Evaluation of Heat Transfer Enhancement and Pressure Drop Penalty of Nanofluid Flow Through a -Channel

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1 American Journal o Aerospace Engineering 18; 5(1): doi: /.aae ISSN: (Print); ISSN: (Online) Evaluation o Heat ranser Enhancement and Pressure Drop Penalty o Nanoluid Flow hrough a -Channel Saeideh Kermani Department o Mechanical Engineering, University o Kashan, Kashan, Iran address: o cite this article: Saeideh Kermani. Evaluation o Heat ranser Enhancement and Pressure Drop Penalty o Nanoluid Flow hrough a -Channel. American Journal o Aerospace Engineering. Vol. 5, No. 1, 18, pp doi: /.aae ceived: February 9, 18; Accepted: February 1, 18; Published: March 1, 18 Abstract: In this research, turbulent low o water based silicon-oxide nanoluid in a channel with -shaped wavy wall has been scrutinized. Governing equations have been solved by control volume method based on SIMPLE algorithm. o reach desirable geometry, optimization has been done by benchmaring the maximum amount o perormance evaluation criteria (PEC) regarding Nusselt number and pressure drop, among ive dierent phase shits and three dierent wave amplitudes. Ater inding optimum phase shit and amplitude, low ield and heat transer in compulsory displacement o water based silicon-oxide (SiO ) nanoluid with volume raction rom 1% to 4% o nanoparticle has been investigated. sult o simulation showed that the unction o wavy channels is almost related to phase shit and amplitude o wavy wall. he topmost unction evaluation scale or phase shit 9,.5 mm amplitude in 6, ynolds number has been obtained. he results indicate that water-sio nanoluid with 4% volume raction has the highest PEC in comparison with the other studied cases. Keywords: Nanoluid, urbulent Flow, Wavy Wall, Silicon-Oxide, Perormance Evaluation Criteria (PEC) 1. Introduction In recent years due to have more useul and aordable heat exchanger, dierent methods have been examined. Maing indentation and groove on the inner surace o heat exchanger is one o the requent methods or breaing smooth substratum o low and maing turbulences o local walls that leads to decreasing thermal resistance and increasing the heat transer noticeably. he mail goal o current wor is to ind a way to reach the minimum pressure drop and maximum rate o heat transer. Some numeral and experimental studies have been done on luid low and heat transer in wavy channel by many experts. Rush et al. [1] investigated manner o low and local heat transer through a sinusoidal wavy-channel or region o transient low regime. It has observed that ynolds number and geometry o channel aect mixture situation and characteristic o low noticeably. A numerical research has been done on turbulent compulsory convection in a channel with wavy wall by Wang and Vana []. sults showed that by increasing wave amplitude, wave length and ynolds number, local Nusselt number has been increased noticeably. Yin et al. [3] do some researches on heat and air hydraulic parameters in sinusoidal wavy channels or dierent phase shits between upper and lower walls numerically. sults showed that by increasing phase shits, riction coeicient and Nusselt number have been decreased. According to Choi [4] nanoluid is mixture o nanoparticles less than 1nm. Nanoluid has the better thermophysical properties than basic luid such as water, oil and ethylene glycol. Many researches show that nanoluid maes more heat transer than base luids. Vanai et al. [5] investigated the eect o nanoluid on heat transer ield and low in channels with sinusoidal wavy-channel numerically. hey realized that simultaneously use o nanoluid and wavy walls can increase remarably. Khorasanizadeh et al. [6] investigated the eects o using corrugated absorber plate on heat transer and turbulent low in solar air-heater collectors numerically. In their paper choosing the proper geometry was carried out based on the best perormance evaluation criteria (PEC) and increasing the air temperature rom collector inlet to outlet (IIO). heir results revealed that using corrugated absorber plate has a considerable inluence on low ield and heat transer. For the whole year the highest PEC was obtained or the sinusoidal corrugated model, however the highest IIO was obtained or rectangular corrugated model. Also it was nown that or the best IIO and the highest PEC, the optimum ynolds

