World Academy of Science, Engineering and Technology International Journal of Aerospace and Mechanical Engineering Vol:8, No:12, 2014

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1 World Academy of Scence, Engneerng and Technology Internatonal Journal of Aerospace and Mechancal Engneerng Entropy Generaton and Heat Transfer of Cu Water Nanoflud Mxed Convecton n a Cavty Mlk Bouchmel, Belgacem Nabl, Abbass Mohamed Ammar, Geudr Kamel, Omr Ahmed Internatonal Scence Index, Aerospace and Mechancal Engneerng waset.org/publcaton/ Abstract In ths numercal work, mxed convecton and entropy generaton of Cu water nanoflud n a ld-drven square cavty have been nvestgated numercally usng the Lattce Boltzmann Method. Horzontal walls of the cavty are adabatc and vertcal walls have constant temperature but dfferent values. The top wall has been consdered as movng from left to rght at a constant speed, U 0. The effects of dfferent parameters such as nanopartcle volume concentraton (0 0.05), Raylegh number ( ) and Reynolds numbers (1, 10 and 100) on the entropy generaton, flow and temperature felds are studed. The results have shown that addton of nanopartcles to the base flud affects the entropy generaton, flow pattern and thermal behavor especally at hgher Raylegh and low Reynolds numbers. For pure flud as well as nanoflud, the ncrease of Reynolds number ncreases the average Nusselt number and the total entropy generaton, lnearly. The maxmum entropy generaton occurs n nanoflud at low Raylegh number and at hgh Reynolds number. The mnmum entropy generaton occurs n pure flud at low Raylegh and Reynolds numbers. Also at hgher Reynolds number, the effect of Cu nanopartcles on enhancement of heat transfer was decreased because the effect of ld-drven cavty was ncreased. The present results are valdated by favorable comparsons wth prevously publshed results. The results of the problem are presented n graphcal and tabular forms and dscussed. Keywords Entropy generaton, mxed convecton, nanoflud, lattce Boltzmann method. O I. INTRODUCTION VER the past few years, the lattce Boltzmann method (LBM) has found wde-rangng applcatons n scence and engneerng [1]-[3]. Ths surge n nterest s manly attrbuted to ts ablty of smple and effcent computatonal procedure, even for complex geometres [4]-[6]. Therefore, the LBE method s able to smulate the complcated flud flows such as multphase flows, chemcally reactng flows and vsco-elastc non-newtonan flows. The term ''nanoflud" refers to a lqud contanng a dsperson of submcronc sold partcles (nanopartcles). The term was coned by Cho [7]. The characterstc feature of nanofluds s thermal conductvty M. Bouchmel s wth Unté de recherche: Matéraux, Energe et Energes Renouvelables (MEER), Faculté des Scences de Gafsa, BP : 19, Zarroug, 2112, Gafsa, Tunse (phone: ; e-mal: mlkbouchmel@yahoo.fr). A. Mohamed Ammar, and O. Ahmed are wth Unté de recherche: Matéraux, Energe et Energes Renouvelables (MEER), Faculté des Scences de Gafsa, BP: 19, Zarroug, 2112, Gafsa, Tunse (e-mal: abbassma@gmal.com, ahom206@yahoo.fr). B. Nabl s wth Unté de recherche Physque, Informatque et mathématques faculté de scences Gafsa, Unversté de Gafsa, Tunse (emal: fstuns@hotmal.fr). G. Kamel s wth Mechancal Engneerng Department, College of Engneerng and Islamc Archtecture, Umm Al-Qura Unversty, KSA (e-mal: kamelguedr@yahoo.fr). enhancement, a phenomenon observed by [8]. Ths s why ntensve researches focus on the heat transfer augmentaton utlzng nanofluds, and ther potental n coolng ndustry has been carred out recently [9]-[15] Natural convecton and forced convecton are two agents for convecton heat transfer. To enhance heat transfer, use of mxed convecton s preferred. Many numercal nvestgatons on enhancement of buoyancy, drven by natural heat transfer usng nanofluds n dfferent geometres have