Partition Effect on Thermo Magnetic Natural Convection and Entropy Generation in Inclined Porous Cavity

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1 Jurnal f Applied Fluid Mechanics, Vl. 9, N. 1, pp , 016. Available nline at ISSN , EISSN Partitin Effect n Therm Magnetic Natural Cnvectin and Entrpy Generatin in Inclined Prus Cavity H. Heidary 1, M. J. Kermani 1 and M. Pirmhammadi 1 Department f Mechanical Engineering, Amirkabir University f Technlgy (Tehran Plytechnic), Tehran, Iran Department f Mechanical Engineering, Pardis Branch, Islamic Azad University, Pardis New City, Tehran, Iran Crrespnding Authr mkermani@aut.ac.ir (Received August, 014; accepted Nvember 10, 014) ABSTRACT In this study natural cnvectin heat transfer fluid flw and entrpy generatin in a prus inclined cavity in the presence f unifrm magnetic field is studied numerically. Fr cntrl f heat transfer and entrpy generatin, ne r tw partitins are attached t hrizntal walls. The left wall f enclsure is heated with a sinusidal functin and right wall is cled isthermally. Hrizntal walls f the enclsure are adiabatic. The gverning equatins are numerically slved in the dmain by the cntrl vlume apprach based n the SIMPLE technique. The influence f rtmann number, inclinatin angle, partitin height, irreversibility distributin rati, and partitin lcatin is investigated n the flw and heat transfer characteristics and the entrpy generatin. The btained results indicated that the partitin, magnetic field and rtatin f enclsure can be used as cntrl elements fr heat transfer, fluid flw and entrpy generatin in prus medium. Keywrds: MHD; Free cnvectin; Partitin; Prus media. 1. INTRODUCTION Flw f an ambient fluid induced slely due t buyancy ccurs in several natural and engineering prcesses. Natural cnvectin in partitined rectangular prus cavity with varius bundary cnditins exists in many engineering applicatin like: high perfrmance insulatin fr buildings, chemical catalytic reactrs, the undergrund spread f pllutants, slar pwer cllectrs, and gethermal energy systems. Effect f nn-unifrm sinusidal heated wall in an pen square cavity with viscse fluid is studied numerically by Basak and Ry (005). Other studies f the natural cnvectin in enclsures with sinusidal temperature bundary cnditin are due t Bilgen and Yedder (007), Stresletten and Pp (1996), Saeid (005) and Heidary et al. (009). They studied natural cnvectin in prus cavity with sinusidal bttm wall temperature variatin. Basak et al. (006) investigated effects f sinusidal bundary cnditins in cavity filled with prus media withut prsity. Cntrl f natural cnvectin can be dne with bundary cnditin r adding divider fr disturbing fluid flw. In last decades, mst f the studies n partitin r divider were taken as nn-prus medium filled partitined rectangular r square enclsures. Als Varl et al. (007) investigated the effects f fin lcatin n the bttm wall f a triangular enclsure filled with prus media. The study f an electrically cnducting fluid in engineering applicatins is f cnsiderable interest, especially in metallurgical and metal wrking prcesses r in separatin f mlten metals frm nnmetallic inclusins by the applicatin f a magnetic field. The phase change prblem ccurs in casting, welding, melting purificatin f metals and in the frmatin f ice layers n the ceans as well as n aircraft surfaces. In that case the fluid experiences a Lrentz frce and its effect is t reduce the flw velcities. This in turn affects the rate f heat and mass transfer. The hmgeneity and quality f single crystals grwn frm dped semicnductr melts is f interest t the manufacturers f electrnic chips. Hence there has been increased interest in the flws f electrically cnducting fluid in cavities subjected t external magnetic field. Natural cnvectin flw in the presence f a magnetic field in enclsure heated frm ne side and cled frm the ther side was cnsidered by Ece and Büyük (006), Jue (006) and Pirmhammadi and Ghassemi (009). Free cnvectin in an pen cavity by lcating partitin is

