Journal of Applied Science and Agriculture. The Effects Of Corrugated Geometry On Flow And Heat Transfer In Corrugated Channel Using Nanofluid

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1 Journal o Applied Science and Agriculture, 9() February 04, Pages: AENSI Journals Journal o Applied Science and Agriculture ISSN 86-9 Journal ome page: Te Eects O Corrugated Geometry On Flow And Heat Transer In Corrugated Cannel Using Nanoluid Alireza Falaat Department o Mecanics, Masar Branc, Islamic Azad University, Masar, Iran. A R T I C L E I N F O Article istory: Received 5 November 03 Received in revised orm 9 December 03 Accepted 6 December 03 Available online 0 Marc 04 Keywords: Laminar orced convection Corrugated cannel Nanoluid Heat transer enancement A B S T R A C T In tis paper, a numerical investigation is perormed to study te eects o corrugated geometry and nanoparticles volume ractions on eat transer and pressure drop troug corrugated cannel under constant eat lux boundary condition. Te governing equations or laminar low are discretized using inite volume metod and solved iteratively using SIMPLE algoritm. Te investigation covers tree dierent corrugated geometries wit Reynolds number and nanoparticles volume ractions in te ranges and 0-0. respectively. Te results indicate tat te Nusselt number increased wit increasing nanoparticles volume raction and Reynolds number and pressure drop increased wit Reynolds number. It is ound tat case 3 sows te best termal-ydraulic enancement actor in all ranges o Reynolds number compared wit oter cases. 04 AENSI Publiser All rigts reserved. To Cite Tis Article: Alireza Falaat., Te Eects O Corrugated Geometry On Flow And Heat Transer In Corrugated Cannel Using Nanoluid. J. Appl. Sci. & Agric., 9(): , 04 INTRODUCTION Te subject o enancement in eat transer is very important or eat transer devices. Te corrugated plate is a suitable tecnique to improve te termal perormance and provide iger compactness in eat excangers. Tere are many experimental and numerical studies on te eat transer and pressure drop in corrugated cannel. Laminar orced convection low and eat transer studied numerically in a wavy-wall cannel by Wang and Cen (00). Te low and eat transer in a cannel wit one-sided corrugated surace investigated numerically by Napon et al. (007). Te low and eat transer in sinusoidal and arc-saped cannel were numerically investigated by Baaidara et al. (005). Te governing equations were solved using inite volume metod (FVM). In teir study, tey ound tat te enancement in eat transer increases wit increasing Reynolds number or sinusoidal and arc-saped cannel coigurations. Napon (007) studied experimentally te eat transer caracteristics and pressure drop in cannel wit V corrugated upper and lower plates. In tis study investigated corrugated plates wit tree dierent corrugated tile angles o 0, 40 and 60 degrees. Result sowed tat te corrugated surace as signiicant eects on te enancement o eat transer and pressure drop. Islamoglu and Parmasizoglu (003 and 004) investigated numerically and experimentally te eect o cannel eigt on te eat transer enancement in a corrugated cannel. Moammed et al. (03) studied numerically orced turbulent convective low and eat transer in a corrugated cannel. In tis study, te corrugated cannel walls are eated at constant eat lux boundary conditions. Tey ound tat te cannel wit corrugated angle o 60 and corrugated eigt o.5 mm wit cannel eigt o 7.5 mm are te optimum parameters. All te experimental results ave demonstrated te enancement o te termal conductivity by addition o nanoparticles. Xuan and Li (003) experimentally studied te low and eat transer caracteristics or cu-water based nanoluids troug a plain tube wit a constant eat lux boundary condition. Tey ound tat te nanoluids give substantial enancement o eat transer rate compared to pure water. For an up to date review o eat transer in nanoluids one may reer to Das et al. (003). Amed et al. (03) investigated numerically laminar orced convection eat transer o cu water nanoluid in trapezoidal corrugated cannel under constant walls temperature boundary condition. Te eect o geometrical parameters, nanoparticle volume raction and Reynolds number on te velocity vectors, temperature contours, pressure drop and average Nusselt number investigated. Tey ound tat wit increasing nanoparticle volume raction and te amplitude o corrugated cannel increases average Nusselt number and increases pressure drop. Santra et al. (009) investigated numerically te eat transer o cu water nanoluid in a two dimensional parallel plat. Te governing equations or laminar low were discretized using inite volume metod. Tey ound tat te average Nusselt number and average wall sear stress increases wit te increase in nanoparticle volume raction. Raisi et al. (0) Corresponding Autor: Alireza Falaat, Mecanical Engineering Researcer and Lecturer, Department o Mecanics, Masar Branc; a.alaat@mriau.ac.ir, Iran, Tel:

