The numerical investigation of heat transfer and pressure drop of turbulent flow in a triangular microchannel

Author’s Accepted Manuscript The numerical investigation of heat transfer and pressure drop of turbulent flow in a triangular microchannel Omid Rezaei, Omid Ali Akbari, Ali Marzban, Davood Toghraie, Farzad Pourfattah, Ramin Mashayekhi www.elsevier.com/locate/physe

PII: DOI: Reference:

S1386-9477(17)30217-5 http://dx.doi.org/10.1016/j.physe.2017.06.013 PHYSE12835

To appear in: Physica E: Low-dimensional Systems and Nanostructures Received date: 10 February 2017 Revised date: 1 April 2017 Accepted date: 16 June 2017 Cite this article as: Omid Rezaei, Omid Ali Akbari, Ali Marzban, Davood Toghraie, Farzad Pourfattah and Ramin Mashayekhi, The numerical investigation of heat transfer and pressure drop of turbulent flow in a triangular microchannel, Physica E: Low-dimensional Systems and Nanostructures, http://dx.doi.org/10.1016/j.physe.2017.06.013 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

The numerical investigation of heat transfer and pressure drop of turbulent flow in a triangular microchannel Omid Rezaei1, Omid Ali Akbari2, Ali Marzban1, Davood Toghraie3*, Farzad Pourfattah4, Ramin Mashayekhi2 1

Department of Mechanical Engineering, Aligoudarz Branch, Islamic Azad University, Aligoudarz, Iran

2

Young Researchers and Elite Club, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran

3

Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran

4

Department of Mechanical and Aerospace Engineering, Malek-Ashtar University of Technology, Shahin-shahr, Isfahan, Iran *

Corresponding author: Davood Toghraie, Department of Mechanical Engineering, Islamic Azad University, Khomeinishahr Branch, Khomeinishahr 84175-119, Iran. Email: [email protected]

Abstract In this presentation, the flow and heat transfer inside a microchannel with a triangular section, have been numerically simulated. In this three-dimensional simulation, the flow has been considered turbulent. In order to increase the heat transfer of the channel walls, the semitruncated and semi-attached ribs have been placed inside the channel and the effect of forms and numbers of ribs has been studied. In this research, the base fluid is Water and the effect of volume fraction of Al2O3 nanoparticles on the amount of heat transfer and physics of flow have been investigated. The presented results are including of the distribution of Nusselt number in the channel, friction coefficient and Performance Evaluation Criterion of each different arrangement. The results indicate that, the ribs affect the physics of flow and their influence is absolutely related to Reynolds number of flow. Also, the investigation of the used semi-truncated and semi-attached ribs in Reynolds number indicates that, although heat transfer increases, but more pressure drop arises. Therefore, in this method, in order to improve the heat transfer from the walls of microchannel on the constant heat flux, using the pump is demanded.

Keywords: computational fluid dynamics, microchannel, Nusselt number, nanoparticle.

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1-Introduction In recent years, the attention to the development of heat transfer issue in the engineering sciences and industries, has grown rapidly, therefore, it has become the main subject of the numerical and experimental researches [1-10].Almost 10% of heat transfer papers in the literature are about the heat transfer development issue [11]. Therefore, in the most of the numerical and experimental papers, the enhancement of the heat transfer rate in modern devices has been proven [12-19]. By using new methods, the improving of heat transfer causes the providence in consumption of energy and preserves the natural environment. The disruption of the laminar sub-layer in the turbulent boundary layer, the creation of secondary flow, the connection of the separated flow to the surface, the delay in the development of boundary layer, the increase of the thermal conductivity of fluid, the increase of the temperature differences between fluid and thermal surface and increase of the flow rate, are the most important passive mechanisms for heat transfer enhancement [20].The using of microchannels is a recent method for the heat transfer issue. Due to the non-use of any external force, this method can be classified in the inactive methods. By advancing of science and technology; researchers have found out that, the downsizing of systems has more advantages than the usual size systems. The most important of these advantages, are the reduction of the occupied space, cooling necessity and the operational costs [21]. Sheikhzadehet.al.[22] studied the influence of pressure drop and heat transfer in the microchannel. They found that by increasing volume fraction of nanoparticles, heat transfer and pressure drop increase. Also, by using nanofluids in higher Reynolds numbers, Nusselt number enhances more than nanofluids in lower Reynolds numbers. Akbari et. al. [23] explored the effects of ribs height on the heat transfer and the computational fluid dynamics of Al2O3/Water laminar flow of the nanofluid in a two-dimensional microchannel. They found out that, the rate 2