2 (a) T/ y = 0, V = 0 ; C T/ y = 0, V = 0 ; (T H -T C )Sin( y/h) +T C, V = 0 ; W L T C, V = 0 ; (T H -T C )Sin( y/h) +T C, V = 0 ; L W L W T C, V = 0 ; T/ y = 0, V = 0 ; T/ y = 0, V = 0 ; C 1 C (b) Fig. 1. (a) - Schematic diagram f the cavity studied in the present cmputatin, (b) - schematic diagram f tw types f partitin lcatin studied in this paper. studied by Kandaswamy et al. (008) and Abdul keem et al. (008). Krakv and Nikifrv (005) and Grsan et al. (009) investigated the effect f magnetic field n free cnvectin heat transfer in prus cavity. Merrikh and Mhamad (000), Khanafer et al. (000) and Mahmud and Fraser (004) have simulated magnet hydrdynamics in prus dmain at different applicatins. Fundamentals f entrpy generatin are presented by Bejan (1994), Rsen (1999) and Narusawa (001). Magherbi et al. (00) numerically analyzed the entrpy generatin due t heat transfer and frictin in transient state fr laminar natural cnvectin. Varl et al. (008) have studied entrpy generatin due t cnjugate natural cnvectin heat transfer and fluid flw inside an enclsure with tw slid massive walls in vertical sides at different thicknesses. Mahmud et al. (007) studied flw, thermal, energy transfer, and entrpy generatin characteristics inside wavy enclsures filled with micrstructures. Famuri and Hman (008) investigated entrpy generatin fr natural cnvectin by heated partitins in a cavity. Kaluri and Basak (011 a,b) studied rle f entrpy generatin n thermal management during natural cnvectin in prus and nn-prus square cavities with distributed heat surces. Baytas (000) investigated entrpy generatin distributin accrding t inclinatin angle fr saturated prus cavity. The imprtance f thermal bundary cnditins in heat transfer and entrpy generatin fr natural cnvectin inside a prus enclsure investigated by Zahmatkesh (008). The effect f magnetic field n entrpy generatin at the nset f natural cnvectin was studied by Magherbi et al. (010). Mahmud and Fraser (004) investigated the effect f magnethydrdynamic free cnvectin and entrpy generatin in a square prus cavity. T the best f ur knwledge n cmprehensive mdel has been published yet t study natural cnvectin n cntrlling heat transfer and entrpy generatin by including rectangular partitin in prus inclined cavity under magnetic field. In the present study, natural cnvectin in an inclined cavity filled with a prus medium cled frm right wall and heated frm the left is analyzed numerically, while flw field is under magnetic field. Als hrizntal walls are assumed adiabatic. Because cnstant thermal bundary cnditin usually desn t ccur in nature, the ht wall temperature is assumed t be nn-unifrm temperature distributin prescribed at the left wall. But the difference between unifrm and nnunifrm bundary cnditins has nt been studied in this paper. We have studied the effects f nnunifrm bundary cnditin in ur earlier paper (009). The main bjective f this study is t cntrl flw pattern, heat transfer and entrpy generatin in the inclined prus enclsure under magnetic field with ne r tw partitin attached t the hrizntal wall. Fr simulating f prus media, Darcy-Brinckman mdel is assumed t hld. 10