been reported [16]-[19]. Ld-drven mxed convecton flow s used for coolng electronc devces, lubrcaton purposes, dryng technologes and so on. Flud flow and heat transfer due to mxed convecton drven by buoyancy and shear n a cavty flled wth ether pure flud or nanoflud have been the subjects of some studes [20] [25]. There have been few numercal nvestgatons on entropy generaton of nanofluds n cavtes utlzed n mxed convecton. In ths study, n order to nvestgate entropy generaton due to heat transfer and to vscous effects, smlar to the geometry used by [26], a square cavty flled wth Cu water nanoflud wth a movng ld at constant velocty has been consdered. The effects of Reynolds number (Re) and Raylegh number (Ra) on the flud flow, heat transfer and entropy generaton have been nvestgated. Smulatons have been carred out for pure flud and Cu water nanoflud wth φ =5% for Ra = (10 4, 10 5 and 10 6 ) and Re = (1, 10 and 100). II. THE LATTICE BOLTZMANN METHOD The LBM used here s the same as that employed n [27]- [29]. The thermal LBM utlzes two dstrbuton functons f and g, for the flow and temperature felds respectvely. It uses modellng of movement of flud partcles to capture macroscopc flud quanttes such as velocty, pressure and temperature. In ths approach the flud doman s dscredted n Cartesan cells. Each cell holds a fxed number of dstrbuton functons, whch represents the number of flud partcles movng n these dscrete drectons. D2Q9 model for flow feld, D2Q4 model for temperature feld and nanopartcle concentraton are used n ths work. The weghtng factors and the dscrete partcle velocty vectors are dfferent for these two models and they are calculated wth (1)-(3) as follows: For the nne-mcroscopc veloctes model (D2Q9) used for densty dstrbuton: ω0 =, ω = for = 1,2,3,4 and ω = for = 5,6,7,8 (1) Internatonal Scholarly and Scentfc Research & Innovaton 8(12)

2 World Academy of Scence, Engneerng and Technology Internatonal Journal of Aerospace and Mechancal Engneerng Internatonal Scence Index, Aerospace and Mechancal Engneerng waset.org/publcaton/ = 0 c = (cos[ ( 1 ) π/2],sn[( 1) π/2]) c = 1,2,3,4 (2) 2( cos[ ( 5 ) π/2 + π/4],sn[( 5) π/2 + π/4] ) c = 5,6,7,8 For the four -mcroscopc veloctes model (D2Q4) used for nternal energy dstrbuton: The temperature weghtng factor for each drecton s equal to ' ω = 1/4. c ( ) = (cos[ 1 π/2],sn[( 1) π/2]) c = 1,2,3,4 The densty and dstrbuton functons.e. the f and g, are calculated by solvng the lattce Boltzmann equaton (LBE), whch s a specal dscretzaton of the knetc Boltzmann equaton. After ntroducng the BGK approxmaton, the general form of lattce Boltzmann equaton wth external force can be wrtten as: For the flow feld: 1 f + Δ, t t + Δ t = f, t f, t f, t + ΔtF ( ) eq ( x c ) ( x ) ( x ) ( x ) τ ν For the temperature feld: 1 g Δ, Δ g, g, g, ( ) eq ( x + c t t + t ) = ( x t ) ( x t ) ( x t ) τ α where t denotes lattce tme step, c s dscrete lattce velocty n drecton, F s the external force n drecton of lattce velocty, τ and ν τ α are the relaxaton tme for the flow and temperature felds, The knematc vscosty ν and thermal dffusvty α are respectvely related to the relaxaton tme by (6): 1 2 ν = τ ν cs Δt α = τ α cs Δt 2 where c s s the lattce speed of sound whch s equal to cs = c/ 3. Furthermore, the local equlbrum dstrbuton functons determne the type of problem that needs to be solved. They also model the equlbrum dstrbuton functons, whch are calculated wth (7) and (8) for flow and temperature felds respectvely. eq f ( ) ( ) 2 2 (3) (4) (5) (6) ω ρ c 1 u cu u (7) = c 2c 2c T c. u (8) 2 c eq ' g = ω ω s the weghtng factor for flow, ' ω s the weghtng factor for temperature and ρ s the lattce flud densty. In order to ncorporate buoyancy force n the model, the force term n (4) needs to be calculated n vertcal drecton (y) as: F = 3 ω. g. β. θ (9) y For natural