2 48 Saeideh Kermani: Evaluation o Heat ranser Enhancement and Pressure Drop Penalty o Nanoluid Flow hrough a -Channel numbers is,5. Sheihzadeh et al. [7, 8], in their papers studied orced turbulent convection low and heat transer o air in a desert helicopter cabin. he main aim o their studies was providing human thermal comort or a desert helicopter pilot in summer (usage o cooling system). In order to ulill this demand, a body subdomain was considered around the pilot that includes the pilot's using area in cabin by them. he governing equations were numerically solved by the control volume approach based on the SIMPLE technique and standard -ε turbulent method. he eects o dierent supply air perormances (velocity and temperature) on pilot thermal comort parameters were presented. hen, the optimization was carried out to reach the optimal case with the minimum predicted percentage dissatisied (PPD). Sadripour et al. [9] investigated numerically the thermal comort parameters and energy saving inside the room with speciied dimensions using a ceiling an with central heating systems during the winter. he low was turbulent in all models and -ε model was used to simulate turbulence. Rayleigh and ynolds numbers were in the range o Ra and 6,48 19,44, respectively. he inite volume method (FVM) and SIMPLE algorithm were used to solve the governing equations. Based on the results, using the ceiling an during the winter had a considerable eect on improving the thermal comort and energy saving inside buildings. By using the ceiling an, the eective room temperature increased by.35 o C that can be used to reduce the radiators temperature, thereby reducing energy consumption. Additionally, the study results indicated that the location o ceiling an did not have any eect on room eective temperature and residents thermal comort. Sheihzadeh et al. [1] numerically studied the eects o speed and place o ceiling ans on thermal comort parameters (PMV and PPD) and energy spending in two dierent oice rooms with certain geometry in winter using district heating system. Based on results, using ceiling ans in winter (heating system) has a considerable inluence on improvement o buildings thermal comort and reducing energy. By using ceiling ans the eective temperature o room increases and thereore radiator energy consumption decreases. Arani et al. [11] in their paper studied orced convection low and heat transer o boehmite alumina in ethylene glycol and water mixture nanoluid in sinusoidal-wavy mini-channel with phase shit and variable wavelength. heir optimization was carried out by using dierent nanoparticle shapes (spherical, spheroidal, platelets, blades, cylindrical and brics) to reach the optimal nanoparticle shape with the maximum perormance evaluation criterion (PEC). From this study, it is concluded that the thermal-hydraulic perormance o channel is greatly inluenced by changing the shape o nanoparticles. Using spherical and spheroidal nanoparticles improves the thermal-hydraulic perormances o channel, while using non-spherical nanoparticle shapes (platelets, blades, cylindrical and brics) leads to lower PEC in channel than the base luid. Sadripour et al. [1] in their study investigated the eects o corrugated absorber plate and using aerosol-carbon blac nanoluid on heat transer and turbulent low in solar collectors with double application and air heating collectors, numerically. In this investigation all the simulations were done or two dierent angles o tilt o collector according to horizon, that these angles were the optimum ones or the period o six months setting. As a result the corrugated absorber plate was inspected in the case o triangle, rectangle and sinuous with the wave length o 1mm and wave amplitude o 3mm in turbulent low regime and ynolds number between,5 to 4,. Choosing the proper geometry was carried out based on the best perormance evaluation criteria (PEC), or collectors with dual usage and increasing the air temperature rom collector inlet to outlet or air heating collector. he results revealed that using corrugated absorber plate has a considerable inluence on low ield and heat transer. For all times o the year the highest PEC was obtained or corrugated Sinusoidal model, however the highest temperature increase rom inlet to outlet was obtained or rectangular corrugated model. Sadripour [13] studied orced convection low and heat transer o MWCNs-water nanoluid in heat sin collector equipped with mixers. he