3 . MATHEMATICAL ANALYSIS A schematic diagram f a tw-dimensinal inclined prus cavity under magnetic field is shwn in Fig. 1. It is assumed that the right wall f the cavity is cled t the cnstant temperature T C and the left wall is heated t the nn-unifrm temperature ( T HTC) Sin( y/ H) TC, where T H > T C, and the hrizntal walls are adiabatic. The interface between the partitin and the prus media is set t adiabatic bundary. In the prus medium, Darcy-Brinckman mdel is assumed t hld, and the fluid is assumed t be a nrmal Bussinesq fluid. With these assumptins, the cntinuity, mmentum and energy equatins fr steady, tw-dimensinal flw in an istrpic and hmgeneus prus medium under magnetic field are: u v 0 (1) x y 1 u u 1 p u u u v x y x x y () u g.sin. T Tc K 1 v v 1 p v v u v x y y x y () B.cs. 0 v v g T Tc K T u v T T T (4) x y x y where u and v are the seepage velcity cmpnents alng x- and y- axes, p is pressure, T is the fluid temperature. Als, K,, and are kinematic viscsity, permeability, inclinatin angle, prsity and density, respectively. B 0 is the magnitude f magnetic field and is the electrical cnductivity. The nn-dimensinal frms f the gverning equatins (1) (4) are: U V 0 (5) X Y 1 U U P Pr U U ( U V ) X Y X X Y Pr U RaPrsin Da (6) 1 V V P Pr V V ( U V ) X Y Y X Y Pr 1 V RaPrcs PrV Da (7) U V (8) X Y X Y where nn-dimensinal variables are defined as fllws: x y uh vh T T X, Y, U, V, C, H H TH TC ph K gth P,Pr, Da, Ra H f, kf ke, ke. kf 1. ks (9) The effect f the electrmagnetic field is intrduced int the equatins f mtin (7) thrugh rtmann number (). is defined as: B0H (10) 1 It is nted that prv in equatin (7) is achieved by simplifying the Lrentz frce term ( J B ) using cnstant magnetic field. Bundary cnditins as shwn in Fig. 1 are: Left wall U(0, Y) 0, V(0, Y) 0, Right wall U(1, Y) 0, V(1, Y) 0, Tp wall U( X,1) 0, V( X,1) 0, Bttm wall U( X,0) 0, V( X,0) 0, On the Partitin: U( X, Y) 0, V( X, Y) 0, And: Left wall (0, Y) SinY, Right wall (1, Y ) 0, Tp wall ( X,1)/ Y 0, Bttm wall ( X,0)/ Y 0, On the Partitin: ( XY, )/ n 0; The heat transfer cefficient in terms f the lcal Nusselt number (Nu y ) and average Nusselt number ( Nu ) at the left wall are defined by: 1 Nuy, Nu Nu 0 ydy X (11) X 0 Als dimensinless temperature cnturs (θ) and streamline cnturs (ψ) are depicted in result sectin. The stream functin ψ is defined as v / x and u / y. The vlumetric entrpy generatin can be btained frm the equatin (1): ''' k f B0 v Sgen T u v T0 KT0 T0 (1) where u and v are seepage velcity (Nield (1999)). The dimensinless frm f entrpy generatin ''' rate S is termed as entrpy generatin number. gen Entrpy generatin number (OEG) is the rati between the vlumetric entrpy generatin rate ''' ''' S gen and a characteristic transfer rate S 0. The characteristic transfer rate fr the present prblem can be estimated frm the fllwing equatin: T ''' kf S0 (1) H T 0 S the dimensinless verall entrpy generatin 11

4 (OEG) can be expressed as: ''' S gen OEG ''' S0 X Y V U V * Where * K * Da. ; B0 r * Da B0H (14) (15) where * is rtmann number in case f prus media. The nn-dimensinal vlumetric entrpy generatin due t heat transfer irreversibilityhti and fluid frictinal irreversibility FFI can be btained by the fllwing equatins: HTI (16) X Y FFI U V * V (17) where, U, V, X, Y are the dimensinless temperature, velcity cmpnents and Cartesian crdinates respectively and is irreversibility distributin rati: T T ; H T T C (18) k f K( T) The verall entrpy generatin (OEG) in the flw field can be btained by: OEG HTI FFI (19) The Bejan number (Be) which describes the cntributin f heat transfer entrpy n verall entrpy generatin is defined by: HTI Be (0) FFI HTI On the ther hand, Bejan number (Be) is the rati f HTI t the ttal entrpy generatin (OEG). Bejan number ranges frm 0 t 1. Accrdingly, Be = 1 is the limit at which the heat transfer irreversibility dminates, Be = 0 is the ppsite limit at which the irreversibility is dminated by fluid frictin effects, and Be = 0.5 is the case in which the heat transfer and fluid frictin entrpy generatin rates are equal.. NUMERICAL PROCEDURES This cde uses Finite Vlume methd and the SIMPLE algrithm develped by Patankar and Spalding (197) fr discretizing the gverning equatins f flw and reslving the pressurevelcity cupling system. In additin, all the variables are stred in same ndes