtures with a sphericity of one was established by Wasp [11].

Two main approaches have been adopted in the literature to investigate the heat transfer enhancement by small solid particles (millimeter and/or micrometer-sized particles) suspended in a fluid. The first approach is the two-phase model, which enables a better understanding of both the fluid and the solid phases role in the heat transfer process. The second approach is the single-phase model in which both the fluid phase and the particles are in thermal equilibrium state and flow with the same local velocity. The latter approach is simpler and more computationally efficient. Several factors may affect heat transfer enhancement using nanofluids. These factors include gravity, Brownian motion, layering at the solid/liquid interface, ballistic phonon transport through the particles, nanoparticles clustering, and the friction between the fluid and the solid particles. The phenomena of Brownian diffusion, sedimentation, and dispersion may coexist in the main flow of a nanofluid. In the absence of any experimental data and suitable theoretical studies in the literature to investigate these factors, the existing macroscopic two-phase model is not applicable for analyzing nanofluids. Accordingly the modified single-phase, taking into the account some of the above factors, is more convenient than the two-phase model if the main interest is focused on the heat transfer process. Moreover, superior characteristics of the nanofluid allow it to behave more like a fluid than the conventional solid–fluid mixtures.

The chaotic movement of the ultrafine particles increases the energy exchange rates in the fluid, i.e., thermal dispersion takes place within the flow of the nanofluid. To account for the random motion of the particles, dispersion model is implemented. So far, there is a lack of theoretical and experimental works published on the thermal diffusivity coefficients of nanofluids. Thermal diffusivity coefficient for nanofluid can be modeled similar to the thermal dispersion models for flow through porous media. The dispersed model was first applied by Taylor [12] to simulate salt diffusion in water. Xuan and Li [13] presented a procedure for preparing a nanofluid which is a suspension consisting of nanophase powders and a base liquid. Later on, Xuan and Roetzel [14], analyzed theoretically the flow of a nanofluid inside a tube using a dispersion model. Recently, Keblinski et al. [3] investigated the mechanisms of heat flow in suspensions of nano-sized particles (nanofluids). Four possible explanations were reported for an increase in the thermal conductivity with decreasing grain size. They developed a fundamental understanding of heat transport in solid nanoparticle colloids under stationery conditions.

To the best knowledge of the authors, the problem of buoyancy-driven heat transfer enhancement of nanofluids in a two-dimensional enclosure has not been analyzed. This problem may be encountered in a number of electronic cooling and MEMS applications. The present study is focused on the analysis of several pertinent parameters on the heat transfer characteristics of nanofluids within the enclosure. The dispersion effect is analyzed in the present investigation. Effective thermal conductivity maps will be developed in the present study for various pertinent parameters.