of heat transfer in the microchannel improves by increasing the height of rib and volume fraction of nanoparticles. However, the increase of rib height makes higher friction coefficient than those microchannels with constant height of rib. In the other study, the effects of ribs on the parameters of the laminar flow and heat transfer of Al2O3/Water nanofluid with different volume fractions of nanoparticles in a three-dimensional rectangular microchannel, have been numerically investigated by Akbari et. al. [24].Their studies showed that, the cooling fluid in the indented parts, comparing to the smooth parts, has higher heat transfer with the heated wall. Also, by increasing Reynolds number, number of ribs and volume fraction of nanoparticles, the temperature of the fluid increases in the outlet section of microchannel.Karimipouret.al. [25] numerically studied an indented two-dimensional rectangular microchannel with the constant temperature boundary condition. In their study, the effect of ribs on the bottom wall, in comparison with the smooth channel, has been investigated. They results indicated that, by increasing the volume fraction of nanoparticles, thermal performance of the microchannel improves, which is due to the increase of volume fraction of nanoparticles with higher thermal conductivity. Also, by enhancing the volume fraction of nanoparticles and numbers of ribbed, in higher Reynolds numbers, the significant increase of Nusselt number is more obvious. Jung et. al. [26] empirically investigated the forced convection heat transfer of nanofluids in the microchannels. His results showed: 1- The nanofluid convection heat transfer coefficient with 1.8% volume fraction of nanoparticles, is 32% more than pure Water. 2- In the small-size microchannels, heat transfer coefficient in low Reynolds numbers is comparable or higher than the large microchannels with high Reynolds numbers which indicates the heat transfer properties of microchannel.Lelea [27] numerically studied the operation of the nanofluid flow in the heat source of microchannel. They figured out that, in low pumping power, the increase of

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nanoparticles concentration improves the rate of heat transfer. In the heating state for lower pumping power, by increasing the nanoparticles diameters, the convection heat transfer coefficient decreases and in the cooling state, the heat transfer coefficient of nanofluid with 9% volume fraction is 20% higher than the pure Water. Diao et. al. [28] numerically studied the thermal performance of a rectangular microchannel. He concluded that, comparing to the pure Water, Water/Al2O3 nanofluid has greater function in the contribution of microchannel heat transfer. Akbari et. al. [29] numerically studied the nanofluid flow in a three-dimensional indented microchannel. In this investigation, a new design of semi-attached ribs form has been studied in a single phase state. His results indicated that, the ratio of the ribs dimension (R/W) has significant effects on the physics of the flow and heat transfer properties of microchannel. Also, in the semi-attached form, by increasing the dimensional ratio (R/W), the created areas with lower heat transfer omitted behind the ribs and the amount of friction coefficient reduces. In this study, the effect of the semi-attached, semi-truncated rib and the nanofluid in a microchannel, have been considered separately. The effects of these two factors in the rib design have been investigated simultaneously in a three-dimensional triangular microchannel. In this research, the number and the length of ribs, different volume fractions of nanoparticles and Reynolds numbers have been compared and studied in a three-dimensional triangular microchannel.

2- Problem statement In this presentation, the main purpose is investigating the effects of the obstacles arrangement inside the triangular microchannel on the turbulent flow and heat transfer properties under the

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constant heat flux with 2 and 4 volume fractions of Al2O3 nanoparticles in Water as the base fluid. For this reason, flow and heat transfer in the microchannel with the length of 7.5 mm in an equilateral triangular section with the height and hydraulic diameter equivalent of 75 µm and the length of each side of the triangle in the cross section equivalent of 86.6 µm, has been numerically simulated. The shape of the channel and the used obstacles will be explained in the following. In this study, flow and heat transfer properties in the microchannel with the semitruncated and semi-attached ribs in different volume fractions of Al2O3 nanoparticles in the Water-based fluid under a constant heat flux, has been investigated. Table (1) indicates the studied effects of ribs arrangement inside the microchannel with a triangular cross section under the constant heat flux with 2 and 4 volume fractions of AL2O3 nanoparticles in the Water-based fluid. In the following, the geometrics of channel and the used ribs will be explained. For this reason, the studied geometrics and the related ribs are indicated and explained in figures (1), (2) and tables (2) and (3).

3- Geometrics, Mesh and boundary conditions In this presentation, the flow and heat transfer inside a microchannel with the length of 7.5 mm has been investigated by using numerical method. In figure (3), the applied netting inside the presented microchannel by using an unsystematic triangular grid, has been indicated. In order to simulate the flow inside the channel, the inlet boundary condition for the inlet channel and the outlet pressure boundary condition for the outlet of channel, are used. For investigating the channel walls, the no-slip principle has been considered. According to the symmetrical geometrics of the studied channel, half of it has been simulated and the symmetrical boundary