optimization was carried out by comparison o dierent parameters to reach the optimal case with the maximum exergy eiciency. From this study, it is concluded that in the case o using heat sin, instead o shell and tubes, the time that the luid is inside the collector increases and leads to outlet temperature increase rom the collector the exergy eiciency increases. Also, it is realized that using mixers enhance the outlet luid temperature, energy eiciency and exergy eiciency. Generally, while the trend o exergy eiciency variation with eective parameters is increasing, applying the mixers precipitate the eiciency increment. Sadripour et al. [14] investigated numerically complex heat transer (turbulent natural convection, conduction and surace thermal radiation) in a rectangular enclosure with a heat source has been carried out. he inite volume method based on SIMPLEC algorithm has been utilized. he eects o Rayleigh number in a range rom 1 8 to 1 11, internal surace emissivity ε 1 on the luid low and heat transer have been extensively explored. Detailed results including temperature ields, low proiles, and average Nusselt numbers have been presented. In this investigation it has been tried to study the shape o heat source inluence on heat transer and luid ield in the considered domain. According to results in low emissivity values usage o circular obstacles is recommended. Although in high emissivity values using rectangular obstacles lead to more eiciency. By analyzing ormer wors collection o this issue obtained that numerical study or displacement turbulent nanoluid with dierent phase shits between upper and lower walls has not been done. In current wor nanoluid water-silicon oxide with volume raction o to 4% o nanoparticles and diameter o 5mm has been used.. Numerical Method.1. Physical Model Schematic schema o studied channel with inlet height o

3 American Journal o Aerospace Engineering 18; 5(1): mm and wave length o 11mm has been shown in Figure 1. he geometry indicating o two-dimensional wavy-wall channel includes six waves through test section. Length o test section is L =66mm and length o upstream section or certainty o entering completely development low to test section is L 1 =15mm. Due to prevent returning low to measurable outlet section has length o L 3 =4mm. For let section o channel inlet velocity boundary condition has been considered in range o ynolds number (6, to 8,) and or outlet section o channel the outlet pressure boundary condition has been considered. Upper and lower walls have been ept in test section with φ and constant temperature o 4K. It has been assumed that low luid in inlet section o channel is steady and turbulent and with environment temperature o 3K... Governing Equations his study is done by using a commercial computational luid dynamics pacage FLUEN 15.. he governing equations or low and heat transer in the cavity can be written in the Cartesian tensor system as [11]: ( ρui ) = x i (1) P ( ρuiu ) = x x u u i + µ + + ρ x x x i x ( ui u ) µ µ t ( ρui ) = + xi x Pr Prt x where ρ is the luid density and ui is the axial velocity, µ, ú and u are the luid viscosity, luctuated velocity and the axial velocity, respectively, and the term ρ ui u is the turbulent shear stress. With using the ynolds averaged approach or modeling the low ield and heat transer in turbulence low regime, it is requires to model the ynolds stresses ρ ui u in (). For closure o the equations, the ε turbulence model was chosen. A common method employs the Boussinesq hypothesis to relate the ynolds stresses to the mean velocity gradient as (4) [11]. Also the turbulent viscosity term µ t is to be computed rom an appropriate turbulence model. he expression or the turbulent viscosity is given as (5) [11]. u u i ρ uiu µ t x x i = + () (3) (4) Figure 1. he domain o corrugated heat sin channel with phase shit o zero degree. µ t ρc µ = (5) ε where, named as turbulence inetic energy (KE), is obtained rom the ollowing equation [11]: µ t [ ρ ui ] = µ + + G ρε xi x σ x Similarly, in the dissipation rate o KE, ε is given by the ollowing equation [45, 46]: µ t ε [ ρε ui ] = µ + xi x σ ε x ε + C G + C 1ε 1 ε ε ρ where G is the rate o generation o the KE while ρε is its (6) (7) destruction rate. G is written as [11]: G u = ρui u x he boundary values or the turbulent quantities near the wall are speciied with the enhanced wall treatment method. hese boundary values such as C µ =.9, C 1ε =1.44, C ε =1.9, σ =1., σ ε =1.3 and Pr t =.9 are chosen as empirical constants in the turbulence transport equations [11, 15]. he luid is considered to be Newtonian, and the physical properties o the luid are temperature dependent. Since the temperature variation is higher than 1 C [13], the ollowing polynomial expressions are used to calculate these parameters: i ρ( ) = (8) (9)