by using cllcated grid. This methd was suggested by Rhie and Chw (198). Cllcated grid has varius advantages ver the staggered grid, e.g. the cntrl vlumes fr all variables cincide with the bundaries f the slutin dmain, facilitating the enfrcement f bundary cnditins, and giving a simplified data strage structure. The diffusin term f the equatins is discretized using a central difference algrithm. As the cnvergence criterin, 10-5 is chsen fr all dependent variables, where the cmputatin is terminated n n1 n 5 if i, ji, j i, j10. Here stands i, j i, j fr either temperature r velcity cmpnents, and n dentes the iteratin step. Table 1 shws the grid-independency test in this study. Fur grid sizes (, 64 64, , and 18 18) are chsen fr analysis. Average Nusselt number fr all fur grid sizes are mnitred at Ra = , = 50, 0 and in case f tw partitins. The magnitude f average Nusselt number at grids shws a very little difference with the result btained at grids (0.%). S we chse a grid size f fr ur calculatin in this paper. Table 1 Validatins Grid independency test fr Ra = , = 50, and tw partitins Grid dimensin (X by Y) 0 Average Nusselt number Difference with previus carse mesh (%) Table Validatins: cmparisn f average Nusselt number btained frm the present cmputatin and that f the literature fr a prus enclsure (cavity) at varius Ra, Da = 10 - and = 0.9 Re Present study Nithiarasu et al. (1997) Deviatin % (Abs) RESULTS AND DISCUSSION Schematic f the cmputatinal dmain is shwn in Figs. 1-(a) and (b). Fig. 1-(b) shws tw types f partitin lcatin studied in this paper. In rder t assess the accuracy f ur numerical prcedure, we have tested ur algrithm fr the classical natural cnvectin prblem in prus and nn-prus cavity with adiabatic tp and bttm walls and differentially heated side walls. Fr the 1

5 / y = 0, V = 0 ; Clear Regin (Cavity) B =0, V=0; =1, V=0; g / y = 0, V= 0 ; (a) Streamline, Present wrk Streamline, Sarris et al. (006) Istherm, Present wrk Istherm, Sarris et al. (006) (b) Ra = 7 10, = 5 Streamline, Present wrk Streamline, Sarris et al. (006) Istherm, Present wrk Istherm, Sarris et al. (006) C (c) Ra = , = 100 Fig.. Validatins; (a) - schematic f the cmputatinal dmain with the specified bundary cnditins fr a buyancy driven flw thrugh square cavity under magnetic field, (b) - cmparisn f present cde with the results btained frm Sarris (006) et al. at Ra = 7 10 and = 5 in cavity, (c) - cmparisn f present cde with the results btained frm Sarris et al. (006) at Ra = and = 100. side walls, we used = 0 and 1, T T where C in which the subscripts C and H TH TC refer t cld and ht walls, respectively. The cmparisn f streamline cnturs and istherm lines btained frm the present cde and thse f Sarris et al. (006) fr natural cnvectin thrugh the enclsure under magnetic field (see Fig. -(a)) are depicted at Ra = 7 10, = 5 and Ra = , = 100 in Figs. (b) and (c). The present numerical results shw excellent accuracy with the literature. Fr validatin f the present algrithm in the case f natural cnvectin in prus media, cmparisn f average Nu are perfrmed with thse f Nithiarasu et al. (1997) with Darcy-Brinckman mdel. These cmputatins are perfrmed at Ra = 10, 10 4, 10 5 and and at Da = 10 - and = 0.9. As it can be seen frm Table 1, there is very gd agreement between present results and data available in the literature. There are many prus enclsure prblems with magnetic effect, but mst f them are based n Darcy mdel; in ur study, the simulatin f prus media is based n Darcy- Brinckman mdel. We culd find n paper abut prus enclsure prblems with magnetic effect which is based n Darcy-Brinckman law. S we validated ur cmputatin fr tw abve cases. Fr cmprise the results f cmputer cde with the results f literature in prus enclsure prblems with magnetic effect, we validated results f present cde against results f Mahmud and Fraser (004): Cnsider a square prus enclsure with differentially heated side walls. Darcy s law is assumed t hld and magnetic frce is acting alng the directin f the gravity. Figure shws the cmparisn f ur cmputatin and Mahmud and Fraser (004) in Ra* = 100 and * = 0, 5 and 10. 1