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condition has been used for the middle plate. In figure (4), the applied boundary conditions are presented in the computational boundary limitation. According to this figure, the used ribs are in distant from the center of the channel and by using the symmetrical boundary condition; there is a space for passing the working fluid through the ribs. Therefore, the used ribs in this research have been considered as the semi-truncated and semi-attached. The wall of microchannel is under the constant flux of 25000 W/m2 and the flow is simulated with Reynolds numbers of 2500, 3500 and 5000 for nanofluid with different volume fractions of nanoparticles. In figure (5) the independent solution of grid is investigated by presenting Nusselt number. As seen, in 120000 computational cells, the achieved results are independent from the numbers of the elements which for all of the simulations, these elements have been used. In this study, the effects of nanoparticles in the base fluid (Water) on the rate of heat transfer in a microchannel with the semi-truncated and semi-attached obstacles have been investigated. For this purpose, Water is the base fluid and Al2O3 nanoparticles with volume fractions of 2 and 4%, are considered. In this simulation, nanofluid has been proposed as homogeneous solution and for computing its properties; the presented equations of the previous sections have been used. The properties of nanofluid in different volume fractions are presented [23]in table (4). 4- Formulations The governing equations of fluid flow are including continuity, momentum and energy equations which are solved in a Cartesian coordinate for the laminar and steady states [30]: Continuity equation:    ui   0 X i

)1(

Momentum equation: 6

ui  P    ui u j 2  ui u j       ij   X j X i X j   X j X i 3 X j





    u /i u / j     X j  





)2(

Energy equation:  u i  E   P    X X i j

 T  k e ff  X j 

  

&

E h

P





u2 2

)3(

The turbulence equations of standard κ– are applied for the simulations. The standard model of κ - is as follows [30]:     k ui   X i X j

  k  (  t )   k X j 

     ui   X i X



G k   u /i u / j

j

 X

  Gk     

    (  t )    X j 

(5)

  2    C 1 G k  C 2  k k 

(6)

u j i

Where Gk is the perturbation energy production, k is effective Prantdl for turbulence energy and k is turbulence energy loss. C1 and C2 are constants and t is perturbation viscosity which is defined as: t  C 

k2



(7)



C is a constant value which equals to 0.09, C1 =1.44 , C2 =1.92 , k=1 and =1.3. 4-1- The equations of the measured parameters in a three-dimensional flow One of the parameters for investigating the operation of the microchannel is friction coefficient which is depended on the geometrical parameters of microchannel and can be computed as [31]:

f  2P

Dh 1 L u in 2

(8)

Where Dh, L, ρ and u are respectively, hydraulic diameter, length, density and inlet velocity.

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The average Nusselt number can be obtained as [32]: Nu(x) 

qDh k f  Tw  Tm 

(9)

Where Tw, Tm and k, are respectively, the temperature of microchannel wall, the average bulk temperature and kf is base fluid thermal conductivity. In order to calculate the average Nusselt number, the equation (10) can be used as [33]: Nu ave 

1 L total



Ltotal

0

(10)

Nu(x) dx

For general evaluation of the Performance Evaluation Criterion of three-dimensional indented microchannel, PEC parameter can be defined as the thermal efficiency and can be obtained from [34]:  Nu ave  Nu ave,s PEC   f     fs 

1/3

  

(11)

4-2- Numerical procedure In the used numerical solution, for discretizing the governing equations of the momentum and pressure, the second-order discretizing method is used and for coupling the velocity and pressure, the SIMPLE method, which is a prediction and improvement method, has been used. In this way, by considering an amount for pressure, the velocity can be obtained. Then, by correcting the values of pressure and velocity, the solution procedure continues. Also, in order to discretizing the energy equation, the second order method has been used and the converging value has been proposed as 10-6. It is noteworthy that, the reason of selecting the discretizing to the second order, is the high accuracy of this method. 8

5- Results 5-1- Validation In order to ensure the accuracy of the numerical results, the internal flow of microchannel has been simulated and the achieved results have been compared with the references presented in literature [29 and 32]. In figure (6-a), the obtained Nusselt number from the simulation of the flow with different Reynolds numbers, have been compared with the presented results of the mentioned references, in the range of turbulent flow for Water/CuO nanofluid with volume fraction of 4%. The comparison of the results indicates that the used numerical method has high accuracy. In figure (6-b), the obtained results from the present numerical simulation are compared with the results of Mancaet. al. [32]. Also, in this figure, by comparing the present results with the empirical equations of Dittus–Boelter and Petukhov relationship, it can be said that the numerical solution is accurate. In this section, the numerical results are presented for each case. The results are including the quantitative results as the distribution of local Nusselt number, the average Nusselt number and Performance Evaluation Criterion. Also, for studying the physics of flow, the qualitative results such as, velocity distribution contours and stream lines along the channel, have been investigated.