4 5 Saeideh Kermani: Evaluation o Heat ranser Enhancement and Pressure Drop Penalty o Nanoluid Flow hrough a -Channel c ( ) = p ( ) = µ ( ) = (1) (11) (1) o analyze and compare the low characteristics and heat transer o dierent suspended nanoparticles volume ractions and dierent nanoparticle sizes and shapes in wavy mini-channels, some deinitions are given as ollows [11]: he ynolds number is deined as: ρ u D = (13) µ m h where is the mean velocity o luid over the cross section. he hydraulic diameter o channel is deined as: D = H + α (14) h he average Nusselt number is deined as: Nu av h Dh = (15) where and h are the thermal conductivity and average heat transer coeicient o base luid, respectively. he pressure drop between inlet and outlet is deined as: P = P P (16) av,inlet av, outlet he riction actor or ully developed low is expressed as: P = L ρn u Dh m (17) he perormance evaluation criteria index (PEC) is used to compare the thermal and luid-dynamic perormances o wavy mini-channels with nanoluid to evaluate heat transer enhancement. It is calculated using the predicted Nusselt numbers and riction actor as ollows: 1 Nuav, n 3 n Nu av, PEC =. (18) where, and, are the averaged Nusselt number or nanoluid and the base luid, respectively. Also, and are the riction actor or nanoluid and the base luid, respectively. o calculate the thermophysical properties o nanoluid with spherical nanoparticle, the ollowing equations are proposed. he eective density and speciic heat ( ) o the nanoluid at the reerence temperature ( ) are as ollow [17]: ( c ) ( 1 ) ρ = φ ρ + φρ (19) n np ( 1 φ )( ρcp ) + φ ( ρcp ) n p = () n ρn By using Brownian motion o nanoparticles in a wavy channel, the eective thermal conductivity can be obtained by using Corcione correlation [11]: 1.3 e.4.66 np.66 = np Pr φ r (1) where is the nanoparticle ynolds number, is the Prandtl number o the base liquid, is the nanoluid temperature, is the reezing point o the base liquid, is the nanoparticle thermal conductivity, and is the volume raction o the suspended nanoparticles. In more detail, the nanoparticle ynolds number is deined as: np ρ ubdnp = () µ where and are the mass density and the dynamic viscosity o the base luid, respectively, and and are the nanoparticle diameter and mean Brownian velocity, respectively. Assuming absence o agglomeration, the nanoparticle Brownian velocity is calculated as the ratio between and the time required to cover such distance, that, according to Keblinsi et al. [11], is: 3 np πµ dnp d τ D = = (3) 6D where is the Einstein diusion coeicient and! is the Boltzmann s constant. Hence: u B b dnp b = (4) πµ By substituting Eq. () in Eq. (), we obtain: ρ = (5) b np πµ dnp Note that in the preceding equations all the physical properties are calculated at the nanoluid temperature [11]. µ e µ d = d.3 np 1.3 φ 1 (6)

5 American Journal o Aerospace Engineering 18; 5(1): where is the equivalent diameter o a base luid molecule, given by: d 6M =.1 N πρ 1 3 (7) in which " is the molecular weight o the base luid, is the Avogadro number, and # is the mass density o the base luid calculated at temperature =93K. he thermophysical properties o SiO and water are listed in able 1. he governing equations were solved by inite volume able 1. he thermophysical properties o water and SiO at =3 K [16]. method with SIMPLEC algorithm. For diusivity and convective terms, the second-order upwind dierence method is used. he convergence criterion is 1-6 and the under relaxation actors or velocity and temperature are.8 and.6, respectively. Since the temperature dierence is insigniicant, by considering the buoyancy orce eects, dependence o energy and low equations on temperature the Boussinesq model has been used. he time step used to solve the dierential equations has been chosen to be τ = 1-3 [11]. Material ρ (g/m 3 ) c p (J/g K) (W/m K) µ (N s/m ) Water SiO Validation (a) 4 Present Study Vanai et al (b) Figure. (a) Grid independence test, and (b) Code validation. he independence o the solution with respect to the grid size has been