Eulerian-Lagrangian investigation of nanoparticle migration in the heat sink by considering different block shape effects

Highlights

• Heat transfer of nanofluid flow through different arrangements of solid ribbed channels.

• Effects of thermophoresis and Brownian motion for nanoparticles in the base fluid.

• Decreasing in entropy generation due to heat transfer by increasing the volume fraction.

• Magnitude of velocity increases due to Brownian motion.

• Entropy generation due to heat transfer is predominant.

Abstract

In this study, the Eulerian-Lagrangian method is employed to inspect the impact of nanoparticle migration on the hydrothermal and entropy generation features of Fe₃O₄–water nanofluid in a ribbed-blocked microchannel with two different arrangements. The results are compared with those of the plain microchannel at different volumes of flow rate and nanoparticle concentration. It was found that the nanoparticle migration results in an increase in the pressure drop, friction factor, heat transfer coefficient, overall hydrothermal performance of nanofluid as well as the thermal and frictional entropy generations. In addition, it was depicted that the increase of mass flow rate is associated with the rise of pressure drop, heat transfer coefficient and frictional entropy generation and the decrease of friction factor and thermal entropy generation. Moreover, the augmentation of nanoparticle volume fraction was associated with increasing pressure drop, friction factor, and heat transfer coefficient and the decrease of thermal entropy generation. Finally, it was found that for all the examined cases, the overall hydrothermal performance of the Fe₃O₄-water nanofluid is better than the pure water.

