Al2O3 nanofluid inside a rectangular ribbed channel

Accepted Manuscript Turbulent flow and heat transfer of Water/Al2O3 nanofluid inside a rectangular ribbed channel Mohammad Parsaiemehr, Farzad Pourfattah, Omid Ali Akbari, Davood Toghraie, Ghanbarali Sheikhzadeh PII:

S1386-9477(17)31495-9

DOI:

10.1016/j.physe.2017.10.012

Reference:

PHYSE 12939

To appear in:

Physica E: Low-dimensional Systems and Nanostructures

Received Date: 29 September 2017 Revised Date:

9 October 2017

Accepted Date: 16 October 2017

Please cite this article as: M. Parsaiemehr, F. Pourfattah, O.A. Akbari, D. Toghraie, G. Sheikhzadeh, Turbulent flow and heat transfer of Water/Al2O3 nanofluid inside a rectangular ribbed channel, Physica E: Low-dimensional Systems and Nanostructures (2017), doi: 10.1016/j.physe.2017.10.012. 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 proof before it is published in its final 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.

ACCEPTED MANUSCRIPT

Turbulent flow and heat transfer of Water/Al2O3 nanofluid inside a rectangular ribbed channel

Ghanbarali Sheikhzadeh4

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

Department of Mechanical and Aerospace Engineering, Malek-Ashtar University of Technology,

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Mohammad Parsaiemehr1, Farzad Pourfattah2, Omid Ali Akbari1, Davood Toghraie3,*,

Shahinshahr, Isfahan, Iran 3

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

*

Department of Mechanical Engineering, University of Kashan, Kashan, Iran

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Corresponding author: Davood Toghraie, Department of Mechanical Engineering, Islamic AzadUniversity, Khomeinishahr Branch, Khomeinishahr 84175-119, Iran.

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Abstract

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Email: [email protected]

In present study, the turbulent flow and heat transfer of Water/Al2O3 nanofluid inside a rectangular channel have been numerically simulated. The main purpose of present study is investigating the effect of attack angle of inclined rectangular rib, Reynolds number and volume fraction of nanoparticles on heat transfer enhancement. For this reason, the turbulent flow of nanofluid has been simulated at Reynolds numbers ranging from 15000- 30000 and volume fractions of nanoparticles from 0- 4%. The changes attack angle of ribs have been

ACCEPTED MANUSCRIPT investigated ranging from 0-180o. The results show that, the changes of attack angle of ribs, due to the changes of flow pattern and created vortexes inside the channel, have significant effect on fluid mixing. Also, the maximum rate of heat transfer enhancement accomplishes in attack angle of 60o. In Reynolds numbers of 15000, 20000 and 30000 and attack angle of 60o,

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comparing to the attack angle of 0o, the amount of Nusselt number enhances to 2.37, 1.96 and 2 times, respectively. Also, it can be concluded that, in high Reynolds numbers, by using ribs and nanofluid, the performance evaluation criterion improves.

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Keywords: nanofluid, turbulent flow, inclined rib, angle of attack, performance evaluation

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criterion.

1. Introduction

In recent years, investigating different methods for increasing heat transfer has become more

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important and using novel fluids with high potential has been considered in the industrial applications obtaining from the distribution of nano-scale particles in the common fluids called nanofluid. The nanoparticles dimensions used in nanofluid are 1-100 nm. These

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nanoparticles are metal particles like Cu, Ag or other metal oxides. The common fluids used

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in heat transfer usually have low heat transfer coefficient, however, using nanoparticles, due to their high conductivity coefficient, causes the enhancement of thermal conductivity coefficient of fluid mixing. Therefore, using nanofluid is an applicable method for heat transfer enhancement [1-7]. According to the high advantages of using nanofluid in heat transfer, numerous studies have been done for investigating the rheological and hydrodynamical behavior of these novel heat transfer methods. Zarringhalam et al. [8] experimentally studied the convective heat transfer coefficient of Water/CuO nanofluid in different volume fractions of nanoparticles in turbulent flow regime inside a double-pipe heat

ACCEPTED MANUSCRIPT exchanger with counter flow. He figured out that, by increasing volume fraction of nanoparticles to 2% in the base fluid, the convective heat transfer coefficient enhances to 57%. Also, his results revealed that, in higher Reynolds numbers, adding nanoparticles has great effect on heat transfer enhancement. By reviewing the presented papers, it is specified

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that, in recent years, in order to have better cooling of industrial equipment, channels and micro channels have been widely used. However, investigating the behavior of common fluids and nanofluid in these geometrics is highly demanded [9-10]. Yongsiri et al. [11]

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numerically studied the air flow in a channel with detached and inclined ribs with the inclination angles ranging from 0-165o. In his research, the numerical solving domain had

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been studied two-dimensionally in Reynolds numbers of 4000 to 24000. His results indicated that, in Reynolds number of 4000, the changes of attack angle do not have impressive effect on friction coefficient, performance evaluation criterion and heat transfer enhancement. Also, he showed that, an attack angle which causes more flow recirculation and creates bigger

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vortexes, has higher amount of Nusselt number and friction coefficient. Kumar et al. [12] numerically studied the effect of using Water-Al2O3 nanofluid in a mini channel with square cross section and protrusion obstacles placed on its surface. The studied Reynolds numbers

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have been considered from 4000 to 18000 and for modeling the turbulent flow, k-ε model has

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been used. His results revealed that, using nanofluid and obstacles on mini channel surface, improves heat transfer to 3.73 times. Akbari et al. [13] studied the effect of rib height on heat transfer parameters and laminar flow of Water/Al2O3 nanofluid in a two-dimensional indented micro channel. His results indicated that, by increasing volume fraction of nanoparticles, the nanoparticles heat transfer mechanism improves and the existence of ribs on the direction of fluid motion and the enhancement of ribs height, cause the elimination and recreation of thermal boundary layer in the indented areas. Also, the mentioned parameters cause the reduction of dimensionless temperature along the microchannel and better mixing

ACCEPTED MANUSCRIPT of fluid layers and finally, heat transfer enhancement. In another study [14], he numerically simulated the heat transfer and turbulent flow of Water/CuO nanofluid in a rectangular microchannel with semi-attached ribs. He indicated that, in higher Reynolds numbers, using rib with higher aspect ratio causes the enhancement of heat transfer. Manca et al. [15] studied

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the forced convective heat transfer of Water/Al2O3 nanofluid in an indented channel and concluded that, the augmentation of nanofluid density does not have significant influence on flow function. Karimipour et al. [16] investigated the effect of rib on flow parameters and

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laminar heat transfer of Water/Ag nanofluid with different volume fractions of nanoparticles in a microchannel. He concluded that, by entering the fluid to the microchannel, the flow

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becomes developed and after colliding with rib, the flow becomes undeveloped. By increasing Reynolds number before and after the rib, the inconsistency of stream lines gets more changes. Khanjian et al. [17] numerically studied the effect of using winglet pair roll angle on heat transfer improvement in a channel. In his research, the flow has been

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considered steady and incompressible and Reynolds number has been studied at the range of 456 to 911. His results showed that, in all Reynolds numbers, the roll angle is not necessarily 90o and the determination of proper winglet roll angle should be studied more. Alipour et al.