studied or a ynolds number range o 6, to 18,. Four dierent grid sizes with 58,793, 61,73, 64,416 and 67,583 nodes have been utilized. Figure a shows the variation o Nusselt number with dierent ynolds numbers and grid sizes. aing into account the conducted grid independence test the uniorm grid with 64,416 nodes has been adopted to get an acceptable compromise between the computational time and the result accuracy. In order to validate the CFD code which is developed in this study, the average Nusselt number o orced convection o SiO -water nanoluid low with volume raction o φ=4% through heated sinusoidal-wavy channel with amplitude o α=.5mm, wavelength o λ=11mm and phase shit o θ=3 were calculated and compared with previous numerical results o Vanai et al. [16]. According to Figure b, the results are in good agreement. 3. sults and Discussion 3.1. he Eect o Dierent Phase Shits In this section, the eect o phase shit between the upper and lower walls o wavy channel on luid low and heat transer has been studied. For this propose ive dierent phase shits or conigurations with wave amplitude o α=1mm are prepared. he eect o dierent phase shits at dierent ynolds numbers or -channel with wave amplitude o α=1mm on the Nusselt number, pressure drop and riction actor is showed in Figure 3. Also the eect o dierent phase shits at dierent ynolds numbers on PEC is reported in Figure 4. As it can be seen in Figure 3a, as the ynolds number increases, the average Nusselt number also increases. he large ynolds number is attributed to the higher velocity which can lead to disturb the low and thus, the heat transer is strengthened. In all cases, the wavy-wall channel lows gave higher values o Nusselt number than that or smooth channel low due to the induction o high disturbance and thin boundary layer in the wavy channels, leading to higher temperature gradients. It is ound that the wavy channel with

6 5 Saeideh Kermani: Evaluation o Heat ranser Enhancement and Pressure Drop Penalty o Nanoluid Flow hrough a -Channel θ=18 phase shit has the highest average Nusselt number at all ynolds numbers and can promote the heat transer by approximately 16% in comparison with smooth channel at the lowest value o ynolds number. θ= 9,, 6 and 3 had the rates o approximately 115%, 11%, 15% and 11%. he pressure drop or various types o wavy-wall channels over the considered range o ynolds numbers is plotted in Figure 3b. It is clearly seen that the wavy-wall channels provide a high amount o pressure drop in comparison with the smooth channel. his behavior is due to the act that wavy corrugations disturb the entire low ield and causes more pressure drop. However, it is observed that θ=18 phase shit channel has the highest pressure drop among all geometries, which is ollowed by θ=, θ=3, θ=6 and θ=9, respectively. In addition, the pressure drop rises sharply with the increment o ynolds number. Figure 3c shows the variation o riction actor along the channel over the investigated ynolds number. he value o riction actor or θ=18 phase shit is the highest compared to other conigurations, while the lowest value is related to θ=9 phase shit. he maximal riction actor o the wavy-wall channel is about 4 times that o the smooth channel. It is obvious that the riction actor decreases gradually or all conigurations with the increase o ynolds number. Figure 4 depicts the PECs calculated using the computed Nusselt numbers and riction actors. he result indicates that or each test channel the values o PEC have quite similar trend in the considered range o ynolds number. It is seen that the PECs or the channels decrease with increasing ynolds number, which means that an optimum ynolds number is corresponding to the maximum PEC or each type o geometry. he optimum ynolds number is related to =6, or all tested geometries. he PEC o wavy channel with θ=9 phase shit is ound to be the best among all geometries and is about 1.17 at the lowest value o ynolds number (a) Smooth Channel deg 3 deg 6 deg 9 deg 18 deg P Smooth Channel deg 3 deg 6 deg 9 deg 18 deg (b) Smooth Channel deg 3 deg 6 deg 9 deg 18 deg (c) Figure 3. he eect o dierent phase shits at dierent ynolds numbers or -channel with wave amplitude o α=1mm on (a) Averaged Nusselt number, (b) Pressure drop, and (c) Friction actor. PEC deg 3 deg 6 deg 9 deg 18 deg.6 Figure 4. he eect o dierent phase shits at dierent ynolds numbers or -channel with wave amplitude o α=1mm on PEC.