6 Ra = 100* * = 0 Ra = 100* - * = 5 Ra = 100* - * = 10 Streamline, Mahmud and Fraser (004) Streamline, Present wrk Istherm, Mahmud and Fraser (004) Istherm, Present wrk Fig.. Validatins; cmparisn f present cde with the results btained frm Mahmud and Fraser (004) at Ra* = 100 and * = 0, 5 and 10 in cavity. Where Ra* is the prduct f Ra and Da and als * is the prduct f and Da. The cmparisn shws excellent accuracy f ur cmputer cde in which prus media cmply frm Darcy law. Entrpy generatin is investigated fr this prblem and effect f different parameters n entrpy generatin is studied. In rder t assess the accuracy f ur numerical prcedure fr calculatin f entrpy generatin, validatin results can be seen in Fig.4. Figure 1 shws the cmputatinal dmain used in this study. As nted in this figure, the cmputatinal dmain cntains f prus inclined cavity with ne/tw rectangular partitins attached t adiabatic walls (see figure 1-(b)); where C 1 and C are partitin center distance frm the ht wall. In this study C 1 and C are cnsidered 0.5H and 0.5H respectively. Als W and L are cnsidered 0.H and 0.H respectively. The present cmputatins have been carried ut within the range f rtmann number : 0 150, inclinatin angle : 0 15, the partitin height L: 0 L 0.4H, and partitin lcatin are perfrmed t individually investigate the influence f each f these parameters. Darcy number (Da) and prsity ( ) f prus dmain is cnsidered 10-4 and 0.9, respectively. Prandtl number (Pr) is cnsidered unity. 14

7 The irreversibility distributin rati is taken equal t 10 - in all calculatins as given in Varl et al. (008). Anyhw we have studied the effect f the irreversibility distributin rati n verall entrpy generatin and Bejan number as shwn in Fig. 5 fr = 0.01, 0.001, and As seen in this figure, as increases, verall entrpy generatin increases, but Bejan number decreases. As shwn in this figure, at lw and mderate Ra, with magnetic frce, cnductin dminates. Mst f the cntributin n verall entrpy generatin cmes frm the heat transfer irreversibility. S, Bejan number shws a value clser t 1 and the variatin f OEG with increasing Ra is insignificant in lw Ra. A significant cntributin n OEG cmes frm the fluid frictin irreversibility (FFI) at higher Ra due t high cnvectin current. Figure 6 depicts the variatin f average Nusselt number versus height f partitin L: 0 L 0.4H and at varius rtmann number: = 0, 50, 100. In this case, ne partitin was attached t bttm wall f cavity (see Fig.1-(b)). It is bserved that as L increases, the Nusselt number decreases which indicates that the cnvectin heat transfer has been damped and this is due t the blckage effect. In each, by lcating f partitin with L = 0.4H, average Nu can decrease by 0%. Als frm this figure, it was cncluded that the magnetic field cnsiderably decreases the average Nusselt number and as the rtmann number increases, heat transfer frm vertical walls decreases. S flw extremity due t therm magnetic natural cnvectin decreases. In = 100, as partitin height increases, average Nu can decrease by 5%. Average Nusselt number = 0 = 50 = 100 Overall entrpy generatin (OEG) Bejan number (Be) Fig. 4. Validatin f entrpy generatin with Magherbi et al. (00) =0.01 = = = Ra x Ra x 10-6 =0.01 = = = Fig. 5. The effect f irreversibility distributin rati ( ) n verall entrpy generatin (OEG) and Bejan number (Be) at different Ra number with ne partitin Partitin height Fig. 6. Effect f partitin height n average Nusselt number at varius in Ra = Figures 7-(a) and (b) shw left wall average Nusselt number versus