Journal of Applied Fluid Mechanics, Vol. 9, No. 5, pp. 2177-2186, 2016. Available online at www.jafmonline.net, ISSN 1735-3572, EISSN 1735-3645. DOI: 10.18869/acadpub.jafm.68.236.25506 Numerical Study of Natural Convection and Entropy Generation of Al2O3-Water Nanofluid within a Cavity Equipped with a Conductive Baffle L. Kolsi College of Engineering, Mechanical Engineering Department, Haïl University, Haïl City, Saudi Arabia Unité de Métrologie et des Systèmes Energétiques, Ecole Nationale d’Ingénieurs, 5000 Monastir, University of Monastir, Tunisia Email: [email protected] (Received August 16, 2015; accepted September 20, 2015) ABSTRACT Heat transfer, fluid flow and entropy generation due to buoyancy forces in a 2-D enclosure equipped with a conductive baffle and containing Al2O3nanofluid is carried out using different conductivities of baffle and different concentrations of nanoparticles. The bottom wall is subjected to constant hot temperature. The right and left vertical walls are maintained at lower temperature and the top wall is insulated. The finite volume method is used to solve the governing equations and calculations were performed for Rayleigh number from 103 to 106, thermal conductivity ratio from 0.01 to 100 and volume fraction of nanoparticles from 0 to 0.2. An increase in mean Nusselt number and a decrease of the total entropy generation were found with the increase of volume fraction of nanoparticles for the whole range of Rayleigh number. Keywords: Natural convection; Nanofluids; Conductive baffle. NOMENCLATURE Be Bejan number density Cp specific heat at constant pressure dynamic viscosity g gravitational acceleration kinematic viscosity k thermal conductivity nanoparticle or solid volume n unit vector normal to the wall. N dimensionless local generated entropy fraction s irreversibility coefficient Nu local Nusselt number Pr Prandtl number dimensionless stream function Ra Rayleigh number Rc thermal conductivity ratio dimensionless vorticity S ' generated entropy T dimensionless temperature gen difference t dimensionless time T dimensionless temperature Subscripts T ' cold temperature av average c x, y, z Cartesian coordinates hot temperature T 'h fr friction To bulk temperature f fluid V dimensionless velocity vector m mean or average W enclosure width and height nf nanofluid x, y, z dimensionless Cartesian coordinates s solid th thermal tot total Thermal diffusivity Thermal expansion coefficient Superscript ‘ dimensional variable 2177 L. Kolsi/JAFM, Vol. 9, No. 5, pp. 2177-2186, 2016. 1. INTRODUCTION total irreversibility) reduces as the Rayleigh number increases, but is insensitive to the volume fraction Natural convection is the main heat transfer mode of Nanoparticles. Parvin and Chamkha (2014) governing performances of numerous applications studied the laminar natural convection and entropy such as solar collectors, thermal storage systems generation in a nanofluid filled complex cavity with and cooling of electrical components. Cavities a horizontal and a vertical portion. The cavity is containing baffles or partitions have important filled with either water or Cu–water nanofluid. The implications in many branches of engineering effects on fluid flow, heat transfer and entropy particularly in microelectronics fabrication industry, generation at various Rayleigh numbers and solid especially for the cooling of components attached to volume fractions are investigated. The results show printed circuit boards, which are placed vertically. that using the nanofluid, generally leads to lowering Fluids used in thermal applications such as water the flow strength whereas increases the Nusselt and mineral oils have restricted designers, because number, entropy generation and the Bejan number. of their low thermal conductivity. Thus, nanofluids By increasing the Rayleigh number, the Nusselt were developed to improve the heat exchange number and Bejan number increase. The purpose of performances. Nanofluids are dilute liquid this work is to numerically investigate the nanofluid suspensions of nanoparticles with at least one free convection heat transfer in a square cavity critical dimension smaller than (100 nm) suspended equipped by a conductive baffle. The effects of the stably and uniformly in a base liquid. The use of Rayleigh number, conductivity ratio and volume nanoparticles having high thermal conductivity fraction of nanoparticles on the flow, heat transfer produces a high thermal conductivity nanofluid. and entropy generation have been examined. Many models have been proposed, focusing mainly on parameters such as geometry of nanoparticles 2. MATHEMATICAL FORMULATION (Hamilton (1962), Jang and Choi (2007), Chon et al. (2005)), Brownian effects (Houshang (2011), Figure 1 shows a schematic diagram of the Nasrin and Alim (2013), Jang and Choi (2004)), enclosure. The fluid in the enclosure is a water temperature and interaction