2 409 Alireza Falaat, 04 Journal o Applied Science and Agriculture, 9() February 04, Pages: investigated numerically laminar orced convection eat transer o cu water nanoluid low in a microcannel. Tey ound tat te velocity and volume raction o nanoparticle ad great iluence on Nusselt number at ig Reynolds numbers. Experiments on eat transer due to natural convection wit nanoluid ave been studied by Putra et al. (003) and Wen and Ding (006). Tey ave observed tat rate o eat transer decreases wit increase in volume raction o nanoparticles. Te viscosity o tis nanoluid increases rapidly wit inclusion o nanoparticles as sear rate decreases. Amed et al. (0) studied numerically eat transer and pressure drop caracteristics o cu-water in corrugated cannel wit triangular corrugations under constant walls temperature boundary condition. Te governing equations solved by Finite Dierence (FD) metod. Tey ound tat te eat transer enancement increases wit increase in te nanoparticle volume raction and Reynolds number, wile tere is sligt increase in pressure drop. In tis study, te orced convection eat transer and pressure drop o cu water nanoluid in tree coigurations o triangular corrugated cannel is numerically studied or nanoparticle volume ractions and Reynolds number wit ranges and 0 0%, respectively. Te governing equation solved by Finite volume metod (FVM). Te eects o Reynolds number, nanoparticles volume raction and coigurations o corrugated cannel on Nusselt number and pressure drop are investigated. Matematical modeling: Pysical model: Te geometries o te present problem ave been sown in Figure. Te geometries consist o two dimensional symmetric triangular corrugated plates wit minimum eigt ( Hmin) and te maximum eigt ( H max) and te ratio o eigt is H max/ Hmin 6. Te widt o te duct is very large compared to te eigt. Te wall o cannel is consisting o a lat wall (adiabatic wall) and a corrugated wall (constant eat lux wall). Te axial lengt o eac cycle is (S) and te lengt o eac smoot adiabatic wall section is ( S ).Te total lengt o corrugated wall is six triangular corrugations. It can be assumed tat te low is steady, ully developed, laminar, incompressible, and two-dimensional. Te nanoluid in te cannel is Newtonian and assumed tat te luid pase and nanoparticles are in te termal equilibrium state and tey low wit te same velocity. Fig. : Scematic diagram o te corrugated cannels studied in te present computation Governing equations and Boundary condition: Te continuity, momentum, and energy equations or te laminar and steady state orced convection in te two-dimensional corrugated cannel can be written in dimensional orm as ollows (Santra et al. 009): u v 0 x y u u p ( u v ) u x y x () ()

3 40 Alireza Falaat, 04 Journal o Applied Science and Agriculture, 9() February 04, Pages: v v p (3) ( u v ) v x y y T T (4) ( u v ) T x y were u and v are te velocity components in te x and y directions, respectively. p is te pressure, T is te temperature. Te termo-pysical properties (Table. ) o te nanoluid are obtained rom te ollowing relations (Kanaer et al. 003): ( ) (5) p s ( c ) ( )( c ) ( c ) (6) s ( s) ( ) s ( ) ( c ) p.5 p s p s (7) (8) (9) Table : Termopysical properties o pure luid and nanoparticles Property Fluid pase(water) C P ( J / g K) ( g / m 3 ) ( W / m K) Solid pase (Cu) Te above equations can be converted to nondimensional orms using te ollowing nondimensional parameters. X x D, Y y D, U u u in, T T q L in, p P u Te governing equations are written in te ollowing dimensionless orm: in (0) U V 0 X Y U U U V X Y P X Re V V P U V X Y Y Re U V X Y P D D D ( ) ( ) P ( c ) ( c ) Re.5.5 T Pr U V Te boundary conditions or equations () (4) in te dimensionless orm are given by: () () (3) (4) At inlet: U, V 0, 0 (5) At outlet: U 0, 0 X X At smoot walls: U 0, V 0, 0 Y At corrugated walls: U 0, V 0, q q W