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[18] investigated the effect of T-shaped semi-attached ribs on flow parameters and turbulent

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heat transfer of Water/Ag nanofluid in a trapezoidal micro channel. Using rib in order to increase the heat transfer has great impact on heat transfer performance in channels and microchannel. Using T-shaped rib, because of less obstruction of channel, causes the elimination of heated areas or lower heat transfer areas (LHTAS) in the channel. In the investigation of Zheng et al. [19], the fluid flow and heat transfer of a tubular exchanger has been modeled and the effect of Reynolds number and number of inclined grooves has been studied. His concluded that, using inclined grooves in flow with higher Reynolds numbers has more effect on heat transfer improvement. Using indented channels and nanofluid in

ACCEPTED MANUSCRIPT order to increase the heat transfer rate has attracted numerous researchers [20–25]. Navayi et al. [26], by using finite volume method, investigated the heat transfer and flow characteristics of different nanofluid in various types of wavy channels (rectangular, semicircular and trapezoidal) under the constant heat flux. His results indicated that, SiO2 nanofluid has the

increasing nanoparticles diameter, Nusselt number reduces.

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highest Nusselt number in the wavy semicircular channel. Also he concluded that, by

Using flow turbulators in channels and microchannel and other geometrics, due to the heat

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transfer conditions on surfaces, causes the creation of heated areas and non-uniform heat transfer distribution in the areas behind the ribs. Comparing to the smooth surfaces, placing

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ribs on the direction of fluid motion causes significant enhancement of pressure drop. In order to eliminate the mentioned disadvantages, in present study, the turbulent flow of Water/Al2O3 nanofluid in a two-dimensional rectangular microchannel with detached ribs, has been numerically investigated. By using detached ribs, numerous disadvantages have

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been eliminated. In present study, the detached ribs with different attack angles in the turbulent flow regime have been investigated and the presented results are the average Nusselt number, pressure drop and performance evaluation criterion. In addition to the

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mentioned quantitative results, in order to study the flow physics, the static temperature

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distribution contours and streamlines have been evaluated.

2. Problem statement, geometrics and boundary conditions

In this presentation, the turbulent flow of Water/Al2O3 nanofluid in different volume fractions of nanoparticles in the two-dimensional rectangular channel has been investigated. This investigation has been done in Reynolds numbers of 15000, 20000 and 30000 and volume fractions of 0, 2 and 4% of nanoparticles. Figure (1-a) indicates the studied geometrics of this research. According to figure (1-b), in each of the studied states, the rectangular ribs with

ACCEPTED MANUSCRIPT attack angles of 0, 30, 60, 960, 120, 150 and 180 have been placed on the bottom wall of the rectangular channel. The height of the studied channel is H and the lengths of channel in the inlet, middle and outlet sections are respectively L1, L2 and L3. Also, the pitches of ribs are constant and are indicated by P. The length, thickness and attack angles of each rib are

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respectively e, t and θ.

In present study, in order to simulate the flow inside the channel, the inlet boundary condition

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for channel inlet and the outlet pressure boundary condition for channel outlet, have been used. For investigating the walls of channel, the no-slip principle has been considered. The

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temperature of inlet water is 300 K. Also, the temperature of top and bottom walls of channel are constant and equal with 310 K and the ribs are considered as adiabatic.

All of the values and geometrical parameters related to figure (1) are indicated in table (1). In the calculation of thermophysical properties of used nanofluid, the nanoparticles have been

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considered as spherical and uniform with the diameter of ds= 50 nm and are in thermal equilibrium with the base fluid. Also, after entering to the channel and crossing the length of L1, the fluid becomes developed. The nanofluid properties used in this research in different

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volume fractions of Al2O3 nanoparticles have been presented in in table (2). According to this

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table, by increasing volume fraction of nanoparticles, the thermal conductivity coefficient and the cooling fluid viscosity enhance and the specific heat capacity reduces. In this numerical simulation, the nanofluid properties are considered constant with the temperature and the no-slip boundary condition has been applied to channel walls. The flow has been considered as two-dimensional, steady and incompressible and the volume forces and radiative heat transfer are not regarded. Also, the cooling nanofluid has been considered as Newtonian and single-phase and the influences of thermophoresis and turbulent diffusion have not been considered.

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3. Governing equations 3.1. The governing equations on turbulent flow The governing equations for solving the present problem are consistency, momentum and

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energy equations in Cartesian coordinate and are defined as [28]. The turbulent model of k-ω SST has been used for modeling the turbulent flow. Each of the mentioned equations are defined as:

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Continuity equation:

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∂ ( ρ ui ) = 0 ∂X i

Momentum equations:

∂ ∂P ∂   ∂ui ∂u j 2 ∂u + + − δ ij i ρ ui u j = − µ   ∂X j ∂X i ∂X j   ∂X j ∂X i 3 ∂X j

(

)

∂ ∂ ui ( E ρ + P ) ) = ( ∂X i ∂X j

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Energy equation:  Cp µt  λ + Prt 

 ∂T + ui τ i j   ∂X j

( )

(

 ∂ − ρ u /i u / j   +   ∂X j

 =0 eff 

(1)

)

(2)

(3)

defined as:

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In the above equation, E is the total energy, (τij)eff is the deviation stress tonsure which is

(

(τ ij )

)

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E = CpT − ( P / ρ ) + u 2 / 2

eff

 =  µeff 

 ∂u j ∂ui +  ∂ X ∂X j i 

  2 ∂ui δ ij   − µ eff ∂X j   3

(4) (5)

Yongsiri et al. [11], numerically examined the turbulent fluid flow of air and heat transfer in a channel with inclined detached-ribs. The shape of the ribs used in his study is same as the ribs used in present investigation. In his numerical study, he compared the turbulence models in

ACCEPTED MANUSCRIPT the channel. From two models of RNG k-ω and k-ω SST, k-ω SST model indicated more accurate results than the experimental findings. Based on the reference [11], k-ω SST turbulence model has been used in this study. The equation of the shear stress transport model of k-ω is as following:  ∂k  Γk  ∂X j 

  + Gk − Yk + S k     + Gω − Yω + Dω + Sω  

(6)

(7)

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∂ ∂  ∂ω  Γω ( ρω k ui ) = ∂X i ∂X j  ∂X j

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∂ ∂ ( ρ k ui ) = ∂X i ∂X j

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In equation (6), Gk is the turbulent kinetic energy generation caused by the average velocity gradients and in equation (7), Gω indicates the generation of ω.

