Strojniški vestnik - Journal of Mechanical Engineering 63(2017)6, 383-393 © 2017 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2017.4449 Original Scientific Paper Received for review: 2017-03-14 Received revised form: 2017-04-18 Accepted for publication: 2017-04-19 Mixed Convection Heat Transfer in a Square Lid-Driven Cavity Filled with Al2O3-Water Nanofluid Yazan Taamneh1* - Kahled Bataineh2 1 Jordan University of Science and Technology, Department of Aeronautical Engineering, Jordan 2 Jordan University of Science and Technology, Department of Mechanical Engineering, Jordan This work is focused on the steady laminar mixed convection flow in a lid-driven square cavity filled with Al2O3 water-nanofluid using computational fluid dynamics. The top lid of the cavity was kept at a higher temperature in comparison with the bottom wall and moving at a constant speed while the left and right walls were kept insulated. Simulations were performed using Fluent ver. 6.3 where the water based nanofluid was considered as a single phase. A parametric study was conducted, and the effects of the Richardson number (0.1 < Ri < 10), the volume fraction of the nanoparticle (0 < < < 0.04) on the fluid flow, and heat transfer inside the cavity were investigated. It was found that when (1 < Ri< 10) the average Nusselt number increases accordingly for the whole range of solid volume fraction of the nanofluid. The simulation results showed that the presence of nanoparticles in the base fluid increases the heat transfer rate. The variations of isotherm and streamline patterns inside the cavity with different volume fractions of nanoparticle and Richardson number were discussed and demonstrated. Keywords: mixed convection, nanofluid, square cavity, CFD, lid-driven Highlights • The research focused on steady laminar mixed convection flow in a lid-driven cavity. • The cavity was filled with Al2O3 water nanofluid. • The effect of the volume fraction of the nanoparticles was investigated. • The heat transfer rate was enhanced by increasing the solid volume fraction. 0 INTRODUCTION The combination of the mixed convection flow and the heat transfer analysis in a lid-driven cavity has recently received significant attention by many researchers due to its significance in many practical engineering and industrial applications. The flow and heat transfer due to mixed (free and forced) convection are a combination of the flow induced by the shear forces resulting from the motion of the upper lid and the bouncy forces due to the temperature gradient. The practical flow situation is considered to be a complex phenomenon because of the interaction and coupling of these effects. In addition, there are various combinations of imposed temperature gradients and many cavity configurations of a lid-driven cavity encountered in several engineering applications. Cha and Jaluria [1] studied in detail the impact of bounciness, velocities, and temperature fields on the heat transfer enhancement inside storage regions. Ghia et al. [2] investigated the driven flow in a square cavity at a high-Re fine-mesh flow. The solid particles are used as an additive suspended in the base fluid to enhance the heat transfer in a variety of applications, such as micro-electromechanical systems (MEMS), oil extraction and automobiles [3], electronic cooling, thermo-hydraulics of nuclear reactors, and solar ponds [4]. Kumar et al. [5] developed bactericidal coatings by using synthesized metal-nanoparticle (MNP)-embedded paint. They showed that the surfaces coated with silver-nanoparticle paint have excellent antimicrobial properties. Choi [6] proposed a new class of engineering fluids with superior nanofluid thermal conductivity by adding nanoparticles. Vajjha and Das [7] studied how nanofluid thermophysical properties varied with temperature and concentration. They analysed their effects on the heat transfer coefficient, the pumping power, and friction factor. They asserted that enhancing the heat transfer rate by adding solid materials reduces operation costs. Numerous experimental and numerical investigations have been conducted on the heat transfer enhancement using nanofluid. Kaheld and Vafai [8] investigated the heat transfer enhancement inside channels by commanding thermal dispersion influences. They found that the distribution of dispersive elements increases the heat transfer. Torrance et al. [9] examined