between nanoparticles based nanofluid containing Al2O3 nanoparticles. and the base fluid (Amrollahi (2008), Chon et al. The nanofluid is assumed incompressible and (2005), Li and Peterson (2006)). The first model laminar. It is assumed that the water and the was proposed by Maxwell (1904) showing that nanoparticles are in thermal equilibrium. The thermal conductivity of nanofluid increases with thermo-physical properties of the nanofluid are increasing volume fraction of solid nanoparticles. presented in Table 1. Various research works have been related with the natural convection in enclosure filled with y Adiabatic nanofluids. Heat transfer enhancement in a two- dimensional enclosure utilizing nanofluids was investigated numerically by Khanafer et al. (2003). The results illustrate that the nanofluid heat transfer rate increases with an increase in the nanoparticles volume fraction. The presence of nanoparticles in Solid the fluid is found to alter the structure of the fluid flow. These main findings are obtainedin Cold wall variousother configurations considered by: Oztop Cold wall and Abu-Nada (2008), Mahmoudi et al. ((2010), Water-Al2O3 (2011)), Mahmoodi (2011), Mahmoodi and Sebdan Nanofluid (2012), Nasrin, and Alim (2013) and Hassan (2014). Kolsi et al. (2014) investigated numerically natural convection and entropy generation inside a x three-dimensional cubical enclosure filled with Hot wall water-Al2O3nanofluid. The second law of Fig.1. Problem geometry and coordinates. thermodynamics was applied to predict entropy generation rate. The results explain that the average Nusselt number increases when the solid volume Table 1 Thermophysical properties of water and fraction of nanoparticles and the Rayleigh number Al2O3 nanoparticle increase. Cho (2014) performed a numerical Physical properties Water Al2O3 investigation into the natural convection heat Cp (J/kg.K) 4179 765 transfer performance and entropy generation in a (kg/m3) 997.1 3970 partially-heated wavy-wall square cavity filled with Al2O3–water nanofluid. For a given Rayleigh k (W/m.K) 0.613 40 number, the mean Nusselt number increases and the x 107 (m2 /s) 1.47 131.7 total entropy generation reduces as the volume -5 fraction of nanoparticles increases. For a given x 10 (1 /K) 21 0.85 volume fraction of nanoparticles, the mean Nusselt number and total entropy generation both increase as the Rayleigh number increases. The Bejan The bottom wall is maintained at a constant number (ratio of heat transfer irreversibility to the temperature (Th) higher than the right and left walls 2178 L. Kolsi/JAFM, Vol. 9, No. 5, pp. 2177-2186, 2016. (Tc) and the top wall is adiabatic. The thermo- Pr 22 physical properties of the nanofluid are assumed to 22 0.25 s xy be constant except for the density variation in the 11 buoyancy term, which is approximated by the f Boussinesq model. The stream function-vorticity formulation is used to 11 T express the governing equations for the laminar and RaPr s 1 f x unsteady state natural convection: ff1 1 1 s s Vorticity Energy (8) ' ' ' 2' 2' u' v' nf t' x' y' 2 2 TTT nf x' y' (1) uv txy g s s 1 f f T' k nf nf x' k 22TT f 22 Energy ()c ps xy 1 2 2 ()c T ' T ' T ' T ' T ' pf u' v' t' x' y' nf 2 2 x' y' for the fluid zone (9) for the fluid zone (2) T 2T 2T R c 2 2 T' 2T' 2T' t x y s for the solid zone (2) 2 2 t' nf x' y' for the solid zone (9’) Kinematics Kinematics 22 (10) 2 2 22 ' ' k xy ' ; nf (3) 2 2 nf x' y' c p nf The foregoing dimensionless parameters are given as follows: The effective density of the nanofluid is given as: 3 f and g. f .T.W 1 (4) Pr Ra nf f s . f f f The heat capacitance of the nanofluid is expressed as (Abu-Nadu, (2008); Khanaferet al. (2003)): The energy equation (conduction) needs to be solved in the solid portion of the domain. The baffle (5) conductivity ks, is assumed constant. c p 1 c p c p nf f s At the solid-fluid interface the temperature and heat The effective thermal conductivity of the nanofluid flux must be continuous. The latter requirement is is approximated by the Maxwell–Garnetts model: mathematically expressed as: k k 2k 2k k nf s f f s (6) TT Rc (11) k f ks 2k f k f ks nnnf s The viscosity of the nanofluid is approximated as where is the thermal conductivity ratio Rc ks knf (Brinkman 1952): between the material of the baffle and the nanofluid. f (7) The associated initial and boundary conditions for nf 2.5 the problem considered are: 1 Scaling length, velocity and time by W , /W and For t 0 : 2 W / , and defining dimensionless temperature as T 0 (everywhere) T T'T'c / T'h T'c , the governing equations x y in dimensionless stream function-vorticity form are: For t 0: Vorticity On the vertical left and right walls: uv T 0 txy x On the horizontal bottom wall: ; 0 y T 1 2179 L. Kolsi/JAFM, Vol. 9, No. 5, pp. 2177-2186, 2016. On the horizontal top wall: the control-volume-finite-difference described by T Patankar (1980).