Introduction

A nanotechnology product that has attracted the attention of many researchers is the colloidal suspension of nanoparticles in a common coolant called nanofluid. In 1995, Choi introduced nanofluids and reported their amazing thermal properties [[1], [2], [3], [4]]. Since then, much research was done on these modern fluids, and hundreds of new nanofluids were synthesized and their thermophysical properties reported. In addition, many studies were performed on the cooling performance of nanostructures in numerous applications including heat exchanger units [5], [6], [7], solar thermal collectors [8], [9], [10], photovoltaic/thermal units, [11], [12], [13], and automotive radiators [14], [15], [16], and in most cases, it has been reported that the performance of nanofluids is better than that of base fluids. Some researchers believe that nanofluids can be used to cool electronic components. Martinez et al. [17] numerically examined the influence of channel height, inlet velocity, and nanoparticle concentration on the cooling performance of aqueous TiO₂ nanofluid in a heat sink. They found that the hydrothermal performance of heat sink improves by up to 19.66% with the rise of nanoparticle concentration and the decrease of channel height. Awais and Kim [18] conducted a numerical-experimental investigation to analyze the influence of header shape on the performance of a nanofluid-cooled heat sink. It was reported that by optimizing the header shape, the heat transfer from the CPU to the fluid could be improved by 17% and the fluid pressure drop could be reduced by 43%. Yan et al. [19] numerically assessed the hydrothermal metrics of a nanofluid-cooled heat sink equipped with a microencapsulated PCM-cooled ceiling. Their purpose in applying PCM to the ceiling was to cool the coolant. They found that the use of water-Al₂O₃ nanofluid with a volume fraction of 10% at Reynolds number 500 entails a 10.88 % decrement in the thermal resistance of the heat sink. Mohammadi et al. [20] experimentally evaluated the possibility of using a nanofluid-based heat sink to cool a chipset. The outcomes revealed that by using the aqueous SiC nanofluid at a flow rate of 100, 150 and 200 ml/min, the highest temperature of the chipset could be reduced to 48.6, 47.3, and 46.3 °C. Kumar and Sarkar [21] experimentally examined the influences of particle ratio for a hybrid Nano-fluid consist of carbon/water-alumina nanotube for the thermal–hydraulic performance of a heat sink. They found that the best hydrothermal performance of the heat sink belongs to the hybrid nanofluid with a 6:4 mixing ratio of alumina and carbon nanotube. Balaji et al. [22] experimentally evaluated the cooling performance of water-functionalized graphene nanofluid in a microchannel heat sink. It was observed that by using the graphene nanofluid, the heat sink temperature, and the Nusselt number can be reduced by 10 °C and 60 %, respectively. Alnaqi et al. [23] simulated the first-law and second-law performances of a non-Newtonian hybrid nanofluid in a heat sink with zig-zag walls. They employed the ethylene glycol–water/carbon nanotube-SiO₂ nanofluid as the coolant. They found that the rise of zig-zag height entails an increase in both the hydrothermal performance and total entropy generation rate of the heat sink. To numerically simulate the flow and heat transfer characteristics of nanofluids, various techniques have been proposed so far that can be classified into two general categories: single-phase (or homogeneous) approach and two-phase approach. In the single-phase method, nanofluids are considered as a homogeneous medium and the effect of nanoparticles is seen only in the thermophysical properties of the fluid [24]. In two-phase scheme, however, the base fluid and nanoparticles are considered as separate phases [25]. The two-phase techniques can be divided into two categories: Eulerian-Eulerian approach and Eulerian-Lagrangian approach. In the Eulerian-Eulerian method, nanoparticles are simulated as a continuous medium. In this model, the governing equations the flow of two phases are expressed in an Eulerian coordinate system and then the equations governing the discrete phase, such as the equations governing the fluid phase, are solved separately. The discrete phase is divided into the separate control volumes, each containing a quantity of particles. Then, by extracting the integral equations of mass and momentum and taking into account all the dynamic effects of the continuous fluid on the particles, the discrete phase is solved like the continuous phase [26]. Eulerian, mixture, and volume of fluid (VOF) models are subdivisions of this model. In the VOF model, two phases are considered as unmixed regimes, while in the mixture model, it is assumed that the nanoparticle velocity and the base fluid velocity are different but their temperatures are the same [27]. Finally, in the Eulerian model, the transfer equations of each phase are considered and solved completely independently of the other phase [28]. In the Eulerian-Lagrangian approach, the particles are traced separately by solving the differential equations governing the dynamics of each particle, and finally the kinematic components are obtained at all moments of solution. The governing equations of the liquid phase are the well-known Navier-Stokes equations, to which only expressions resulting from the interaction of particles and liquids are added as source terms. Also, for the particle phase, the governing equations must be solved for each particle and the coordinates for the particles must be obtained by following each particle [29]. The discrete phase can exchange mass, momentum and energy with the continuous phase. Thakar et al. [30] studied the heat transfer properties of a heat sink consisting of circular arrays of air jets under thermal load. They used ANSYS-FLUENT software and the K-ε model and finally managed to reduce the temperature from 85 ℃ to 65 ℃. Al-Baghdadi et al. [31] examined the thermal management in a heat sink using the CFD method. They developed a complete fully 3-D, steady-state, and non-isothermal model. Their results show that the use of nanofluid in micro heat sink is impractical because water can be a cheaper and safer liquid in terms of heat dissipation. Shahsavar et al. [32] analyzed the first and second laws of thermodynamics on a heat sink with a new design filled with porous foam. Using ANSYS-FLUENT software and presenting a three-dimensional model, they investigated the effect of inlet velocity and volume fraction of nanofluid on thermal performance. They found that increasing the velocity increases the frictional entropy generation, decreases the thermal resistance, and thermal entropy generation. Mohammadpour et al. [33] conducted a parametric study on heat sink cooling with multiple synthetic jets using alumina water nanofluid. They investigated the effects of geometric parameters on cooling and used a hybrid algorithm to predict optimal values and maximize heat transfer. The results of their study showed that when two jets are separated, heat transfer increases and increasing the amplitude could have a better effect on cooling. Krishna et al. [34] studied heat transfer and pressure drop in a heat sink using a hybrid nanofluid. Using the finite volume method, they showed that the use of hybrid nanofluid could provide better heat transfer than non-hybrid nanofluid. However, the amount of pressure drop of the hybrid nanofluid compared to non-hybrid nanofluid is almost negligible. Awais and Kim [18] presented an experimental and numerical study on the performance of a multi-channel heat sink with different configurations using nanofluid. In the numerical method, they used a single-phase approach and showed that using a multi-channel heat sink can improve heat transfer by up to 41%. An acceptable correlation of the experimental results with the numerical results was seen in their study. Further study on the performance of heat sinks in cooling [35], [36], [37] and the nature of nanofluids as potential heat dissipation [38], [39] is recommended.

A review of the available literature shows that so far no study was conducted on the effect of nanoparticle migration on the cooling performance of nanofluid in a heat sink. Therefore, the present study is devoted to this topic. In this investigation, the Eulerian-Lagrangian technique is employed to inspect the effect of nanoparticle migration on the heat transfer, pressure drop and entropy generation aspects of Fe₃O₄–water nanofluid flowing inside a ribbed-blocked microchannel with two different arrangements. The results are compared with those of the plain microchannel at different volume of flow rates and nanoparticle concentrations. ]In the following sections, first, the problem statement and governing equations are stated. Then, the grid study and validation are studied and at the last, the results are presented in the form of graphs and contours.