early the fluid motion inside different aspect ratio cavities generated by a moving wall under natural and mixed convection. They revealed that when Grashof number increases especially in cavities with high aspect ratio, the buoyancy effect would be significant. The buoyancy-driven heat transfer enhancement of nanofluid in a two-dimensional enclosure has been analysed by Khanafer et al. [10]. Furthermore, various studies of *Corr. Author's Address: Jordan Univesity of Science and Technology, P. O. Box 3030, 22110 Irbid, Jordan, ymtaamneh@just.edu.jo 383 Strojniski vestnik - Journal of Mechanical Engineering 63(2017)6, 383-393 the thermophysical properties of nanofluid and energy transport were carried out. Jung et al. [11], Kang et al. [12], and Lee et al. [13] measured the effective thermal conductivity for different types of nanofluid using the transient hot wire method. Wang and Mujumdar [14] outlined the recent research on fluid flow and heat transfer characteristics of nanofluid in forced and free convection flows. Pak and Cho [15] showed experimentally that the convection heat transfer coefficient for Al2O3-water and TiO2-water nanofluid was enhanced by increasing the volume fraction as well as the average velocity. Xuan and Li [16] and [17] conducted an experimental study to investigate the effect of copper nanoparticles on the thermal conductivity of the nanofluid. Their results demonstrated that the suspended nanoparticles clearly enhanced the thermal conductivity of the base liquid. Furthermore, increasing the volume fraction of the nanoparticles leads to an increase of the thermal conductivity of the nanofluid. Abu-Nada and Oztop [18] carried out a numerical investigation of a mixed convection in an inclined square cavity of an aluminium-based nanofluid. They concluded that convection heat transfer was significantly enhanced by the existence of different types of nanoparticles. Tiwari and Das [19] confirmed that increasing the volume fraction of nanoparticles significantly enhances the convection heat transfer coefficient. They inspected the flow and heat transfer in a square enclosure utilizing the finite volume method by considering that the top and the bottom were insulated and the side walls remain at different constant temperatures. It is evident from the literature that the thermal conductivity of nanofluid highly depends on the volume fraction, the thermal conductivity (of both the base fluid and the nanoparticle material), the surface area, and the shape of the nanoparticles suspended in the base liquid. There are few studies in the literature that investigated the effect of a nanofluid in forced convection. In contrast, a large number of studies were devoted to the effect of nanoparticle in the natural convection. The free convection in a rectangular cavity was numerically studied by Jang and Choi [19] and Jou and Tzeng [21]. They presented their numerical results of the heat transfer enhancement of nanofluid in a two-dimensional cavity. The influence of gravity on sedimentation and the agglomeration of nanoparticle on a natural convection heat transfer was investigated by Jafari et al. [22]. They proposed a single-phase approach and a mixture model. Ismail et al. [23] studied the buoyancy forces as the driving heat transfer of nanofluid, using FLUENT. The effect of particle sizes and shapes on the heat transfer characteristics and the pressure losses were studied by Merilainen [24]. They determined that the average convective heat transfer coefficients of nanofluid were improved up to 40 % compared to clear fluids. The mixed convection flow and the heat transfer analyses in a lid-driven inclined enclosure filled with a nanofluid were conducted by Iwatsu et al. [25]. The flow and the heat transfer in a square cavity with insulated top and bottom walls, and differentially-heated moving sidewalls were also investigated using the finite volume approach by Mansour and Ahmed [26]. They investigated the effects of the Richardson number and the volume fraction of the nanoparticles on the heat transfer. It was observed that when the Richardson number equals unity, the average Nusselt number increased substantially with the increase in the volume fraction of the nanoparticles. The mixed convection flow in a lid-driven enclosure filled with a fluid-saturated porous medium was investigated by Abu-Nada and Chamakha [27]. They reported the effects