3.2. The equations related to the measured parameters

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One of the parameters for investigating the hydrodynamical performance of channel is the friction coefficient which is calculated from following equation [29]: Dh 1 L ρuin2

(8)

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f = 2∆P

In equation (8), Dh is the hydraulic diameter of channel equals with channel height (H), L is

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the length, ρ is the density and uin is the inlet velocity. For calculating the amount of average Nusselt number following equation is used [30]: Nuave =

q′′Dh k f (Tw − Tm )

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In equation (9), Tw parameter is the temperature of milichannel wall and Tm is the average Bulk temperature. For total evaluation of performance evaluation criterion (PEC) of the indented milichannel, comparing to the smooth one, PEC parameter is defined as follow [3133]:

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 Nu ave    Nu ave, s  PEC =  (1/3)  f     fs 

The amount of the changes of inlet and outlet pressure drop is calculated as [34]: ∆ P = Pin − Pout

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(11)

In equation (11), in and out indexes are respectively the inlet and outlet sections. For calculating the pumping power, following equation is used [35]:

(12)

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Pp = A × uin × ∆ P

and the pressure drop.

4. Independency from grid

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In the above equation, A, uin and ∆P are respectively the inlet section of flow, inlet velocity

In order to investigate the effect of grid number on the obtained results and accuracy of the

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numerical results and their independency from the computational grid number, the studied grid number has been changed from 30000 to 100000 cells. In this research, the changes of average Nusselt number have been studied as a criterion for choosing the proper grid number.

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Figure (2) indicates the changes of average Nusselt number in θ=0 and Reynolds number of 15000 for pure water flow. As it can be seen, in element number more than 70000, the

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augmentation of grid number does not have significant effect on the results; therefore, in all of the simulations, this element number has been used. Also, in this article, the grid mesh is unstructured and the grid adoption for y+<5 near the solid wall region has been taken into account in the mesh generation.

5. Numerical solving procedure and validation

ACCEPTED MANUSCRIPT In this study, the first attempt to employ the forced convection of water/Al2O3 nanofluid in the rectangular ribbed channel has been carried out. The main goal is investigating the turbulent flow and heat transfer characteristics of two-dimensional ribbed channel with different attack angles of ribs. In this study, the turbulent flow has been considered as single-

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phase. Nanofluid with 0-4% volume fraction of nanoparticles have Newtonian behavior. In this research, the governing equations of fluid flow have been solved by using finite volume method [36-38]. With the use of finite volume method, the governing equations with

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mentioned boundary conditions have been solved by pressure based solver. In the numerical solving procedure, for discretizing the governing equations, the second-order discretization

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[39-43] and for coupling the velocity and pressure, SIMPLEC algorithm has been used [44, 45]. In present study, k-ω sst model has been used for modeling the turbulent flow [46]. In order to obtain accurate numerical results, the convergence criterion for all variables of this simulation has been considered 10-6 [47-49].

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In order to ensure from the obtained numerical results, the empirical results of Thianpong and Promvonge [50] have been used. Thianpong and Promvonge empirically studied the hydrodynamics and heat transfer of air flow in an indented channel with different geometrics

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of rib. In this validation, the air has been investigated in Reynolds number of 6000 in the

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indented channel with the condition of 90o and Nusselt number distribution at the bottom wall of channel has been plotted. In figure (3), the results have been compared with the results of reference [50]. As it can be observed, the obtained numerical results have proper coincidence with the empirical results. Therefore, it can be said that, the gridding, numerical solving procedure and the applied turbulent model have acceptable accuracy.

6. Results and discussions

ACCEPTED MANUSCRIPT 6.1. Effect of the changes of Reynolds number, solid fractions of nanoparticles and attack angles on average Nusselt number In this section, the results obtained from the numerical simulation of flow inside the channel

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with ribs in different attack angles ranging from (0-180o) have been presented. The results include the average Nusselt number, pumping power ratio and performance evaluation criterion. In figure (4), the effect of using nanoparticles in the base fluid in flow with Reynolds numbers of 15000-30000 and the effect of attack angles on the average Nusselt

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number enhancement are indicated. As it is seen, by increasing volume fraction of

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nanoparticles (Al2O3) in the base fluid (water), Nusselt number enhances. Also, the increase of nanoparticles causes the enhancement of conductive heat transfer coefficient and the augmentation of mass motion of fluid causes the improvement of heat transfer. By studying the effect of attack angle of ribs, it is specified that, attack angles are more impressive than adding nanoparticles for increasing the heat transfer. By influencing the shape of the created

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vortexes behind the ribs, the attack angle of rib changes the flow pattern and fluid mixing which enhances the heat transfer. As it can be seen, in each three studied Reynolds numbers and volume fractions, due to better mixing of fluid, the maximum amount of Nusselt number

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has been obtained in attack angles of 60o and 120o.

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In figure (5), the effect of attack angle on the changes of average Nusselt number in different Reynolds numbers, has been investigated. As it is observed, by increasing Reynolds number of flow, which accompanies with the enhancement of momentum and turbulence flow, Nusselt number increases. The results presented in figures (4) and (5) revealed that, in flow with Reynolds number of 30000, the effect of attack angle enhancement from 0 to 60o is different from the pure water and nanofluid with volume fractions of 2 and 4%. Hence, in pure water and nanofluid flow with volume fractions of 2 and 4%, the enhancement of attack angle from 0o to 60o causes the increase of heat transfer to 2, 2.2 and 2.4 times, respectively.

ACCEPTED MANUSCRIPT This result indicate that, flow mixing rate and the created vortex behind the ribs are under the influence of fluid properties. By increasing fluid viscosity, this vortex becomes stronger and leads to the accomplishment of maximum heat transfer in nanofluid with 4% volume fraction of Al2O3 nanoparticles. In general, by increasing Reynolds number, because of higher

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turbulence intensity (TI) of fluid flow between the ribs, Nusselt number increases. According to this behavior, by increasing fluid velocity, the level of Nusselt number diagrams increases. Generally, ribs position (angle of attack) can be effective on the changes of flow physics.

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Also, the mentioned changes affect the mixing and separation of flow. With the consideration

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of all above factors, by increasing attack angle of rib, Nusselt number behavior changes.