inclinatin angle in Ra = fr varius rtmann number: = 0, 50, 100 and 150 with 1 and partitins attached t hrizntal wall (see Fig. 1-(b)). These figures shw that as the rtmann number increases, heat transfer frm vertical walls decreases. S flw extremity due t therm magnetic natural cnvectin decreases. That is, the applicatin f a lngitudinal magnetic field results in a frce ppsite t the flw directin that tends t drag the flw and as strength f the magnetic field is increased, cnvectin is suppressed and the heat transfer in the enclsure decreases. As seen frm these figures, with increase f inclinatin angle, Nu number firstly increases, but after 0, it starts t decrease and als after = 105 Nu increases. In inclinatin angle abut = 90, average Nu fr ne and tw partitins has different trends (see figures 7-(a) and (b)). In case f tw partitins, Nu has lwest value. But in case f ne partitin, Nu is scillated and afterwards that increases t = 15. In this case, Nu in = 90 has lcal maximum. Als it's shwed that in Varius, average Nu versus inclinatin angle has same trend (see figures 7-(a) and (b) again). 15

8 Average Nusselt Number Average Nusselt number = 0 = 50 = 100 = Inclinatin angle () (a) One partitin attached t hrizntal wall 5.5 = 0 5 = 50 = = Inclinatin angle () (b) Tw partitins attached t bttm wall Fig. 7. The average Nusselt number versus inclinatin angle in Ra = , (a) - ne partitin attached t bttm wall, (b) - tw partitins attached t hrizntal walls. Figure 8 shws verall entrpy generatin, heat transfer entrpy generatin and Bejan number in varius inclinatin angle fr varius and Ra = with 1 and partitins attached t hrizntal walls. As seen these figures, as increases, because the cnvectin term becmes less effective, s heat transfer entrpy generatin (HTI) decreases. Therefre verall entrpy generatin (OEG) decreases t. Increasing in the value f has a tendency t slwdwn the fluid mvement inside the cavity, thus Bejan number enhances. These figures shw that verall entrpy generatin and heat transfer entrpy generatin diagram has same trend with the average Nusselt number diagram except in = 90 fr ne partitin. In each inclinatin angle, as Nu increases, heat transfer entrpy generatin enhances and therefre verall entrpy generatin (OEG) increases. But Bejan number diagram has reverse trend with entrpy generatin diagram. As nted in Fig. 7, in inclinatin angle between 0 and 45, OEG and HTI diagram has maximum value in case f ne and tw partitins. The minimum value f OEG and HTI diagram is in inclinatin angle abut 105 fr ne partitin and abut 90 fr tw partitins. Als in inclinatin angle abut 60, Bejan number diagram has minimum value in case f ne and tw partitins. The maximum value f Bejan number diagram is in inclinatin angle abut 105 fr ne partitin, while it is abut 90 fr the case f tw partitins. In the ther hand, in inclinatin angles which OEG and HTI diagram has lwest value, mst f the cntributin n verall entrpy generatin cmes frm the heat transfer irreversibility. S, Bejan number shws a higher value and in these angles, Be has maximum value. But in lcal maximum f OEG and HTI diagram, OEG and HTI curves have mre difference, s the effect f fluid frictin entrpy generatin increases and Be decreases. Istherms and streamlines cnturs fr Ra = with 1 and partitins attached t hrizntal walls depicted in Figs. 9 and 10 fr = 0 and 150. It is shwn that as increases the cnvectin term becmes less effective. As shwn these figures, in inclinatin angle equal t 90 with 1 partitin, tw vertices are frmed but with partitins and als in ther angles, ne primary vrtex is appeared in the enclsure. Als it is bserved that in = 0, 45 and 15 in the middle f left wall and in the tp f right wall thermal bundary layer is frmed but in = 90 fr ne partitin, this bundary layer is diminished. With cmparing f figures 7 t 10 in = 