of the Darcy and Richardson numbers on the flow and the heat transfer characteristics. A numerical study of laminar mixed convection in shallow driven cavities with a hot moving lid on top and cooled from the bottom has been carried out by Sharif [28]. It was observed that the average convection heat transfer increased slightly with the cavity inclination angle for the forced convection while it increased more significantly under natural convection. Oztop et al. [29] investigated the heat transfer and the fluid flow due to buoyancy forces in a partially heated enclosure using different nanofluids. Calculations were performed for different Rayleigh numbers, heights of heater, locations of heater, aspect ratios, and volume fractions of nanoparticles. They found that the heat transfer increases with increases of the Rayleigh number, the height of heater and the volume fraction of nanoparticles. Furthermore, the heat transfer enhancement was found to be dependent on the type of nanofluid and more pronounced at lower aspect ratios. Polidori et al. [30] utilized the integral formalism approach to investigate the natural convection heat transfer of a Newtonian nanofluid in a laminar external boundary-layer. They dealt with y-Al2O3/ water nanofluid whose Newtonian behaviour was experimentally confirmed for particle volume fractions less than 0.04. They concluded that generalized conclusions about the heat transfer enhancement with the use of a nanofluid needs to be carefully drawn. In addition, they found that the natural convection heat 384 Taamneh, Y. - Bataineh, K. Strojniški vestnik - Journal of Mechanical Engineering 63(2017)6, 383-393 transfer is not solely characterized by the nanofluid's effective thermal conductivity. Moreover, they concluded that the sensitivity to the used viscosity model cannot be ignored as it plays a key role in the heat transfer behaviour. Putra et al. [31] executed an experimental work on the natural convection of Al2O3 and CuO-water nanofluid inside a horizontal cylinder heated and cooled from both ends, respectively. They found that the presence of nanoparticles spoiled the natural convective heat transfer systematically. They also observed a systematic degradation of the natural convective heat transfer with increased concentrations of particles. Haddad et al. [32] and [33] studied numerically the natural convection heat transfer and fluid flow of CuO-water nanofluid in an open cavity heated from the bottom. They considered in their calculation the variation in the viscosity and the thermal conductivity. They found that the heat transfer decreases with increasing of solid volume fraction as a result of increasing the viscosity of the nanofluid. Although many studies are found in the literature investigating the heat transfer characteristics of nanofluids, there is a lack of studies devoted to combined mixed convection flow and heat transfer. Moreover, due to nanofluid's superior thermophysical properties, utilizing nanofluids in industrial applications has recently witnessed rapid growth. However, there is still no accurate understanding of the effect of using nanoparticles in the combined convection heat transfer. Therefore, the main objective of this study is to investigate numerically the combined convection flow and heat transfer in a square lid-driven cavity utilizing nanofluid. General correlations for the effective thermal conductivity, the viscosity, and the thermal expansion coefficient of a nanofluid were adopted in this study in terms of the volume fraction, the particle diameter, the temperature, and the base fluid physical properties. These theoretical models were employed utilizing a user-defined function (UDF) in Fluent. move at a constant speed The physical model considered in this study is shown in Fig. 1. The shape and the size of particles are assumed to be uniform with diameter equal to 100 nm. The fluid properties of the nanofluid vary when nanoparticles are suspended. In this study, the nanofluid is treated as a single phase. The thermophysical properties of the nanoparticles and the fluid phase at T = 300 K are presented in Table 1. Mixed convection flow and heat transfer in a square lid driven cavity are simulated by using the mass, momentum, and energy conservation equations. The governing non-linear partial differential equations can be written as follows: dU dV n -+ — = 0, dX dY U dU + V dU = -P + ± -f dX dY dX Re Vf peff U dV+V dV= -, Ri = , (6) + 1 MATHEMATICAL FORMULATION A steady, laminar, two-dimensional combined convective flow and heat transfer in a square lid-driven cavity filled with nanofluid is considered. The fluid in the cavity is water-based nanofluid containing Al2O3. The left and right walls of the cavity are insulated. The top wall is heated to temperature Th while the bottom wall is maintained at a temperature Tc such that Th > Tc. The top wall of the cavity is allowed to where L is the reference length, U^ is the reference velocity, and v is the kinematic viscosity. The Reynold's number Re is the ratio of inertial to viscous forces, which influences the fluid flow features within the cavity. The ratio of Gr/Re2 is the convection parameter and is called the Richardson number Ri. It measures the relative strength of the natural convection and the forced convection for the present problem. Mixed Convection Heat Transfer in a Square Lid-Driven Cavity Filled with Al2O3-Water Nanofluid 385 Strojniski vestnik - Journal of Mechanical Engineering 63(2017)6, 383-393 Table 1. Thermophysical properties of the base fluid and aluminium [26] Physical properties Water AI2O3 Cv [J/(kg K)] 4179 765 k [W/(m2-K)] 0.613 25 p [kg/m3] 997.1 3970 j [Pa-s] 0.000891 - P [1/K] 0.00021 0.0000017 1.1 Boundary Conditions A schematic of the configuration analysed in this study is shown in Fig. 1. The appropriate dimensionless boundary conditions for the present study are as follows: dû — = 0, U = V = 0, X = 0, dY dû — = 0, U = V = 0, X = 1, dY 0 = o, U = V = 0, Y = 0, 0 = 1, U = 1, V = 0, Y = 1. (7) coefficient of nanofluid were developed in terms of the solid volume fraction, the particle diameter, the temperature, and the base fluid physical properties, Kahnafer et al. [10]. These correlations have been implemented in Fluent using a user defined function. 1.2.1 Density The density of nanofluid is based on the physical principle of the mixture rule [10]. = (1- Vp )Pf VpP p' (8) Fig. 1. Schematic of the square lid-driven cavity where f and p refer to the fluid and nanoparticle respectively, q>p is the solid volume fraction of the nanoparticles, and p is the density. 1.2.2 Viscosity Different models of viscosity have been used by researchers to model the effective viscosity of nanofluid as a function of solid volume fraction. For low solid volume fraction, Einstein's model can be used to predict the viscosity of the nanofluid. It is worth mentioning that Einstein's model underestimates the nanofluid viscosity and does not consider the effect of temperature variations [34]. In this study, general correlation formulas to determine the effective viscosity of Al2O3-water considering the temperature effect proposed by Nguyen et al. [35] are used. Meff = (1.125 - 0.0007 x T , Vp = 1%, 20 < T [ oC]< 70, (9) = (2.1275 - 0.0215 x T + 0.0002 x T 2)^f, yp = 4%, 20 < T[ oC]< 70. (10) 1.2.3 Thermal Conductivity 1.2 Thermo-Physical Properties of A|2O3-Water Nanofluid The nanofluid mixture is considered as a single phase; thus, the nanoparticles and the base fluid are in a thermal equilibrium with each other and the relative velocity is negligible or equal to zero. Therefore, the effective thermophysical properties that depend mainly on the temperature, volume concentration of the nanoparticles, and the properties of the base fluid and the suspended particles are adopted in this study. General correlations for the effective thermal conductivity, the viscosity, and thermal expansion Numerous studies were conducted in the literature to model the thermal conductivity of nanofluid. A general thermal conductivity correlation for Al2O3-water nanofluid was proposed by Kahnafer et al. [10] for various temperatures, nanoparticles diameter, and solid volume fraction. The proposed correlation is given as follows: ^ = 1.0 +1.0112® + k p +2.4375® ( 47 d (nm) 0.0248® ). (11) p 0.613 386 Taamneh, Y. - Bataineh, K. Strojniški vestnik - Journal of Mechanical Engineering 63(2017)6, 383-393 1.2.4 Thermal Expansion Coefficient The effect of temperature and solid volume fraction on the thermal expansion coefficient of Al2O3-water nanofluid were investigated by Ho et al. [36]. They developed a correlation for the thermal expansion coefficient of Al2O3 water nanofluid as a function of the temperature and the solid volume fraction of nanoparticles. This correlation is given as: peff = (-0A79