6.2. Investigating the behavior of pumping power in different Reynolds numbers and attack angles of ribs

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The pumping power ratio in each of the studied attack angles in Reynolds numbers of 15000, 20000 and 30000 and three volume fractions of nanoparticles, comparing to the pumping power of pure water flow in the smooth channel, are indicated in figure (6). As it is observed,

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in each three Reynolds numbers, by increasing volume fraction of nanoparticles in the base fluid, the pumping power ratio enhances. The augmentation of this factor is due to the

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enhancement of pressure drop. In fluid with higher viscosity and density, because of adding nanoparticles to the base fluid, pressure drop increases significantly. The pressure drop in attack angles of 90 and 120o, due to the high aspect ratios of ribs in these angles and bigger vortexes behind the ribs, pumping power ratio enhances. The fluid with higher density and viscosity requires higher momentum. By increasing attack angle, due to the collision of fluid with ribs, the depreciation of momentum becomes impressive. By preventing the fluid motion with attack angles, the pressure drop and pumping power will be reduced. In general, by decreasing the kinetic energy of fluid, the pressure drop and the pumping power enhance.

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6.3. The effect of volume fraction of nanoparticles and Reynolds number on PEC PEC is a criterion for evaluating the performance of heat transfer enhancement method.

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According to the definition of this quantity, when the amount of this coefficient is more than 1, the heat transfer enhancement is prevailed on the friction coefficient applied to the heat transfer surfaces. Therefore, the used heat transfer enhancement method is logical from the engineering and economical perspectives. In figure (7) the effect of volume fraction of

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nanoparticles and attack angles of ribs on PEC in flow with Reynolds number of 15000,

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20000 and 30000 has been presented. As it can be seen, in flow with Reynolds number of 15000, by increasing volume fraction of nanoparticles, the performance evaluation criterion enhances. The maximum amount of performance evaluation criterion has been obtained in attack angle of 60o and 4% volume fraction of nanoparticles in the base fluid. According to figure (7), in flow with Reynolds numbers of 20000 and 30000, the maximum amount of

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performance evaluation criterion has been achieved in attack angle of 60o, indicating that, in this attack angle, the changes of flow pattern and created vortexes are very impressive on

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flow domain, heat transfer and the enhancement of fluid mixing. Therefore, the heat transfer enhancement is prevailed on the friction coefficient applied to the studied heat transfer

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surfaces. According to the behavior of figure (7), by increasing Reynolds number, the level of PEC diagrams reduces. Of course, the main reason of this behavior is the considerable enhancement of friction coefficient. Generally, for increasing the heat transfer in high Reynolds numbers, using rib it is not recommended.

6.4. Streamlines contours and temperature distribution In the contours of figure (8), the temperature distribution (top figure) and streamlines (bottom figure) of water/Al2O3 nanofluid with volume fraction of 4% and Reynolds number of 30000

ACCEPTED MANUSCRIPT in different attack angles have been shown . As it is seen, in attack angle of 0o, the streamlines cross through the ribs without deviation and by increasing attack angle to 30o, a small vortex has been created behind the rib and by enhancing the attack angle to 60, 90 and 120o, the flow crossing through the ribs becomes influenced and the created vortex has been

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improved. In fact, by increasing the dimensions of vortex behind the rib, the turbulence of flow enhances and consequently, better mixing of flow, augmentation of temperature gradient and heat transfer have been accomplished. As it is understood from figure (8), the physics of

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created gradients in attack angle of 150o, is same as the attack angle of 30o and the flow physics in the attack angle of 120o is same as the attack angle of 60o. The similarity of created

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vortexes and the uniformity of heat transfer values in these attack angles are the main factors of heat transfer enhancement, because of using ribs and the creation of vortexes. Physical properties of vortex, like its largeness and extension are highly important in its impressionability on heat transfer enhancement and temperature gradients. According to the

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contours of figure (8), it can be seen that, the largest vortex has been created in attack angles of 60 and 120o and regarding the presented results, the maximum amount of Nusselt number

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7. Conclusion

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has been obtained in these attack angles.

The main purpose of this investigation is studying the effect of ribs, the changes attack angles of ribs and different volume fractions of Al2O3 nanoparticles on heat transfer enhancement. For this reason, the turbulent flow of water/Al2O3 nanofluid with Reynolds numbers ranging from 15000 to 30000 and volume fractions of 0-4% has been numerically simulated. The investigated attack angles have been changed at the range of 0-150o. The results indicate that, using ribs inside the channel is more impressive than adding nanoparticles on heat transfer enhancement and also, the simultaneous use of nanofluid and inclined ribs causes the

ACCEPTED MANUSCRIPT improvement of heat transfer. According to the results, the maximum rate of heat transfer accomplishes in attack angles of 60o and 120o, due to better mixing of flow and strong vortexes created behind the ribs. It should be said that, comparing to the augmentation of friction coefficient, the amount of heat transfer enhancement in attack angles of 60o and 120o

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significantly enhances. Consequently, higher amount of performance evaluation criterion accomplishes in these two attack angles. The extension of this paper in nanofluid studies according our previous works [51–98] affords a good option for the engineers and

Heat capacity, J/kg K

e

Height of obstacles, m

f

Friction factor

h

Convective heat transfer coefficient, W/m2.K

H

Microchannel height or Dh, m

k

Thermal conductivity coefficient, W/m K

L1

Input length, m

L2

Middle length, m

L3 Nu p

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Cp

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8. Nomenclature

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industrialists to investigate the micro and nano simulations.

Output length, m

Nusselt number

Pitch of obstacles, m

P

Pressure, Pa

PEC

Performance Evaluation Criterion

Pp

Pumping power, W

q"

Thermal heat flux, W/ m2

Re

Reynolds number

T

Temperature, K

t

Thickness of obstacles

U

Velocity component along the x, (m/s)

V

Velocity component along the y, (m/s)

x,y

Cartesian coordinates components

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8.1. Greek symbols

b

Balk

f

Base fluid (Pure Water)

H

Hot

in

Inlet

nf

Nanofluid

out

Outlet

P

Solid nanoparticles

s

Smooth

ϕ µ

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∆

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Average

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8.2. Super- and Sub-scripts Ave

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Difference

Nanoparticles volume fraction Dynamic viscosity, Pa.s

θ

Angle of attack the obstacles, deg

ρ

Density, kg/m3

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a turbulent channel flow with inclined detached-ribs, Case Studiesin Thermal Engineering, 3 (2014) 1–10.

[12] S. Kumar, A.D. Kothiyal, M.S. Bisht, A. Kumar, Numerical analysis of thermal

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hydraulic performance of Al2O3–H2O nanofluid flowing through a protrusion obstacles square minichannel, Case Studies in Thermal Engineering., 9 (2017) 108–121.

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[13] O.A. Akbari, A. Karimipour, D. Toghraie Semiromi, M.R. Safaei, H. Alipour, M. Goodarzi and M. Dahari, Investigation of Rib's Height Effect on Heat Transfer and Flow Parameters of Laminar Water-Al2O3 Nanofluid in a Two Dimensional Rib-Microchannel, Appl. Math. Comp., 290 (2016) 135–153.