5-2- Four semi-attached ribbed with the length of 10 µm (Case A) In this section, the distribution of the local Nusselt number has been presented for four semiattached ribbed with the length of 10 µm in the channel with Reynolds numbers of 2500, 3500 and 5000 with fractions volume of Al2O3nanoparticles 0, 2 and 4%. Figures (7-9) investigate the 9

effects of the increasing volume fraction of nanoparticles on the distribution of local Nusselt number in the constant Reynolds number and for three different volume fractions of nanoparticles. According to these figures, in all three studied Reynolds numbers, by increasing of particles volume fractions, the amount of Nusselt number increases in the channel [35, 36]. The reason of this augment of Nusselt number is the enhancement of volume fraction, increase of heat transfer coefficient of the working fluid mixed with nanoparticles and increase of the boundary layers turbulence due to the mass motion of nanoparticles and also increase of conduction heat transfer of nanofluid due to the existence of nanoparticles [37-38]. It can be concluded from these figures that, in a volume fraction and a constant Reynolds number, the distribution of Nusselt number, in some parts of channel, increases. This enhancement is due to the created ribs which cause eddies in the flow. The existence of eddies in flow causes the increase of the turbulence and mixing of flow, therefore heat transfer and Nusselt number increase. In order to investigate the effect of Reynolds number on heat transfer, figure (10) presents the distribution of the local Nusselt number for the base fluid. According to this figure, by increasing volume fraction of nanoparticles in each studied state, Nusselt number enhances. This increase of Nusselt number, by enhancing of Reynolds number, is because of the augment of fluid momentum and high flow turbulence. In figure (11), the average Nusselt number for a case of which four semi-attached ribbed are in the bottom of channel with the length of 10 µm in a flow with Reynolds numbers of 2500, 3500 and 5000 with volume fractions of nanoparticles 0, 2 and 4%, have been indicated. According to this figure, by increasing volume fraction of nanoparticles of 0-4%, Nusselt numbers increases on the average of 27% in the flow with Reynolds numbers 2500, 3500 and 5000. In the following, by studying the fluid and heat transfer

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parameters of each studied case, the appropriate arrangement and efficient particle volume fractions will be introduced. 5-3- Five semi-attached ribbed with the length of 10 µm (Case A5) In this sections, the effect of Reynolds number and volume fraction of Al2O3 nanoparticles on Nusselt number in the microchannel with five semi-attached ribbed with the length of 10µm, have been investigated. For studying the effects of volume fractions of nanoparticles on the distribution of local Nusselt number in the flow with constant Reynolds numbers 2500 and 3500, have been indicated in figures (12) and (13). According to these figures, by increasing volume fraction of nanoparticles, Nusselt number increases. As it can be seen from the previous section, the existence of Al2O3 nanoparticles in the base fluid causes the enhancement of heat transfer coefficient and consequently, increases of Nusselt number. By investigating the changing process of local Nusselt number, it can be concluded that, by increasing the thickness of boundary layer along the microchannel, Nusselt number increases and by passing the fluid through the ribs in the bottom of microchannel, Nusselt number, due to the creation of eddies, enhances. It is noteworthy that, although the enhancement of heat transfer is one of the advantages of using ribs and nanoparticles, these two factors, by applying higher turbulence to the flow causes the increase of the pressure drops. It is necessary to study the effects of ribs and nanoparticles according to the fluid dynamics, in order to reach the appropriate condition, which is the highest heat transfer with less pressure drop in the fluid direction. In the following, by investigating the Performance Evaluation Criterion Evaluation Criterion, this issue will be explained.

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5-4- Four semi-attached ribbed with the length of 20 µm (Case B4) In this sections, the effect of Reynolds number and volume fraction of Al2O3 nanoparticles on Nusselt number inside the microchannel with five semi-attached ribbed with the length of 20µm, have been investigated. In order to study the effect of volume fraction of nanoparticles, figure (14) indicates the local Nusselt number distribution of the flow with constant Reynolds number 5000. According to this figures, by increasing volume fraction of nanoparticles, Nusselt number increases. As mentioned in the previous section, the existence of nanoparticles of Al2O3 nanoparticles in the base fluid causes the increase of heat transfer coefficient and consequently Nusselt number enhancement. By exploring the changing process of the local Nusselt number, it can be seen that, by increasing the thickness of boundary layer along the microchannel, Nusselt number decreases and by passing the fluid through the ribs of bottom microchannel, Nusselt number, due to the creation of eddies, increases. It is noteworthy that, although heat transfer increment is one of the advantages of using nanoparticles and indented microchannel, but these two factors, by applying higher turbulences to the flow, cause the increase of the pressure drop. Consequently, in order to arise the best and appropriate state, the highest heat transfer with lowest pressure drop, the effects of ribs and nanoparticles should be investigated according to fluid dynamics. In the following, by studying the fluid-thermal coefficient, these issues will be explained. Figure (15) presents the average Nusselt number for four semi-attached ribs with the length of 20 µm in the microchannel in a flow with Reynolds numbers of 2500, 3500 and 5000 and particle volume fraction of 2%. According to this figure, by increasing the volume fraction of nanoparticles, in all of the studied Reynolds numbers, Nusselt number enhances. By investigating this figure, it can be seen that, in all studied Reynolds numbers, by increasing volume fraction of nanoparticles to 4%, Nusselt number increases on the average of 25%. 12