7 American Journal o Aerospace Engineering 18; 5(1): he Eect o Dierent Wave Amplitudes he combined eect o wavy amplitude o channel on the heat transer perormance o channels is analyzed. he range o wavy amplitude varies rom.5 to 1.5 mm. P mm 1 mm 1.5 mm (a) mm 1 mm 1.5 mm (b) (c).5 mm 1 mm 1.5 mm Figure 5. he eect o dierent wave amplitudes at dierent ynolds numbers or -channel with phase shit o θ=18 on (a) Averaged Nusselt number, (b) Pressure drop, and (c) Friction actor. he variation o Nusselt number with ynolds number or wavy channel with θ=9 phase shit is presented in Figure 5a. As shown in this igure the Nusselt number increases with the increase o ynolds number. It is observed that the wavy amplitude o α=1.5mm has the best heat transer compared with other amplitudes o α=1mm and α=.5mm respectively. his can be explained by a strong turbulence intensity generated by greater wavy amplitude, leading to a rapid mixing o the low especially at higher ynolds number. Figure 5b the higher wavy amplitude would cause more turbulent low which consequently increases the pressure drop. Figure 5c shows the variation o riction actor with ynolds number or dierent wavy amplitudes. It is seen that the wavy amplitude o α=1.5 mm has the highest riction actor and it is ollowed by α=1mm and α=.5mm respectively. Figure 6 illustrates the eect o dierent wavy amplitudes on PEC index in the investigated range o ynolds numbers. It is seen that the wavy amplitude o α=.5mm has the highest PEC index in all ranges o ynolds numbers and the highest value o that is around at =6. As a result, it is concluded that by using an aspect ratio o α=.5mm would lead to achieve better heat transer augmentation. Based on the obtained results, the wavy wall channel with the phase shit o θ=9 and the wavy amplitude o α=.5mm is the most eicient geometry, thus it is adopted or the rest o studies. PEC (d) Figure 6. he eect o dierent wave amplitudes at dierent ynolds numbers or -channel with phase shit o θ=9 on PEC he Eect o Using Nanoluid.5 mm 1 mm 1.5 mm he eect o SiO water nanoluid with 5 nm nanoparticle diameter and volume ractions o, 1,, 3 and 4% on the heat transer enhancement in the terms o average Nusselt number is plotted in Figure 7. he results indicate that the average Nusselt number o SiO water nanoluid increases with increasing particle volume concentration. According to Eq. (1), nanoluids with higher particle concentration have higher static and dynamic thermal conductivities, which in turn increase the average Nusselt number. For example, in the case

8 54 Saeideh Kermani: Evaluation o Heat ranser Enhancement and Pressure Drop Penalty o Nanoluid Flow hrough a -Channel o 4% volume raction, the average Nusselt number is about 36.5% larger than pure water at the lowest ynolds number in testing range through the wavy channel. Figure 8 shows the variation o local Nusselt number along the lower wavy wall or dierent volume ractions in the range o to 4% and =6, through wavy channel with θ=18 and α=.5mm. It is ound that as the nanoluid volume raction increases, the pea value o the local Nusselt number increases as well. In addition, at the start point o each hump a considerable velocity gradient increase can be observed which leads to a sudden increase in local Nusselt number over that point. On the other hand, the local sin riction coeicient is independent o the nanoparticle volume concentration as shown in Figure 9. However, with increasing the ynolds number, irregular and random movements o the nanoparticles enhance the energy exchange rates in the luid with penalty on the wall shear stress Figure 7. Variation o the average Nusselt number versus ynolds number at dierent values o SiO nanoparticle volume ractions, d np=5nm, θ=18 and α=.5mm. Nu x 6 % 1 % 4 % 3 % 4 % % 1 % % 3 % 4 % C x 5 % 1 % % 3 % 4 % X (m) Figure 9. Variation o the local Nusselt number along the lower wavy wall or dierent ynolds numbers at ϕ=4%, θ=18 and α=.5mm. In their paper choosing the proper geometry was carried out based on the best PEC. hereore based on the obtained results, the wavy wall channel with the phase shit o θ=9 and the wavy amplitude o α=.5mm using SiO -water nanoluid with volume raction o φ=4% at =6, has the most value o PEC and is the most eicient geometry between all dierent investigated conigurations and models. 4. Conclusion Numerical study was perormed to investigate the thermal and hydraulic characteristics o orced convection nanoluid low in wavy wall channels or turbulent regime with ynolds number o 6 to 18,. he emphasis was given on the heat transer augmentation resulting rom various actors, which include dierent phase shits between the upper and lower walls, dierent wavy amplitudes, volume ractions o nanoparticle and ynolds number. Finite volume method was adopted to solve the governing equations throughout this study. According to the results, the wavy wall channel with the phase shit o θ=9 and the wavy amplitude o α=.5mm have the best PEC index with the value o at = 6. However, the channel with wavy amplitude o α=1.5 mm and θ=18 gives the highest Nusselt number which is accompanied by increased riction actor and pressure drop penalty. It is also ound that SiO water nanoluid with 5nm particle diameter and 4% concentration provides the highest values o average Nusselt number compared to pure water due to its higher thermal conductivity. As the low ynolds number increases, the pea value o the local Nusselt number and local sin riction coeicient increase considerably X (m) Figure 8. Variation o the local Nusselt number along the lower wavy wall or dierent nanoparticle volume ractions at = 6, at ϕ=4%, θ=18 and α=.5mm. erences [1] Rush,., Newell, A., and Jacobi, A., An experimental study o low and heat transer in sinusoidal wavy passages, International Journal o Heat and Mass ranser, Vol. 4, No. 9, pp , 1999.