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[14] O.A. Akbari, D. Toghraie, A. Karimipour, Numerical simulation of heat transfer and turbulent flow of Water nanofluids copper oxide in rectangular microchannel with semi attached rib, Adv. Mech. Eng., 8 (4) (2016) 1–25.

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[15] O. Manca, S. Nardini, D. Ricci, Numerical investigation of air forced convection in

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channels with differently shaped transverse ribs, Int. J. Numer. Method Heat Fluid Flow., 21 (2010) 618-639.

[16] A. Karimipour, H. Alipour, O.A. Akbari, D. Toghraie Semiromi and M.H. Esfe, Studying the effect of indentation on flow parameters and slow heat transfer of Water-silver nanofluid with vrying volume fraction in a rectangular Two-Dimensional microchannel, Ind. J. Sci. Tech., 8(15) (2015) 51707.

ACCEPTED MANUSCRIPT [17] A. Khanjian, C. Habchi, S. Russeil, D. Bougeard, T. Lemenand, Effect of rectangular winglet pair roll angle on the heat transfer enhancement in laminar channel flow, Int. J. Therm. Sci., 114 (2017) 1-14. [18] H. Alipour, A. Karimipour, M.R. Safaei, D. Toghraie Semiromi, O.A. Akbari, Influence

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of T-semi attached rib on turbulent flow and heat transfer parameters of a silver-Water nanofluid with different volume fractions in a three-dimensional trapezoidal microchannel, Phys E., 88 (2017) 60–76.

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[19] N. Zheng, P. Liu, F. Shan, Z. Liu, W. Liu, Turbulent flow and heat transfer enhancement in a heat exchanger tube fitted with novel discrete inclined grooves, Int. J. Therm. Sci., 111

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(2017) 289-300.

[20] Al-asadi MT , Mohammed HA , Sh Kherbeet A , Al-aswadi AA . Numerical study of assisting and opposing mixed convective nanofluid flows in an inclined circular pipe. Int Commun Heat Mass Transfer 2017;85:81–91.

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[21] Ahmed HamdiE , YusoffMZ , Hawlader MNA , Ahmed MI , Salman BH , Kerbeet ASh . Turbulent heat transfer and nanofluid flow in a triangular duct with vortex genera- tors. Int J

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Heat Mass Transfer 2017;105:495–504.

[22] Khoshvaght-Aliabadi M , Rahnama P , Zanganeh A , Akbari MH . Experimental study

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on metallic water nanofluids flow inside rectangular duct equipped with circular pins (pin channel). Exp Therm Sci 2016;72:8–30. [23] Ghasemi SE , Ranjbar AA , Hosseini MJ . Experimental evaluation of cooling performance of circular heat sinks for heat dissipation from electronic chips using nanofluid. Mech Res Commun 2017;84:85–9.

ACCEPTED MANUSCRIPT [24] Malvandi A , Zamani M , Hosseini SJ , Moshizi SA . Figure of merit for optimization of nanofluid flow in circular microchannel by adapting nanoparticle migration. Appl Therm Eng 2017;118:328–33. [25] Dondapati RS , Saini V , Verma KN , Usurumarti PR . Computational prediction of pres-

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sure drop and heat transfer with cryogen based nanofluids to be used in micro-heat exchangers. Int J Mech Sci 2017;130:133–42.

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[26] Navaei A , Mohammed H , Munisamy K , Yarmand H , Gharehkhani S . Heat transfer en- hancement of turbulent nanofluids flow over various types of internally corrugated

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channels. Powder Technol 2015;15:332–41.

[27] O.A. Akbari, D. Toghraie, A. Karimipour, Impact of ribs on flow parameters and laminar heat transfer of Water–aluminum oxide nanofluid with different nanoparticle volume fractions in a three-dimensional rectangular microchannel, Adv. Mech. Eng., 7 (11) (2015) 1–

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11.

[28] A. Andreozzi, O. Manca, S. Nardini, D. Ricci, Forced convection enhancement in channels with transversal ribs and nanofluids, Appl. Therm. Eng., 98 (2016) 1044-1053.

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[29] O.A. Akbari, D. Toghraie, A. Karimipour, A. Marzban, Gh.R. Ahmadi, The effect of velocity and dimension of solid nanoparticles on heat transfer in non-Newtonian nanofluid,

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Phys E., 86 (2017) 68–75.

[30] A. Datta, D. Sanyal, A.K. Das, Numerical investigation of heat transfer in microchannel using

inclined

longitudinal

vortex

generator,

Appl.

Therm.

Eng.,

(2016),

doi:

http://dx.doi.org/10.1016/j.applthermaleng.2016.07.165. [31] P. Li, D. Zhang, Y. Xie, Heat transfer and flow analysis of Al2O3eWater nanofluids in microchannel with dimple and protrusion, Int. J. Heat Mass Transf., 73 (2014) 456-467.

ACCEPTED MANUSCRIPT [32] T.K. Nandi, H. Chattopadhyay, Numerical investigations of developing flow and heat transfer in raccoon type microchannels under inlet pulsation, Int. Commun. Heat Mass Transf., 56 (2014) 37-41. [33] Y.L. Zhai , G.D. Xia , X.F. Liu , Y.F. Li, Heat transfer in the microchannels with fan-

generation analysis, Int. J. Heat Mass Transf., 68 (2014) 224-233.

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shaped reentrant cavities and different ribs based on field synergy principle and entropy

[34] A.A. Gholami, Mazlan A. Wahid, H.A. Mohammed, Heat transfer enhancement and

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pressure drop for fin-and-tube compact heat exchangers with wavy rectangular winglet-type vortex generators, Int. Commun. Heat Mass Trans., 54 (2014) 132–140.

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[35] A. Ebrahimi, E. Roohi, S. Kheradmand, Numerical study of liquid flow and heat transfer in rectangular microchannel with longitudinal vortex generators, Appl. Therm. Eng., 78 (2015) 576-583.

[36] A.A.A. Arani, O.A. Akbari, M.R. Safaei, A. Marzban, A.A.A.A. Alrashed, G.R.

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Ahmadi, T.K. Nguyen, Heat transfer improvement of Water/single-wall carbon nanotubes (SWCNT) nanofluid in a novel design of a truncated double layered microchannel heat sink, Int. J. Heat Mass Transf, 113 (2017) 780–795.