90, it culd be seen that with 1 partitin the average Nusselt number diagram has lcal maximum, because in this case, the number f stream line lps in stream line cnturs changes t tw lps and the average Nusselt number increases suddenly. But verall entrpy generatin in this case has lw value and Bejan number in this angle has high value. S when we need lcal maximum in heat transfer, additin f the partitin and rtating f cavity t 90 wuld be best methd. REFERENCES Abdul keem, A. K., S. Saravanan and P. Kandaswamy (008). Buyancy cnvectin in a square cavity with mutually rthgnal heat generating baffles. Internatinal Jurnal f Heat and Fluid Flw 9, Basak, T. and S. Ry (005). Finite element analysis f natural cnvectin flws in a square cavity with nn-unifrmly heated wall(s). Internatinal Jurnal f Engineering Science 4, Basak, T., S. Ry, T. Paul, and I. Pp (006). Natural cnvectin in a square cavity filled with a prus medium: Effects f varius thermal bundary cnditins. Internatinal Jurnal f Heat and Mass Transfer 49, Baytas, A. C. (000). Entrpy generatin fr natural cnvectin in an inclined prus cavity. Internatinal jurnal f Heat and Mass Transfer 4, Bejan, A. (1994). Entrpy Generatin Thrugh Heat and Fluid Flw, Jhn Wiley & Sns Bilgen, E. and R. B. Yedder (007) Natural cnvectin in enclsure with heating and cling by sinusidal temperature prfiles n ne side. Internatinal Jurnal f Heat and Mass Transfer 50,

9 Bejan number (a) One partitin attached t hrizntal wall = 0 = 50 = Inclinatin angle () (b) Tw partitins attached t hrizntal walls Bejan number = 0 = 50 = Inclinatin angle () Overall entrpy generatin = 0 = 50 = Inclinatin angle () Overallentrpy generatin = 0 = 50 = Inclinatin angle () Heat transfer irreversibility = 0 = 50 = Inclinatin angle () Heat transfer irreversibility 4 = 0 = 50.5 = Inclinatin angle () Fig. 8. The effect f inclinatin angle n verall entrpy generatin (OEG), heat transfer irreversibility (HTI) and Bejan number (Be), Ra =5 10 6, (a) - ne partitin attached t bttm wall, (b) - tw partitins attached t hrizntal walls. Ece, M. C. and E. Büyük (006). Natural cnvectin flw under a magnetic field in an inclined rectangular enclsure heated and cled n adjacent walls. Fluid Dynamics Researc 8, Famuri, M. and K. Hman, (008). Entrpy generatin fr natural cnvectin by heated partitins in a cavity. Internatinal Cmmunicatins in Heat and Mass Transfe 5, Grsan, T., C. Revnic, I. Pp and D. B. Ingham (009). Magnetic field and internal heat generatin effects n the free cnvectin in a rectangular cavity filled with a prus medium. Internatinal Jurnal f Heat and Mass Transfer 5, Heidary, H., M. Davdi and M. J. Kermani (009). Numerical slutin f free cnvectin in a rectangular cavity filled with a prus medium and nn unifrm bundary cnditin, Prc. 4 th Internatinal Cnference n Applicatin f Prus Media, Istanbul, Turkey. Jue, T. (006). Analysis f cmbined thermal and magnetic cnvectin ferrfluid flw in a cavity. Internatinal Cmmunicatins in Heat and Mass Transfer, Kaluri, R. S., and T. Basak (011). Rle f entrpy generatin n thermal management during natural cnvectin in prus square cavities with distributed heat surces. Chemical Engineering Science 66, Kaluri, R. S. and T. Basak (011). Analysis f entrpy generatin fr distributed heating in prcessing f materials by thermal cnvectin. Internatinal Jurnal f Heat and Mass Transfer 54, Kandaswamy, P., J. Lee, A. K. Abdul keem and S. Saravanan (008). Effect f baffle cavity ratis n buyancy cnvectin in a cavity with mutually rthgnal heated baffles. Internatinal Jurnal f Heat and Mass Transfer 51,