5-5- Five semi-attached ribbed with the length of 20 µm (Case B5) This section discuses about the effect of Reynolds number and the amount of volume fraction of nanoparticles on the distribution of the local Nusselt number with five semi-attached ribbed with the length of 20 µm in the microchannel. Figures (16) to (18) indicate the distribution of Nusselt number in the flow with Reynolds numbers of 2500, 3500 and 5000 in three different volume fractions of nanoparticles in the base fluid. According to these figures, by growing the boundary layer in the inlet of channel, heat transfer coefficient and consequently, Nusselt number decrease and by colliding the flow with the first semi-attached tooth, due to the increase of flow turbulence and the changes made in the behavior of boundary layer, the Nusselt number increases. Figure (19) presents the average Nusselt number in a microchannelin the flow with five semiattached ribbed, with three different Reynolds numbers and volume fractions of nanoparticles. According to this figure, by increasing Reynolds number and volume fraction, the average Nusselt number enhances. 5-6- Study of flow physics This section presents the study of flow physics such as velocity distribution and stream lines in the investigated cases. In figure (20) and (21), the velocity distribution contours and stream lines in the case with four ribs with the length of 10 and 20 µm placed along the microchannel with Reynolds number 2500, are presented. According to these figures, due to the colliding of the flow with the ribs, flow twisted. This twisting causes the turbulence of flow and increase of fluid mixing and as a result, the rate of heat transfer enhances. 13

Figure (22) to (25) indicate the fluid Performance Evaluation Criterion for four different studied geometrics in flow with Reynolds numbers 2500, 3500 and 5000 in three different volume fractions of nanoparticles Al2O3. According to these figures, by increasing volume fraction of nanoparticles in all geometrical conditions and studied Reynolds numbers, the Performance Evaluation Criterion enhances which shows that the increase of applied pressure to the system due to the adding of nanoparticles, comparing to the increase of heat transfer, is reasonable. By comparing the Performance Evaluation Criterion in different studied states, it is specified that, the maximum Performance Evaluation Criterion of fluid with Reynolds number of 5000 and volume fraction of 4% inside the microchannel with five semi-attached ribbed with the length of 20 µm, accomplishes. In Figure (26), effect of the ribs width on the turbulence kinetic energy is shown. As seen on the back of the ribs, the turbulence kinetic energy increase. Also, it is observed that by increasing the width ribs (Case B5) the turbulence kinetic energy increases and it leads to better mixing of flow and increase heat transfer. 6-Conclusions In this study, the turbulent flow and heat transfer in a microchannel with a triangular section, has been simulated and the effect of the semi-attached ribs in the microchannel has been investigated. Also, the influence of ribs in the microchannel and the effects of Al2O3 nanoparticles on flow and heat transfer have been investigated. It is mentionable that, the solution of the base fluid and nanoparticles has been proposed as a homogenous mixture. The studied parameters are Reynolds number, the form and number of ribs and volume fractions of nanoparticles. In this presentation, for ensuring the accuracy of the numerical procedure, the problem conditions of one of the numerical studies in the literature, have been simulated and the results of have been compared with the references. The conformity of the results indicated that, 14

the numerical procedure has good accuracy. The indicated results involve the distribution of the local and average Nusselt number and the Performance Evaluation Criterion Evaluation Criterion with the stream lines and velocity distribution contours. The results indicated that: 1- By increasing Reynolds number, Nusselt number enhances. 2- Due to the existence of ribs in the fluid direction, the velocity profile in microchannel is affected and the convection heat transfer, due to the increase of flow turbulence, enhances. 3- Adding nanoparticles to the base fluid, causes the increase of heat transfer and it has great influence on the flow with high Reynolds numbers. 4- In the flow with lower Reynolds numbers, using the indented microchannel without nanoparticles, has less than one Performance Evaluation Criterion, indicated that, in this range of Reynolds number, the simultaneous using of nanoparticles and indented microchannel, due to the economical and engineering vindications, is inevitable. 5- The maximum operational coefficient is in a microchannel with five ribs with the length of stick section 20 µm, with volume fraction of nanoparticles 4% in the base fluid. The extension of this paper for nanofluid according previous works [39-71] affords engineers a good option for Nano scale and micro scale simulation.