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[37] Ramin Mashayekhi, Erfan Khodabandeh, Mehdi Bahiraei, Leyli Bahrami, Davood

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Toghraiee, Omid Ali Akbari, Application of a novel conical strip insert to improve the efficacy of water–Ag nanofluid for utilization in thermal systems: A two-phase simulation, Energy Conversion and Management 151 (2017) 573–586. [38] Davood Toghraie, Mohammad Mehdi Davood Abdollah, Farzad Pourfattah, Omid Ali Akbari, Behrooz Ruhani, Numerical investigation of flow and heat transfer characteristics in smooth, sinusoidal and zigzag-shaped microchannel with and without nanofluid, J Therm Anal Calorim, DOI 10.1007/s10973-017-6624-6.

ACCEPTED MANUSCRIPT [39] E. Khodabandeh, M. Pourramezan, M.H. Pakravan, Effects of excess air and preheating on the flow pattern and efficiency of the radiative section of a fired heater, Appl Therm Eng, 105 (2016) 537-548. [40] Farzad Pourfattah, Mahdi Motamedian, Ghanbarali Sheikhzadeh, Davood Toghraie,

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Omid Ali Akbari, The numerical investigation of angle of attack of inclined rectangular rib on the turbulent heat transfer of Water-Al2O3 nanofluid in a tube, International Journal of Mechanical Sciences 000–132 (2017) 1–11.

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[41] E. Khodabandeh, M. Ghaderi, A. Afzalabadi, A. Rouboa, A. Salarifard, Parametric Study of Heat Transfer in an Electric Arc Furnace and Cooling System, Appl Therm Eng,

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123 (2017) 1190–1200.

[42] E. Khodabandeh, A. Rahbari, M.A. Rosen, Z. Najafian Ashrafi, O.A. Akbari, A. Masoud Anvari, Experimental and numerical investigations on heat transfer of a Watercooled lance for blowing oxidizing gas in an electrical arc furnace, Energ Conv Manag, 148 (2017) 43–56.

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[43] M. Heydari, D. Toghraie, O.A. Akbari, The effect of semi-attached and offset midtruncated ribs and Water/TiO2 nanofluid on flow and heat transfer properties in a triangular microchannel, Therm Sci Eng Prog, 2 (2017) 140–150.

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[44] O.A. Akbari, M. Goodarzi, M. Reza Safaei, M. Zarringhalam, G.R. Ahmadi Sheikh,

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Shabaniand M. Dahari, A modified two-phase mixture model of nanofluid flow and heat transfer in 3-d curved microtube, Adv. Powd. Tech., 27 (2016) 2175–2185. [45] M.R. Safaei, M. Goodarzi, O.A. Akbari, M. Safdari Shadloo and M. Dahari (2016), Performance Evaluation of Nanofluids in an Inclined Ribbed Microchannel for Electronic Cooling Applications, Electronics Cooling, Prof. S M SohelMurshed (Ed.), InTech, DOI: 10.5772/62898.

Available

from:

http://www.intechopen.com/books/electronics-

cooling/performance-evaluation-of-nanofluids-in-an-inclined-ribbed-microchannelforelectronic-cooling-appli.

ACCEPTED MANUSCRIPT [46] O.A. Akbari, H. Hassanzadeh Afrouzi, A. Marzban, D. Toghraie, H. Malekzade & A. Arabpour, Investigation of volume fraction of nanoparticles effect and aspect ratio of the twisted tape in the tube, J Therm Anal Calorim, DOI 10.1007/s10973-017-6372-7. [47] O. Rezaei, O.A. Akbari, A. Marzban, D. Toghraie, F. Pourfattah, R. Mashayekhi, The

microchannel, Physica E 93 (2017) 179–189.

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

[48] A. Behnampour, O.A. Akbari, M.R. Safaei, M. Ghavami, A. Marzban, Gh.R. Ahmadi

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Sheikh Shabani, M. zarringhalam and R. Mashayekhi, Analysis of heat transfer and nanofluid

E, 91 (2017) 15–31

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fluid flow in microchannels with trapezoidal, rectangular and triangular shaped ribs, Physica

[49] M.R. Shamsi, O.A. Akbari, A. Marzban, D. Toghraie, R. Mashayekhi, Increasing heat transfer of non-Newtonian nanofluid in rectangular microchannel with triangular ribs,

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Physica E 93 (2017) 167–178.

[50] P. Promvonge, C. Thianpong, Thermal performance assessment of turbulent channel flow over different shape ribs, Int. Commun. Heat Mass Transf., 35 (10) (2008) 1327–34.

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[51] Semiromi DT, Azimian AR. Molecular dynamics simulation of annular flow boil- ing

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with the modified Lennard–Jones potential function. Heat Mass Transfer 2012;48:141–52 . [52] AA Mehrizi, M Farhadi, H. Hassanzadeh Afroozi, K Sedighi, AAR Darz, Mixed convection heat transfer in a ventilated cavity with hot obstacle: effect of nanofluid and outlet port location, International Communications in Heat and Mass Transfer,2012, 39 (7), 10001008. [53] Toghraie D , Alempour SMB , Afrand M . Experimental determination of viscosity of Water based magnetite nanofluid for application in heating and cooling systems. J Magn Magn Mater 2016;417:243–8.

ACCEPTED MANUSCRIPT [54] H.Hassanzadeh Afrouzi, M Farhadi, Mix convection heat transfer in a lid driven enclosure filled by nanofluid, Iranica J. Energy Environ. 2013, 4, 376-384. [55] Hemmat Esfe M , Saedodin S , Wongwises S , Toghraie D . An experimental study on

J Therm Anal Calorim 2015;119:1817–24.

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the effect of diameter on thermal conductivity and dynamic viscosity of Fe/Water nanofluids.

[56] H Pourmirzaagha, HH Afrouzi, AA Mehrizi, Nano-particles transport in a concentric

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annulus: a lattice Boltzmann approach, Journal of Theoretical and Applied Mechanics 2015, 53 (3), 683-695.

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[57] AA Mehrizi, M Farhadi, S Shayamehr, Natural convection flow of Cu–Water nanofluid in horizontal cylindrical annuli with inner triangular cylinder using lattice Boltzmann method, International Communications in Heat and Mass Transfer, 2013 44, 147-156. [58] Hemmat Esfe M , Afrand M , Gharehkhani S , Rostamiand H , Toghraie D , Dahari M .

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An experimental study on viscosity of alumina-engine oil: effects of temperature and nanoparticles concentration. Int Commun Heat Mass Transfer 2016;76:202–8.