convecton the Boussnesq approxmaton s appled and heat transfer s neglgble. To ensure that the code works n near ncompressble regme, the characterstc velocty of the flow for both natural ( V = β. g. TH. ) and force ( V = Re. ν H) regmes must be small compared wth the force flud speed of sound. The Reynolds number s gven by: 0 natural Re = u. H ν (10) Fnally, macroscopc quanttes ρ, u and T can be calculated respectvely by (11)-(13). ρ = f j j y (11) ρ u = f c (12) T = (13) g For pure flud n the absence of nanopartcles n the enclosure, the governng equatons are (4)-(13). However for modelng the nanoflud because of changng the flud thermal conductvty, densty, heat capactance and thermal expanson, some of the governng equatons should be changed. The thermal dffusvty s wrtten as: knf α = (14) nf ( ρc ) The effect of densty at reference temperature s gven by: p nf ρ = (1 φ) ρ + φρ (15) nf f p And the heat capactance and thermal expanson of nanoflud can be gven as [22]: ( ρc) = (1 φ)( ρc ) + φ( ρc ) (16) p nf p f p p ( ρβ) = (1 φ)( ρβ) + φ( ρβ) (17) nf f p In the above equatons φ s the sold volume fracton, ρ s the densty, α s the thermal dffusvty, c p s the specfc heat at constant pressure and β s the thermal expanson coeffcent. Internatonal Scholarly and Scentfc Research & Innovaton 8(12)

3 World Academy of Scence, Engneerng and Technology Internatonal Journal of Aerospace and Mechancal Engneerng TABLE I THERMO PHYSICAL PROPERTIES OF FLUID AND NANOPARTICLES Physcal Propertes Flud phase (Water) Cu C p(j/kgk) ρ (kg/m 3 ) k (W/mK) β 10-5 (1/K) The effectve dynamc vscosty and thermal conductvty of the nanoflud as gven by (18) and (19) [30]: µ µ nf = (1 φ) f 2.5 kp + 2kf 2 φ( kf kp) knf = kf k + 2 k + φ( k k ) P f f P (18) (19) In the convecton process, the entropy generaton s assocated to the heat transfer and to the flud flow frcton. Accordng to [31], the local entropy generaton (s gen ) can be determned by: Internatonal Scence Index, Aerospace and Mechancal Engneerng waset.org/publcaton/ where T ( T T ) s ''' gen = +. 0 H C k nf T T µ nf u v u v = T0 x y T0 x y x y The frst term n (12) represents the dmensonal entropy generaton due to heat transfer (s gen,h ), whle the second term represents the dmensonal entropy generaton due to the vscous effects of the flud (s gen,μ ). III. NON-DIMENSIONAL PARAMETERS Raylegh number, Prandtl number and vscosty are calculated from the defnton of these non-dmensonal parameters [32]. gβ 3 fh ( Th Tc) Ra = (21) ν α f f νf Pr =, Pr ν f = NMac (22) s α Ra f Mach number should be less than Ma = 0.3 to nsure an ncompressble flow. Therefore, n the present study, Mach number was fxed at Ma = 0.1. The local Nusselt number, the local Sherwood number and ther average values at the left walls are calculated as: Nu k H nf θ 1 nf θ l =, Nul = L kf X k x 0 0 f X = x= 0 IV. VALIDATION OF THE NUMERICAL CODE k (23) Fg. 1 shows a two-dmensonal square cavty wth the aspect rato equal to unty. The heght of the cavty s H and ts wdth s W. The cavty s flled ether wth pure water or wth a suspenson of copper nanopartcles n water wth a volume fracton of φ. The left and rght vertcal walls are at hot and cold temperatures, respectvely. The two horzontal walls are nsulated and the top wall sldes from left to rght wth unform velocty. The thermophyscal propertes of nanopartcles and flud shown n Table I are assumed constant, evaluated at the reference temperature. It s further assumed that the Boussnesq approxmaton s vald for buoyancy force. H A B T h Insulated Water + nanopartcles Insulated Fg. 1 Geometry and boundary condtons cavty (20) To valdate the numercal smulaton, the results for natural convecton flow n an enclosed cavty flled by nanoflud have been compared wth those obtaned by [33]. The horzontal and vertcal velocty components on the vertcal and horzontal