4 4 Alireza Falaat, 04 Journal o Applied Science and Agriculture, 9() February 04, Pages: Nu x Te local Nusselt number at te corrugated walls o cannel is deined as: ( x) D Local eat transer coeicient (x) can be evaluated as ollow:: q (7) ( x) Tw ( x) Tb ( x) were q represents te eat lux, T b (x) and T w (x) are te bul temperature and local wall temperature, respectively. Te average Nusselt number (Nu) at corrugated wall is determined by integrating Nu along te corrugated wall. 8S (8) Nu Nu x dx 6S S Te Reynolds number is deined as: (6) Re D u in D (9) Te ydraulic diameter is computed as (Incropera and Dewitt., 0): D H min H max (0) Te average value o Fanning riction actor and riction actor or corrugated cannel is (Incropera and Dewitt., 0): C u w m 4C () () were te ΔP is pressure drop in te corrugated cannel is deined as: P (6S) u D in () To estimate te enancement o eat transer between pure luid and nanoluid, a augmentation average Nusselt number ( Nu, a ) is deined as te ratio o Nusselt number at any volume raction o nanoparticles to tat o pure Water tat is: Nu, a Nu( ) Nu( 0) (3) Te eectiveness o using corrugated cannels was evaluated by studying by eat transer perormance ratio because te improvements in eat transer are also accompanied by increase in te rictional losses. Te termal-ydraulic enancement actor ( ) or pure water can be calculated using te predicted Nusselt numbers and riction actors as ollows: ( Nu / Nu o )( / ) 3 o Te value o Nusselt number in smoot cannel ( Nu o) and riction actor in smoot cannel ( o ) as given by many autors (Incropera and Dewitt., 0). (4)

5 4 Alireza Falaat, 04 Journal o Applied Science and Agriculture, 9() February 04, Pages: Numerical metod: Te governing equations, equations ()-(4), and te associated boundary conditions are solved numerically using te Finite volume metod (FVM) and solved iteratively using SIMPLE algoritm (Patanar, 980). Te governing equations are non-linear and coupled; te solution loop must be carried out iteratively in order to obtain a converged numerical solution. Discretization o te momentum and energy equations is perormed by a second order upwind sceme and pressure interpolation is provided by Standard sceme (Versteeg and Malalaseera., 995). Convergence criterion considered as residuals is admitted or momentum, continuity and energy equations it is lower tan 0-6. Grid independent study and validation: For te grid independence test, ive dierent grid arrangements into te tree case corrugated cannels are tested. Tey ave mes layout wit approximately 4900, 8000, 3500, 9500 and 9500 nodes, respectively. Te ort grid coiguration (9500 nodes) coirms te grid-independence and it is tereore used trougout te present study to get an acceptable compromise between te computational time and te result accuracy (see Figure ). To validate te numerical algoritm used in te present study, te local Nusselt number or cu-water low wit 5% nanoparticls volume raction troug a case3 was calculated and compared wit te numerical results o Amed et al. (0). Te comparison sows tat te results are in a good agreement as sown in Fig. 3a. Also, Fig. 3b sows te comparison o te present numerical results or Nusselt number troug a smoot cannel or pure water and cu-water low wit 5% nanoparticls volume raction wit te results o Santra et al. (009). Te comparison sows tat te results are also in a good agreement. Fig. : Grid point independence study or Re=500 Fig. 3a: Comparison o te local Nusselt number versus lengt wit te results o Amed et al(0) or case3 and nanoparticles volume raction 5%.

6 43 Alireza Falaat, 04 Journal o Applied Science and Agriculture, 9() February 04, Pages: Fig. 3b: Comparison o te Nusselt number versus Reynolds number wit te results o Santra et al. (009) or smoot cannel. Results: Figure 4 sows Comparison o te corrugated geometries o corrugated cannel on te streamlines and isoterms. Te igure sows tat geometry o corrugated surace o cannel as a signiicant eect on te cange in te low structure. Also it can be seen tat temperature gradient increases in case tan oter cases tus te enancement in eat transer is decreases in tis case. In addition recirculation zone near te wall in case lower tan oter cases, so te eat transer in cases and 3 is increases because recirculation zone near te wall in tese cases is bigger tan case. case case case 3 Fig. 4: Streamlines (let) and isoterms (rigt) or dierent cases at Re=400 and χ=5% Figure 5 sows variation o Nusselt number wit Reynolds number or dierent nanoparticles volume raction values in every case. It can be seen tat increasing nanoparticles volume raction enances te Nusselt number in all cases. In cases and 3, wit increasing te Reynolds number, te Nusselt number increases owever in case, te Nusselt number gradually increase wit increasing Reynolds number up to nearly Re=00, ater wic it trend to decrease up to nearly Re=400, ater tat it trend to increase.