9 American Journal o Aerospace Engineering 18; 5(1): [] Wang, G., and Vana, S. P., Convective heat transer in periodic wavy passages, International Journal o Heat and Mass ranser, Vol. 38, No. 17, pp , [3] Yin, J., Yang, G., and Li, Y., he eects o wavy plate phase shit on low and heat transer characteristics in corrugated channel, Energy Procedia, Vol. 14, pp , 1. [4] Choi, S. U. S., and Eastman, J. A., Enhancing thermal conductivity o luids with nanoparticles, Conerence: Enhancing thermal conductivity o luids with nanoparticles, [5] Wen, D., Lin, G., Vaaei, S., and Zhang, K., view o nanoluids or heat transer applications, Particuology, Vol. 7, No., pp , 9. [6] Khorasanizadeh, H., Sadripour, S., and Aghaei, A., Numerical investigation o thermo-hydraulic characteristics o corrugated air-heater solar collectors, Modares Mechanical Engineering, Vol. 16, No. 13, pp. 4-46, 16. (In Persian) [7] Sheihzadeh, Gh. A., Sadripour, S., Aghaei, A., and Shahrezaee, M. B., An investigation o human thermal comort in a desert helicopter, Conerence: International Conerence on air conditioning and heating / cooling installations, Vol., 16. ile:///c:/users/1_mk/downloads/paper_56687.pd. [8] Sheihzadeh, Gh. A., Sadripour, S., Aghaei, A., Shahrezaee, M. B., and Babaei, M. R., Providing human thermal comort conditions or pilot in a desert helicopter, Modares Mechanical Engineering, Vol. 16, No. 13, pp. 1-13, 16. (In Persian) [9] Sadripour, S., Mollamahdi, M., Sheihzadeh, Gh. A., and Adibi, M., Providing thermal comort and saving energy inside the buildings using a ceiling an in heating systems, Journal o the Brazilian Society o Mechanical Sciences and Engineering, Vol. 39, No. 1, pp , 17. [1] Sheihzadeh, Gh. A., Sadripour, and Mollamahdi, M., Numerical study o eect o speed and place o ceiling ans on thermal comort and reducing energy in oice buildings, Amirabir Journal o Mechanical Engineering, Article in Press, 18. DOI: 1.6/MEJ [11] Abbasian Arani, A. A., Sadripour, S., and Kermani, S., Nanoparticle shape eects on thermal-hydraulic perormance o boehmite alumina nanoluids in a sinusoidal wavy mini-channel with phase shit and variable wavelength, International Journal o Mechanical Sciences, Vol , pp , 17. [1] Sadripour, S., Adibi, M., and Sheihzadeh, Gh. A., wo dierent viewpoints about using aerosol-carbon nanoluid in corrugated solar collectors: hermal-hydraulic perormance, and heating perormance, Global Journal o searches in Engineering A: Mechanical and Mechanics, Vol. 17, No. 5, 37 48, 17. [13] Sadripour, S., First and second laws analysis and optimization o a solar absorber; using insulator mixers and MWCNs nanoparticles, Global Journal o searches in Engineering A: Mechanical and Mechanics, Vol. 17, No. 5, 37 48, 17. [14] Sadripour, S., Ghorashi, S. A., Estaloo. M., Numerical Investigation o a Corrugated Heat Source Cavity: A Full Convection-Conduction-Radiation Coupling. American Journal o Aerospace Engineering. Vol. 4, No. 3, pp. 7-37, 17. DOI: /.aae [15] Hashemi, S. A. M., Sadripour, S., and Estaloo, M., Energy and exergy analyzes and evaluation o uel consumption reduction techniques in traditional latbreads baeries, Amirabir Journal o Mechanical Engineering, Article in Press, 18. DOI: 1.6/MEJ [16] Vanai, Sh. M., Mohammed, H. A., Abdollahi, A., and Wahid, M. A., Eect o nanoparticle shapes on the heat transer enhancement in a wavy channel with dierent phase shits, Journal o Molecular Liquids, Vol. 196, pp. 3-4, 14.