mddle lnes, presented n Fg. 2, show good agreement wth those of [33]. In order to verfy the accuracy of streamlnes obtaned the confguraton of the cavty problem of [26] was consdered. The streamlnes for ths cavty problem have been compared n Fg. 3 showng very good agreement. In order to valdate the accuracy of entropy generaton, obtaned n Fg. 4 for the cavty problem of [34] at two Ra and φ values, we have presented the present results of contours of total entropy generaton of base flud and of Cu- Water nanoflud. Based on the aforementoned comparsons, the developed code s relable for studyng mxed convecton of a nanoflud confned n a cavty. H T c D C Internatonal Scholarly and Scentfc Research & Innovaton 8(12)

4 World Academy of Scence, Engneerng and Technology Internatonal Journal of Aerospace and Mechancal Engneerng Khorasanzadeh et al. [34] Present work Internatonal Scence Index, Aerospace and Mechancal Engneerng waset.org/publcaton/ Fg. 2 U velocty at X = 0.5. V velocty at Y = 0.5 comparson wth [33] Nemate et al. [26] Present work Fg. 3 Valdaton of Streamlnes, Ra=10 4, Re=10 φ=0.0, CuO, φ=0.05 Fg. 3 Valdaton of Contours of total entropy generaton for base flud (sold lnes) and nanoflud wth φ = 5% (dashed lnes) at dfferent Ra and Re=1. Ra=10 4, Ra =10 6 V. RESULTS AND DISCUSSION Fg. 5 demonstrates that the streamlnes are mostly symmetrc, showng that the effect of natural convecton flow domnates ld-drven effects at Ra = As can be seen from Fg. 5, use of nanoflud has not changed the flow pattern but has augmented the flow ntensty, so that the value of the stream functon at the center of the cavty has changed from 0.8 to 1.1. As the value of Ra ncreases to 10 6, the ntensty of buoyancy wthn the cavty ncreases such that the effect of ld drven flow s neglgble. Also, the effect of the presence of nanopartcles on the thermal feld, and temperature dstrbuton contours, for nanoflud overlad on that for pure flud, the streamlnes and sotherms are presented n Fg. 5 for Re = 10, Ra = 10 5 and As can be seen, use of nanoflud at Ra of 10 5 has more effect on ncreasng the heat penetraton, because of the most effectve role of the conducton heat transfer. The effect of conducton heat transfer decreases wth the ncrease n Ra, so the nanoflud has a smaller effect on the thermal dstrbuton. To study the effect of the presence of nanopartcles on the streamlnes, sotherms, for nanoflud and for pure flud are presented n Fg. 6 for Re = 10 and 100 and Ra = As can be seen the ncrease n Re augments the ld-drven forced convecton flow and for Re = 100, the effect of ld-drven flow s more domnant. In ths case, the nanoflud does not have a consderable effect on the flow pattern because the buoyancy effect s nsgnfcant. Internatonal Scholarly and Scentfc Research & Innovaton 8(12)

5 World Academy of Scence, Engneerng and Technology Internatonal Journal of Aerospace and Mechancal Engneerng Internatonal Scence Index, Aerospace and Mechancal Engneerng waset.org/publcaton/ Isotherms Streamlnes Fg. 5 Streamlnes and Isotherms for base flud (sold lnes) and nanoflud wth φ = 5% (dashed lnes) at Re = 10, Ra=10 4, Ra =10 6 Streamlnes Isotherms Fg. 6 Streamlnes and Isotherms for base flud (sold lnes) and nanoflud wth φ = 5% (dashed lnes) at Ra=10 4, Re = 10, Re = 100 The average Nusselt number (Nu) on the left hot wall n terms of Re s shown n Fg. 7. The use of nanoflud, whch ncreases the flow ntensty, nduces the rate of heat transfer, thus ncreases the Nu. Also ncreasng Re, meanng hgher velocty of the top ld, ncreases forced convecton and hence the Nu. Except for the Ra = 10 4, ths ncrease seems to be not lnear. Increasng Ra ncreases the Nu sharply for pure flud as well as nanoflud and ths ncrease s lnear. However, use of nanoflud nstead of pure flud causes a greater ncrease of Nu, such that the relatve ncrease