7 44 Alireza Falaat, 04 Journal o Applied Science and Agriculture, 9() February 04, Pages: case case case 3 Fig. 5: Variation o Nusselt number wit Reynolds number or dierent nanoparticles volume raction values Figure 6 sows variation o Nusselt number wit Reynolds number or dierent cases and nanoparticles volume raction 5%. It can be seen tat in all Reynolds number, te enancement in eat transer is increases in case 3, because te temperature gradient in tis case lower tan oter cases and also recirculation zone is bigger tan oter cases (see igure 4). Figure 7 sows te iluence o te Reynolds number and te nanoparticles volume raction on te augmentation Nusselt number along te corrugated cannel or case 3. It is clearly observed tat te addition o nanoparticles causes te values o augmentation average Nusselt number to increase. Also, te percentage o eat transer enancement decreases wit increasing o Reynolds number or all nanoparticles volume ractions. For example in case 3, at Re=00, te addition o 0% nanoparticles by volume, augmentation average Nusselt number enance about 5% owever or Re=400 enance about 3%. Figure 8 sows Variation o riction actor wit Reynolds number or dierent cases at nanoparticles volume raction 5%. It can be seen tat te riction actor decreases wit increasing te Reynolds number in all cases and te case 3 as maximum values in all Reynolds number. Figure 9 sows variation o pressure drop wit Reynolds number or dierent cases at nanoparticles volume raction 5%. It can be seen tat te pressure drop increases wit increasing te Reynolds number in all cases because te drag orce increases. Te case 3 as te igest pressure drop, tis is because te recirculation zone in tis case is te igest and te drag as maximum value.

8 45 Alireza Falaat, 04 Journal o Applied Science and Agriculture, 9() February 04, Pages: Fig. 6: Variation o Nusselt number wit Reynolds number or dierent cases and χ=5% Fig. 7: Variation o te augmentation Nusselt number wit Reynolds number or case 3 Fig. 8: Variation o riction actor wit Reynolds number or dierent cases at χ=5% Fig. 9: Variation o pressure drop wit Reynolds number or dierent cases at χ=5%

9 46 Alireza Falaat, 04 Journal o Applied Science and Agriculture, 9() February 04, Pages: Figure 0 sows variation o termal-ydraulic enancement actor wit Reynolds number or dierent cases. It can be seen tat te termal enancement actor increases wit increasing te Reynolds number in all cases and te case 3 as te igest te termal-ydraulic enancement actor. Fig. 0: Variation o termal-ydraulic enancement actor wit Reynolds number or dierent cases Conclusion: In tis paper, Numerical simulations o laminar orced convection eat transer o Cu-water nanoluid in tree dierent geometry o te corrugated cannel under constant eat lux boundary conditions were carried out. Te nanoparticles volume ractions and Reynolds number are in te ranges o 0 0. and respectively. Te governing equations were solved numerically using inite volume metod (FVM) wit te SIMPLE algoritm. Te ollowing results can be de derived rom tis study: Te Nusselt number increased wit increasing Reynolds number owever in case, te Nusselt number gradually increase wit increasing Reynolds number in te ranges and decreasing between Re=00-400, ater tat it trend to increase. Te Nusselt number increased wit increasing nanoparticles volume ractions in all cases. However, te percentage o eat transer enancement decreases wit increasing o Reynolds number or all nanoparticles volume ractions. Te riction actor decreased wit increasing Reynolds number and pressure drop increased wit increasing Reynolds number in all cases. Te termal-ydraulic enancement actor increased wit increasing Reynolds number in all cases and te igest value o termal-ydraulic enancement actor related case 3 in all ranges o Reynolds number. ACKNOWLEDGEMENTS Tis manuscript was resulted rom Numerical analysis o laminar low orced convection in corrugated cannel using nanoluid" as a researc proposal by te inancial supports o Islamic Azad University, Masar Branc. REFERENCES Amed, M.A., N.H. Suaib, M.Z. Yuso and A.H. Al-Falai, 0. Numerical investigations o low and eat transer enancement in a corrugated cannel using nanoluid. International journal o Communication Heat and Mass Transer, 38: Amed, M.A., M.Z. Yuso and N.H. Suaib, 03. Eects o geometrical parameters on te low and eat transer caracteristics in trapezoidal-corrugated cannel using nanoluid. International journal o Communication Heat and Mass Transer, Article in press. Baaidara, H.M.S., N.K. Anand and H.C. Cen, 005. Numerical study o eat and momentum transer in cannels wit wavy walls. Numerical Heat Transer, 47: Das, S.K. N.K.N. Putra, P. Tiesen and W. Roetzel, 003. Temperature dependence o termal conductivity enancement or nanoluids. Journal o Heat Transer, 5: Islamoglu, Y and C. Parmasizoglu, 003. Te eect o cannel eigt on te enanced eat transer caracteristics in a corrugated eat excanger cannel. Applied Termal Engineering, 3: Islamoglu,Y and C. Parmasizoglu, 004. Numerical investigation o convective eat transer and pressure drop in a corrugated eat excanger cannel. Applied Termal Engineering, 4: 4-47.

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