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and temperature jump, Physica E: Low-Dimensional Systems and Nanostructures, 86 (2017) 146-153. [2] H.R. Goshayeshi, M. Goodarzi, M.R. Safaei and M. Dahari, Experimental Study on the Effect of Inclination Angle on Heat Transfer Enhancement of a Ferro-nanofluid in a Closed Loop Oscillating Heat Pipe under Magnetic Field, Exp. Therm. Fluid. Sci, 74 (2016) 265–270. [3] M. Goodarzi, A. ShKherbeet, M. Afrand, E. Sadeghinezhad, M. Mehrali, P. Zahedi, S. Wongwises, and M. Dahari, Investigation of heat transfer performance and friction factor of a counter-flow double-pipe heat exchanger using nitrogen-doped, Graphene-based nanofluids. Int. Commun. Heat. Mass, 76 (2016) 16-23. [4] H.R. Goshayeshi, M. Goodarzi, & M. Dahari, Effect of magnetic field on the heat transfer rate of kerosene/Fe2O3 nanofluid in a copper oscillating heat pipe. Exp. Therm. Fluid. Sci, 68 (2015) 663-668. [5] A. Malvandi, M.R. Safaei, M.H. Kaffash, D.D. Ganji, MHD mixed convection in a vertical annulus filled with Al2O3-Water nanofluid considering nanoparticle migration,

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19

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21

[44] M. Hemmat Esfe, M. Afrand, S. Gharehkhani, H. Rostamiand, D. Toghraie, M. Dahari, An experimental study on viscosity of alumina-engine oil: Effects of temperature and nanoparticles concentration, Int Commun Heat Mass Transf, 76 (2016) 202–208. [45] M. Hemmat Esfe, M. Afrand, W.M. Yan, H. Yarmand, D. Toghraie, M. Dahari, Effects of temperature and concentration on rheological behavior of MWCNTs/SiO2 (20–80)-SAE40 hybrid nano-lubricant, Int Commun Heat Mass Transf, 76 (2016)133–138. [46] M. Hemmat Esfe, M. R. Hassani Ahangar, M. Rejvani, D. Toghraie, M. H. Hajmohammad, Designing an artificial neural network to predict dynamic viscosity of aqueous nanofluid of TiO2 using experimental data, Int Commun Heat Mass Transf, 75 (2016) 192–196. [47] M. Afrand, D. Toghraie, N. Sina, Experimental study on thermal conductivity of Waterbased Fe3O4 nanofluid: Development of a new correlation and modeled by artificial neural network, Int Commun Heat Mass Transf , 75 (2016) 262–269. [48] G.L. Morini, L. Baldas, Laminar forced convection of liquid flows through silicon microchannels, Houille Blanche, 1 (2006) 20-25. [49] M. Afrand, N. Sina, H. Teimouri, A. Mazaheri, M. R. Safaei, M. Hemmat Esfe, J. Kamali, D. Toghraie, Effect of magnetic field on free convection in inclined cylindrical annulus containing molten potassium, International Journal of Applied Mechanics 7 (04) (2015) 1550052. [50] H. Noorian, D. Toghraie, A.R. Azimian, Molecular dynamics simulation of Poiseuille flow in a rough nano channel with checker surface roughnesses geometry, Heat mass transf, 50 (1) (2014) 105-113.

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[51] K. Hooman, J. Li, M. Dahari, Slip flow forced convection through microducts of arbitrary cross-section: Heat and momentum analogy, Int. Commun. Heat Mass Transf, 71 (2016) 176179. [52] D. Toghraie, Numerical thermal analysis of Water's boiling heat transfer based on a turbulent jet impingement on heated surface, Physica E, 84 (2016) 454-465 [53] S. Oveissi, D. Toghraie, S.A. Eftekhari, Longitudinal vibration and stability analysis of carbon nanotubes conveying viscous fluid, Physica E, 83 (2016) 275-283 [54] Faridzadeh M.R. Semiromi D.T. Niroomand A. Analysis of laminar mixed convection in an inclined square lid-driven cavity with a nanofluid by using an artificial neural network. Heat Transfer Research. 2014; 45 [55] Semiromi D.T. Azimian A.R. Molecular dynamics simulation of liquid–vapor phase equilibrium by using the modified Lennard-Jones potential function, Heat and mass transfer, 46 (2010) 287-294 [56] Semiromi D.T. Azimian A.R. Nanoscale Poiseuille flow and effects of modified Lennard– Jones potential function, Heat and mass transfer, 46 (2010) 791-801 [57] Toghraie D. Mokhtari M. Afrand M. Molecular dynamic simulation of Copper and Platinum nanoparticles Poiseuille flow in a nanochannel. Physica E, 84, (2016) 152-161 [58] Afrand M. Toghraie D. Karimipour A. Wongwises SA. Numerical Study of Natural Convection in a Vertical Annulus Filled with Gallium in the Presence of Magnetic Field, Journal of Magnetism and Magnetic Materials, 430 (2017) 22–28 [59] Aghanajafi A, Toghraie D. Mehmandoust B., Numerical simulation of laminar forced convection of Water-CuO nanofluid inside a triangular duct, Physica E, 85 (2017) 103-108