s 52% at Ra = 10 6 and 28% at Ra = Fg. 7 Average Nusselt number on the left hot wall Fg. 8 shows the contours of total entropy generaton at Re = 1 and 100 for Ra = 10 4 and 10 6 for pure flud as well as nanoflud. Although the symmetrcal shape of contours for Re =1 has remaned unchanged, the total entropy generaton has ncreased for nanoflud except n the vcnty of nsulated walls. At Re = 100 and at Ra = 10 4 the symmetry does not exst anymore, but by ncreasng the Ra to 10 6 a change toward symmetry s somehow observed. Ths s the sgn of the mportance of effects of natural convecton compared to forced convecton. Ra = 10 4 Ra = 10 6 (c) Fg. 8 Contours of total entropy generaton for base flud (sold lnes) and nanoflud wth φ = 5% (dashed lnes) at dfferent Ra and Re At Re = 100 and Ra = 10 4 from Fg. 8 (c) t s seen that, due to forced vscous effects, the ntensty of contours s pronounced at the upper edge. By ncreasng Ra to 10 6 (Fg. 8 (d)) ths ntensty s also taken to the vcnty of the hot and cold walls. From Fgs. 8 -(c) t s seen that at the vcnty of (d) Internatonal Scholarly and Scentfc Research & Innovaton 8(12)

6 World Academy of Scence, Engneerng and Technology Internatonal Journal of Aerospace and Mechancal Engneerng Internatonal Scence Index, Aerospace and Mechancal Engneerng waset.org/publcaton/ the walls the ntensty of contours s generally pronounced such that at hgher Ra numbers ths ntensty s observed close to the vertcal walls and at hgher Re numbers but low Ra numbers close to the movng top ld. Fg. 9 Total entropy generaton VI. CONCLUSION The lattce Boltzman method s used to nvestgate mxed convecton of cu water nanoflud n a cavty. The LBM results are compared wth the exstng conventonal CFD results and a good agreement s observed. The effects of the pertnent parameters such as Raylegh number and Reynolds number and nanopartcle volume fracton on thermal flow characterstcs and on entropy generaton have been nvestgated for a ld-drven cavty. Ths nvestgaton was performed for varous mentoned parameters and some conclusons were summarzed as follows: The use of nanoflud causes a hgher ntensty flow and thus nduces the heat transfer and produces a hgher Nu. Increasng the values of nanopartcle volume fracton, the flow strength wll be reduced n the cavty. Increasng the Reynolds numbers leads to a decrease n the effect of nanopartcle volume fracton because the effect of ld-drven cavty s ncreased. In genera thel ncrease of Re, Ra or use of nanoflud nstead of pure flud are resulted n hgher Nu. Increase of the Re results, ncreases both terms of entropy generaton. Except at Re = 100, the ncrease of Ra results, ncreases total entropy generaton. The maxmum and mnmum entropy generatons occur for nanoflud and pure flud, respectvely, use of nanoflud nduces the heat transfer rate more than ncreasng entropy generaton. At Ra = 10 4, the change of Re from 1 to 100 ncreases Nu almost100% and ncreases the total entropy generaton almost 900%, whle the change of Re from 1 to 10 ncreases Nu 23% but total entropy generaton only 40%. At hgher Ra (10 5, 10 6 ) numbers, ncrease Re has a better effect n terms of enhanced heat transfer n comparson wth ncreased entropy generaton. REFERENCES [1] M. Aghajan Delavar, M. Farhad, K. Sedgh, Effect of the heater locaton on heat transfer and entropy generaton n the cavty usng the lattce Boltzmann method, Heat Trans. Res, vol. 40, 2009, pp [2] E. Fattah, M. Farhad, K. Sedgh, Lattce Boltzmann smulaton of natural convecton heat transfer n eccentrc annulus, Int. J. Therm. Sc, vol. 49, 2010, pp [3] H. Huang, Z. L, S. Lu, X.Y. Lu, Shan-and-Chen-type multphase lattce Boltzmann study of vscous couplng effects for two-phase flow n porous meda, Int. J. Numercal Methods Fluds, vol. 61, 2009, pp [4] M. Mahmod, S. M. 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