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[59] Hemmat Esfe M , Afrand M , Yan WM , Yarmand H , Toghraie D , Dahari M . Effects of temperature and concentration on rheological behavior of MWC- NTs/SiO2(20–80)-

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SAE40 hybrid nano lubricant. Int Commun Heat Mass Transfer 2016;76:133–8 . [60] Hemmat Esfe M , Ahangar Hassani , Rejvani M , Toghraie D , Hajmohammad MH . Designing an artificial neural network to predict dynamic viscosity of aqueous nanofluid of TiO2 using experimental data. Int Commun Heat Mass Transfer 2016;75:192–6 . [61] Hamid Reza Goshayeshi, Marjan Goodarzi, Mohammad Reza Safaei and Mahidzal Dahari, Experimental Study on the Effect of Inclination Angle on Heat Transfer

ACCEPTED MANUSCRIPT Enhancement of a Ferro-nanofluid in a Closed Loop Oscillating Heat Pipe under Magnetic Field, Experimental Thermal and Fluid Science, 74, 265–270, 2016. [62] J.A. Esfahani, Mohammad Reza Safaei, Masoud Goharimanesh, Letícia Raquel de

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Oliveira, Marjan Goodarzi, Shahaboddin Shamshirband and Enio Pedone Bandarra Filho, Comparison of Experimental Data, Modelling and non-linear Regression on Transport Properties of Mineral Oil Based Nanofluids, Powder Technology, 317, 458-470, 2017.

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[63] Mohammad Reza Safaei, AminHossein Jahanbin, Ali Kianifar, Samira Gharehkhani, Akeel Shebeeb Kherbeet, Marjan Goodarzi and Mahidzal Dahari, Mathematical Modeling for

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Nanofluids Simulation: A Review of the Latest Works, Modeling and Simulation in Engineering Sciences, Dr. Noreen Sher Akbar (Ed.), InTech, DOI: 10.5772/64154. Available from:

http://www.intechopen.com/books/modeling-and-simulation-in-engineering

sciences/mathematical-modeling-for-nanofluids-simulation-a-review-of-the-latest-works,

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2016.

[64] Afrand M, Toghraie D , Sina N . Experimental study on thermal conductivity of Wa- terbased Fe3O4 nanofluid: development of a new correlation and modeled by arti- ficial neural

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network. Int Commun Heat Mass Transfer 2016; 75:262–9.

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[65] Afrand M , Sina N , Teimouri H , Mazaheri A , Safaei MR , Hemmat Esfe M , et al. Effect of magnetic field on free convection in inclined cylindrical annulus containing molten potassium. Int J Appl Mech 2015; 7:1550052. [66] Noorian H., Toghraie D., Azimian AR., Molecular dynamics simulation of Poiseuille flow in a rough nanochannel with checker surface roughnesses geometry, Heat and Mass Transfer, 2014; 50: 105–113.

ACCEPTED MANUSCRIPT [67] Toghraie D, Chaharsoghi VA, Afrand M. Measurement of thermal conduc- tivity of ZnO–TiO2/EG

hybrid

nanofluid.

J

Therm

Anal

Calorim

2016:1–9.

http://dx.doi.org/10.1007/s10973-016-5436-4 .

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[68] Hemmat Esfe M , Yan WM , Afrand M , Sarraf M , Toghraie D , Dahari M . Estimation of thermal conductivity of Al 2 O 3 /Water (40%)–ethylene-glycol (60%) by artificial neural network and correlation using experimental data. Int Commun Heat Mass Transf 2016; 74:

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125–8.

[69] Afrand M, Toghraie D, Karimipour A , Wongwises SA . Numerical study of natural

Magn Mater 2017; 430: 22–8.

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convection in a vertical annulus filled with gallium in the presence of magnetic field. J Magn

[70] Semiromi DT, Azimian AR. Nanoscale Poiseuille flow and effects of modified Lennard– Jones potential function. Heat Mass Transfer 2010; 46: 791–801 .

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[71] Semiromi DT, Azimian AR . Molecular dynamics simulation of liquid–vapor phase equilibrium by using the modified Lennard–Jones potential function. Heat Mass Transfer

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2010;46:287–94 .

[72] Semiromi DT , Azimian AR . Molecular dynamics simulation of nonodroplets with the

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modified Lennard–Jones potential function. Heat Mass Transfer 2010;47:579–88 . [73] Faridzadeh MR , Semiromi DT , 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 Res 2014;45 . [74] Oveissi S . D Toghraie, SA Eftekhari, Longitudinal vibration and stability analysis of carbon nanotubes conveying viscous fluid. Physica E 2016;83:275–83 .

ACCEPTED MANUSCRIPT [75] Toghraie D. Numerical thermal analysis of Water’s boiling heat transfer based on a turbulent jet impingement on heated surface. Physica E 2016;84:454–65 . [76] Mohammad Reza Safaei, Goodarz Ahmadi, Mohammad Shahab Goodarzi, Mostafa

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Safdari Shadloo, Hamid Reza Goshayeshi and Mahidzal Dahari, Heat Transfer and Pressure Drop in Fully Developed Turbulent Flow of Graphene Nanoplatelets–Silver/Water Nanofluids, Fluids, 1(3), 1-20, 2016.

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[77] SA Mirkalantari, M Hashemian, SA Eftekhari, D Toghraie, Pull-in instability analysis of rectangular nanoplate based on strain gradient theory considering surface stress effects,

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Physica B: Condensed Matter 519, 1-14, 2017

[78] S Saffari, M Hashemian, D Toghraie, Dynamic stability of functionally graded nanobeam based on nonlocal Timoshenko theory considering surface effects, Physica B: Condensed Matter, Volume 520, 2017, Pages 97-105

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[79] M Farzinpour, S Rasouli, DS Toghraie, Experimental and numerical investigations of bubbling fluidized bed apparatus to investigate heat transfer coefficient for different fins,

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Computational Thermal Sciences: An International Journal 9 (3), 2017 [80] E Keshavarz, D Toghraie, M Haratian, Modeling industrial scale reaction furnace using

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computational fluid dynamics: A case study in Ilam gas treating plant, Applied Thermal Engineering 123, 277-289, 2017 [81] M Nemati, ARSN Abady, D Toghraie, A Karimipour, Numerical investigation of the pseudopotential lattice Boltzmann modeling of liquid–vapor for multi-phase flows, Physica A: Statistical Mechanics and its Applications 489, 65-77, 2018

ACCEPTED MANUSCRIPT [82] A Moraveji, D Toghraie, Computational fluid dynamics simulation of heat transfer and fluid flow characteristics in a vortex tube by considering the various parameters, International Journal of Heat and Mass Transfer 113, 432-443, 2017

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[83] M Tohidi, D Toghraie, The effect of geometrical parameters, roughness and the number of nanoparticles on the self-diffusion coefficient in Couette flow in a nanochannel by using of molecular dynamics simulation, . Physica B: Condensed Matter 518, 20-32, 2017

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[84] H Noorian, D Toghraie, AR Azimian, . The effects of surface roughness geometry of flow undergoing Poiseuille flow by molecular dynamics simulation, Heat and Mass Transfer

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50 (1), 95-104, 2014

[85] Tasawar Hayat, Ikram Ullah, Ahmed Alsaedi, Muhammad Waqas, Bashir Ahmad, Three-dimensional mixed convection flow of Sisko nanoliquid, International Journal of Mechanical Sciences, Volume 133, November 2017, Pages 273-282.