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[60] Sajadifar S.A. Karimipour A. Toghraie D. Fluid flow and heat transfer of non-Newtonian nanofluid in a microtube considering slip velocity and temperature jump boundary conditions, European Journal of Mechanics-B/Fluids, 61 (2017) 25-32 [61] Nazari S. Toghraie D. Numerical simulation of heat transfer and fluid flow of Water-CuO Nanofluid in a sinusoidal channel with a porous medium. Physica E, 123; 87 (2017) 134-140 [62] Noorian H. Toghraie D. Azimian AR., Molecular dynamics simulation of Poiseuille flow in a rough nano channel with checker surface roughnesses geometry, Heat and mass transfer, 50 (2014) 105-113 [63] Rezaei M. Azimian AR. Toghraie D. Molecular dynamics study of an electro-kinetic fluid transport in a charged nanochannel based on the role of the stern layer, Physica A, 426 (2015) 25-34 [64] S. Oveisi, H. Nahvi, D. Toghraie, Investigation of Dynamical Behavior (Transverse Vibration) and Instability Analysis of Carbon Nanotubes Conveying Nanofluid, Journal of Solid Mechanics in Engineering 6 (2013)15-23 [65] S. Oveissi, S.A. Eftekhari, D. Toghraie, Longitudinal vibration and instabilities of carbon nanotubes conveying fluid considering size effects of nanoflow and nanostructure, Physica E, 83 (2016) 164-173 [66] Rezaei M. Azimian AR. Toghraie D. The surface charge density effect on the electroosmotic flow in a nanochannel: a molecular dynamics study, Heat and Mass Transfer, 51 (2015) 661-670 [67] MA Esfahani, D Toghraie, Experimental investigation for developing a new model for the thermal conductivity of Silica/Water-Ethylene glycol (40%–60%) nanofluid at different temperatures and solid volume fractions, Journal of Molecular Liquids, 232 (2017) 105-112

24

[68] M. Zadkhast D. Toghraie, A. Karimipour, Developing a new correlation to estimate the thermal conductivity of MWCNT-CuO/Water hybrid nanofluid via an experimental investigation, Journal of Thermal Analysis and Calorimetry, DOI: 10.1007/s10973-017-6213-8 [69] D Toghraie Semiromi, AR Azimian, Molecular Dynamics Simulation of Slab Geometry and the Effect of Cut-Off Radius, Proceeding of the 13th Asian Congress of Fluid Mechanics, 2010 [70] S. Shareghi, D. Toghraie, Numerical Simulation of Blood Flow in Healthy Arteries by Use of the Sisko Model, Computational Thermal Sciences: An International Journal 8 (4), 2016 [71] D.T. Semiromi, AR Azimian, Molecular Dynamics Simulation of Slab Geometry and the Effect of Cut-Off Radius, Proceeding of the 13th Asian Congress of Fluid Me-chanics. Bangladesh, 2010

25

Figure (1).The geometrical schematic of this presentation

26

Figure (2). The schematic and dimensions of used ribs inside the channel

27

Figure (3).The mesh of microchannel

28

Figure (4).Boundary conditions of this simulation.

29

130

128

126

Nuave

selected Grid for in this simulation

124

122

120 3e+4

7e+4

1e+5

2e+5

Grid Size

Figure (5).The grid independence in this numerical simulation

30

200

180

=0.04

R / W=0

160

Nuave

R / W=0.25

(a)

140

120 Smooth channel

100 Akbari et al. [29].

Current Study.

80

60 10000

12000

14000

16000

Re

360 Current Study 320

280

Nuave

Manca et. al. [32]. 240

(b) 200

Pure Water 160

120 20000

30000

40000

50000

Re

Figure (6).The validation of numerical results

31

60000

130 Case A4

=0.00 =0.02 =0.04

120 110

Re=2500

Nu

100 90 80 70 60 50 0.0015

0.0030

0.0045

0.0060

0.0075

x(m)

Figure (7).The distribution of local Nusselt number in Reynolds number 2500 (case A4)

32

Case A4

=0.00 =0.02 =0.04

160

Re=3500

Nu

140

120

100

80

0.0015

0.0030

0.0045

0.0060

0.0075

x(m)

Figure (8).The distribution of local Nusselt number in Reynolds number 3500 (case A4)

33

Case A4

=0.00 =0.02 =0.04

220 200

Re=5000

Nu

180 160

140 120

100 0.0015

0.0030

0.0045

0.0060

0.0075

x(m)

Figure (9).The distribution of local Nusselt number in Reynolds number 5000 (case A4)

34

180 Case A4

Re=2500 Re=3500 Re=5000

160



Nu

140

120

100

80

60

0.0015

0.0030

0.0045

0.0060

0.0075

x(m)

Figure (10).The distribution of local Nusselt number of the base fluid (case A4)

35

165

150

Case A4

Nuave

135

Re=2500 Re=3500 Re=5000

120

105

90

75

60 0

2

(%)

Figure (11).The average Nusselt number (case A4)

36

4

120

Case A5

=0.00 =0.02 =0.04

110

Re=2500

Nu

100 90 80 70 60

0.0015

0.0030

0.0045

0.0060

0.0075

x(m)

Figure (12).The distribution of local Nusselt number in Reynolds number 2500 (case A5)