10 = 150 = 0 (a) Streamline Cnturs, One partitin attached t bttm wall 90, max , max , max , max , max , max , max , max 7.9 (b) Streamline Cnturs, Tw partitins attached t hrizntal walls 90, max 7. 90, max , max , max , max , max , max 7.5 0, max 18.0 Fig. 9. Streamlines cnturs fr = 00, 450, 900 and 150 in cunterclckwise directin fr Ra = fr = 0 and 150; (a) - ne partitin attached t bttm wall, (b) - tw partitins attached t hrizntal walls. Prceedings in Engineering Sciences 5, Khanafer, K., N. M. Al-Najem and M. M. ElRefaee (000). Natural Cnvectin in Tilted Prus Enclsures in the Presence f a Transverse Magnetic Field. Jurnal f prus media, Mahmud, S. and R. A. Fraser (004). Magnethydrdynamic free cnvectin and entrpy generatin in a square prus cavity. Internatinal Jurnal f Heat and Mass Transfer 47, Krakv, M., and I. V. Nikifrv (005). Therm magnetic cnvectin in a prus enclsure in the presence f uter unifrm magnetic field. Jurnal f Magnetism and Magnetic Materials 89, Mahmud, S., R. A. Fraser and I. Pp (007). Flw, thermal, energy transfer, and entrpy generatin characteristics inside wavy enclsures filled with micrstructures. Jurnal f Heat Transfer 19, Magherbi, M., H. Abbasi and A. Ben-Brahim (00). Entrpy generatin at the nset f natural cnvectin. Internatinal Jurnal f Heat and Mass Transfer 46, Merrikh, A. A. and A. Mhamad (000). Transient Natural Cnvectin in Differentially Heated Prus Enclsures. Jurnal f prus media. Magherbi, M., A. El Jery, N. Hiduri and A. Ben Brahim (010). Evanescent magnetic field effects n entrpy generatin at the nset f natural cnvectin. Sadhana - Academy Narusawa, U. (001). The secnd-law analysis f mixed cnvectin in rectangular ducts. Heat 18

11 = 150 = 0 (a) Istherm Cnturs, One partitin attached t bttm wall (b) Istherm Cnturs, Tw partitins attached t hrizntal walls Fig. 10. Istherm cnturs fr = 0 0, 45 0, 90 0 and 15 0 in cunterclckwise directin fr Ra = fr = 0 and 150; (a) - ne partitin attached t bttm wall, (b) - tw partitins attached t hrizntal walls. and Mass Transfer 7, Nield, D. A. (1999). Mdeling the effects f a magnetic field r rtatin n flw in a prus medium: mmentum equatin and anistrpic permeability analgy. Internatinal Jurnal f Heat and Mass Transfer 4, Nithiarasu, P., K. N. Seetharamu and T. Sundararaja (1997). Natural cnvective heat transfer in a fluid saturated variable prsity medium. Internatinal Jurnal f Heat and Mass Transfer 40, Patankar, S. V. and D. B. Spalding, (197). A calculatin prcedure fr heat, mass and mmentum transfer in three-dimensinal parablic flws. Internatinal Jurnal f Heat and Mass Transfer 15, Pirmhammadi, M. and M. Ghassemi (009). Effect f magnetic field n cnvectin heat transfer inside a tilted square enclsure. Internatinal Cmmunicatins in Heat and Mass Transfer 6, Rhie, C. M. and W. L. Chw (198). Numerical study f the turbulent flw past an airfil with trailing edge separatin. AIAA jurnal 1, Rsen, M. A. (1999). Secnd-law analysis: appraches and implicatins. Internatinal Jurnal f Energy Research, Saeid, N. H. (005). Natural cnvectin in prus 19

12 cavity with sinusidal bttm wall temperature variatin, Internatinal Cmmunicatins in Heat and Mass Transfer, Sarris, I. E., G. K. Ziks, A. P. Grecs and N. S. Vlachs (006). On the limits f validity f the lw magnetic Reynlds number apprximatin in MHD natural-cnvectin heat transfer. Numerical Heat Transfer 50, Stresletten, L. and I. Pp(1996)., Free cnvectin in a vertical prus layer with walls at nnunifrm temperature. Fluid Dynamic Research 17, Varl, Y., H. F. Oztp and A. Kca (008). Entrpy generatin due t cnjugate natural cnvectin in enclsures bunded by vertical slid walls with different thicknesses. Internatinal Cmmunicatins in Heat and Mass Transfer 5, Varl, Y., H. F. Oztp and A. Varl (007). Natural cnvectin in prus triangular enclsures with a slid adiabatic fin attached t the hrizntal wall. Internatinal Cmmunicatins in Heat and Mass Transfer 4, Zahmatkesh, I. (008). On the imprtance f thermal bundary cnditins in heat transfer and entrpy generatin fr natural cnvectin inside a prus enclsure. Internatinal Jurnal f Thermal Sciences 47,