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[86] GR Ahmadi, D Toghraie, . Energy and exergy analysis of Montazeri steam power plant in Iran, Renewable and Sustainable Energy Reviews 56, 454-463, 2016

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[87] Zadkhast M , Toghraie D , Karimipour A . Developing a new correlation to estimate the thermal conductivity of MWCNT-CuO/Water hybrid nanofluid via an experimental

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investigation. J Therm Anal Calorim 2017;129:859–67 . [88] Toghraie Semiromi D , Azimian AR . Molecular dynamics simulation of slab geome- try and the effect of cut-offradius. Proceeding of the 13th Asian congress of fluid mechanics; 2010 . [89] Shareghi S, Toghraie D . Numerical simulation of blood flow in healthy arteries by use of the Sisko Model. Comput Thermal Sci Int J 2016;8(4):309–20 .

ACCEPTED MANUSCRIPT [90] Oveisi S, Nahvi H , Toghraie D . Investigation of dynamical behavior (transverse vibration) and instability analysis of carbon nanotubes conveying nanofluid. J Solid Mech Eng 2013;6(118):15–23 .

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[91] Oveissi S , Eftekhari SA , Toghraie D . Longitudinal vibration and instabilities of carbon nanotubes conveying fluid considering size effects of nanoflow and nanostructure. Physica E 2016; 83: 164–73.

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[92] Rezaei M , Azimian AR , Toghraie D . The surface charge density effect on the elec- troosmotic flow in a nanochannel: a molecular dynamics study. Heat Mass Transfer 2015; 51:

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661–70 .

[93] 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 2015;426:25–34 .

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[94] Esfe MH , Saedodin S , Bahiraei M , Toghraie D , Mahian O , Wongwises S . Thermal conductivity modeling of MgO/EG nanofluids using experimental data and artificial neural

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network. J Therm Anal Calorim 2014;118:287–94 . [95] Esfe MH , Akbari M , Semiromi DT , Karimiopour A , Afrand M . Effect of nanofluid

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variable properties on mixed convection flow and heat transfer in an inclined two-sided liddriven cavity with sinusoidal heating on sidewalls. Heat Transfer Res 2014;45:409–32 . [96] Karimipour A, Esfe MH , Safaei MR , Semiromi DT , Jafari S , Kazi SN . Mixed convection of Copper–Water nanofluid in a shallow inclined lid driven cavity using the lattice Boltzmann method. Physica A 2014; 402: 150–68 .

ACCEPTED MANUSCRIPT [97] Afrand M , Toghraie D , Ruhani B . Effects of temperature and nanoparticles concentration on rheological behavior of Fe3O4 –Ag/EG hybrid nanofluid: an experimental study. Exp Therm Fluid Sci 2016;77:2016 .

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[98] Ramin Sarlak, Shahrouz Yousefzadeh, Omid Ali Akbari, Davood Toghraie, Sajad Sarlak, Fattah assadi, The investigation of simultaneous heat transfer of Water/Al2O3 nanoßuid in a close enclosure by applying homogeneous magnetic field, International Journal

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of Mechanical Sciences, DOI: 10.1016/j.ijmecsci.2017.09.035.

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Table (2) .The properties of Water-Al2O3 nanofluid [27].

Table (1). Introduction of parameters and geometrics dimensions of problems.

Dimension

Quantity

60 mm

L1

60 mm

L2

600 mm

L3

60 mm

p

60 mm

T

1mm

E

6 mm

θ

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Table (2) .The properties of Water-A2O3 nanofluid [27]

Water

Al2O3

Nanofluid

Nanofluid

ϕ=0.02

ϕ=0.04

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Properties

4179

765

3922.4

3693.2

ρ (kg/m3)

997.1

3970

1056.6

1116

k (W/m.K)

0.613

40

0.6691

0.7276

µ (Pa .s)

8.91×10-4

-

9.37×10-4

9.87×10-4

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Cp(J/kg.K)

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Figure (5). The effect angle of attack on the average Nusselt number in different volume

Figure (6). The changes of pumping ratio of the indented channel comparing to the smooth

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Figure (7). The effect of volume fraction of nanoparticles and Reynolds number on the

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3

PP/PP,s 3

2 2 ϕ=0 ϕ=0.02 ϕ=0.04

1

0

0 30

60

90

120

150

a. Re=15000

8

Re=30000

2

30

60

90

ϕ=0 ϕ=0.02 ϕ=0.04

120

θ

b. Re=20000

TE D

4

EP

PP/PP,s

6

0

M AN U

θ

AC C

0

SC

1

ϕ=0 ϕ=0.02 ϕ=0.04

0

0

30

60

90

120

150

θ

c. Re=30000

Figure (6). The changes of pumping ratio of the indented channel comparing to the smooth channel in different volume fractions and Reynolds numbers

150

ACCEPTED MANUSCRIPT 1.4

1.6

1.4

ϕ=0 ϕ=0.02 ϕ=0.04

Re=20000

Re=15000 1.2

1.2

0.8

0.8 ϕ=0 ϕ=0.02 ϕ=0.04

0.6

0.6

0.4

0.4 30

60

90

120

150

0

180

30

60

SC

θ

90

120

150

θ

b. Re=20000

M AN U

a. Re=15000

1.2

ϕ=0 ϕ=0.02 ϕ=0.04

Re=30000 1.0

0.8

TE D

PEC

0.6

EP

0

RI PT

PEC

1.0

0.4

0

AC C

PEC

1.0

30

60

90

120

150

180

θ

c. Re=30000

Figure (7). The effect of volume fraction of nanoparticles and Reynolds number on the performance evaluation criterion coefficient in the channel according to the angle of attack ribs

180

ACCEPTED MANUSCRIPT

θ=0 deg

M AN U

θ=30 deg

RI PT

300 301 302 303 304 305 306 307 308 309 310

SC

Temperature:

TE D

θ=60 deg

AC C

EP

θ=90 deg

θ=120 deg

θ=150 deg Figure (8). The contours of temperature distribution (top) and stream lines (bottom) in different angles of attack rib

ACCEPTED MANUSCRIPT Research highlights •

Turbulent flow and heat transfer of nanofluid inside a rectangular channel have been simulated.

•

Effect angle of attack of inclined rectangular ribs, Reynolds number and volume fraction of nanoparticles was investigated. Turbulent flow of nanofluid have been simulated at the range of Reynolds numbers of 15000-

RI PT

•

AC C

EP

TE D

M AN U

SC

30000.