37

Case A5

=0.00 =0.02 =0.04

160

Re=3500

Nu

140

120

100

80

0.0015

0.0030

0.0045

0.0060

0.0075

x(m)

Figure (13).The distribution of local Nusselt number in Reynolds number 3500 (case A5)

38

240 Case B4

=0.00 =0.02 =0.04

220

Re=5000

200

Nu

180

160

140

120

0.0015

0.0030

0.0045

0.0060

0.0075

x(m)

Figure (14).The distribution of the local Nusselt number in Reynolds number 5000 (case B4)

39

200

Case B4

Re=2500 Re=3500 Re=5000

180



Nu

160 140 120 100 80 60 0.0015

0.0030

0.0045

0.0060

0.0075

x(m)

Figure (15).The distribution of the local Nusselt number with volume fraction of 2% nanoparticles in the base fluid (case B4) 40

130 Case B5

=0.00 =0.02 =0.04

120 110

Re=2500

Nu

100 90 80 70 60 0.0015

0.0030

0.0045

0.0060

0.0075

x(m)

Figure (16).The distribution of local Nusselt number in Reynolds number 2500 (case B5)

42

180 Case B5

=0.00 =0.02 =0.04

160

Re=3500

Nu

140

120

100

80 0.0015

0.0030

0.0045

0.0060

0.0075

x(m)

Figure (17).The distribution of local Nusselt number in Reynolds number 3500 (case B5)

43

240 Case B5

=0.00 =0.02 =0.04

220

Re=5000

200

Nu

180

160

140

120

0.0015

0.0030

0.0045

0.0060

0.0075

x(m)

Figure (18).The distribution of local Nusselt number in Reynolds number 5000 (case B5)

44

165

150

Case B5

Nuave

135 Re=2500 Re=3500 Re=5000

120

105

90

75

0

2

4

(%)

Figure (19).The averages Nusselt number for (case B5)

45

Figure (20). The velocity distribution of symmetric plate with four semi-attached ribbed with the length of 10 µm in flow with Reynolds number of 2500 (Case A4).

46

Figure (21). The stream lines of flow with four semi-attached ribbed with the length of 10 µm in Reynolds number of 2500 (Case A4).

47

1.44 Re=2500 Re=3500 Re=5000

1.36

Case A4

PEC

1.28

1.20

1.12

1.04

0.96 0

2

(%)

Figure (22).Performance Evaluation Criterion (Case A4)

48

4

1.5

1.4 Re=2500 Re=3500 Re=5000

PEC

1.3

Case A5

1.2

1.1

1.0

0.9 0

2

(%)

Figure (23).Performance Evaluation Criterion (Case A5)

49

4

1.44 Re=2500 Re=3500 Re=5000

1.36

Case B4

PEC

1.28

1.20

1.12

1.04

0.96 0

2

(%)

Figure (24).Performance Evaluation Criterion (Case B4)

50

4

1.80 Re=2500 Re=3500 Re=5000

1.65

Case B5

PEC

1.50

1.35

1.20

1.05

0

2

(%)

Figure (25). Performance Evaluation Criterion (Case B5)

51

4

a. Ribbed with the length of 20 μm , Case B5

b. Ribbed with the length of 10 μm , Case A5 Figure (26). The turbulence kinetic energy with five semi-attached ribbed with the length of 20 and 10 μm (respectively Case B5 and A5) in Reynolds number of 5000

52

Table (1).The introduction of investigated cases of this presentation Case

Rib,s length (m)

Number of rib,s

Case A4

10

4

Case A5

10

5

Case B4

20

4

Case B5

20

5

Volume fraction ()

Reynolds number

0, 0.02, 0.04

2500, 3500, 5000

Table (2).The introduction of investigated dimensions of microchannel Case

Entrance length

Outlet length

L2

Dh&H

L1 )mm(

L3(mm)

)mm)

)m(

4

1.5

2

75

A&B

Table (3).The introduction cases investigated in this study. Case

y

z

X

q

L

)m( )m( )m( )m( )m( A

20

10

10

50

28.4

B

20

10

20

50

18.4

53

Table (4).Thermophysical properties of Al2O3/Water nanofluid [23] Properties

Water

Al2O3

Nanofluid

Nanofluid

0.02

0.04

Cp(J/kg.K)

4179

765

3922.4

3693.2

(kg/m3)

997.1

3970

1056.6

1116

k (W/m.K)

0.613

40

0.6691

0.7276

Pa .s)

8.9110-4

-

9.3710-4

9.8710-4

Highlights    

The flow and heat transfer inside a microchannel with a triangular section, have been numerically simulated. The presented results are including of the distribution of Nusselt number in the channel, friction coefficient and Performance Evaluation Criterion of each different arrangement. The ribs affect the physics of flow and their influence is absolutely related to Reynolds number of flow. In order to improve the heat transfer from the walls of microchannel on the constant heat flux, using the pump is demanded.

54