Thermal and hydraulic characteristics of turbulent nanofluids flow in trapezoidal-corrugated channel: Symmetry and zigzag shaped

Author’s Accepted Manuscript Thermal and hydraulic characteristics of turbulent nanofluids flow in trapezoidal-corrugated channel: Symmetry and zigzag shaped Raheem K. Ajeel, W. Saiful-Islam, Khalid B. Hasnan www.elsevier.com/locate/csite

PII: DOI: Reference:

S2214-157X(18)30059-5 https://doi.org/10.1016/j.csite.2018.08.002 CSITE323

To appear in: Case Studies in Thermal Engineering Received date: 8 March 2018 Revised date: 5 July 2018 Accepted date: 9 August 2018 Cite this article as: Raheem K. Ajeel, W. Saiful-Islam and Khalid B. Hasnan, Thermal and hydraulic characteristics of turbulent nanofluids flow in trapezoidalcorrugated channel: Symmetry and zigzag shaped, Case Studies in Thermal Engineering, https://doi.org/10.1016/j.csite.2018.08.002 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.

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Thermal and hydraulic characteristics of turbulent nanofluids flow in trapezoidalcorrugated channel: Symmetry and zigzag shaped Raheem K. Ajeel1, 2*, W. Saiful-Islam1, Khalid B. Hasnan1 1 Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Batu Pahat, Johor, Malaysia. 2 Department of Mechanical Engineering, College of Engineering, University of Babylon, Babylon, Iraq. * E-mail address: [email protected], Phone:+60183599483 Abstract Thermal and hydraulic characteristics of turbulent nanofluids flow in a trapezoidal-corrugated channel are numerically investigated by implementing the finite volume method to solve the governing equations. The adiabatic condition for the straight walls, constant heat flux for the corrugated walls, and two configurations of trapezoidal channel symmetry and zigzag shape were examined. The performance of a trapezoidal-corrugated channel with four different kinds of nanofluids ( ZnO, Al2O3, CuO, and SiO2), with four various nanoparticle volume fractions of 2%, 4 %, 6% and 8% using water as base fluid is thoroughly analyzed and discussed. The nanoparticles diameter, another parameter is taken into consideration, varied from 20 to 80 nm. Results show that the symmetry profile of trapezoidal-corrugated channel has a great effect on the thermal performance compared with a straight profile and zigzag profile. The Nusselt number dropped as the nanoparticle diameter grew; however, it grew as the nanoparticle volume fraction and Reynolds number dropped. The best improvement in heat transfer among the nanofluids types was by SiO2-water. The present investigation uncovers that these trapezoidal symmetrycorrugated channels have favorable circumstances by utilizing nanofluids and in this manner fill in as a promising contender for incorporation in more compact heat exchanger devices. Keywords: Heat transfer enhancement; Turbulent flow; Trapezoidal-corrugated channel; Nanofluids; Symmetry profile. 1. Introduction In recent years, many industries have a strong need to achieve higher thermal performance in order to gain high efficiency, reduce the cost and weight, and minimize the size of heat exchangers. Use of corrugated channels can decrease the thermal resistance where its acts to reduce the thermal boundary layer thickness of the heat exchanger surface. Therefore, corrugated surface geometry is one of the numerous appropriate procedures to upgrade the heat transfer in these devices due to the appearance of the secondary flow regions in the trough of the corrugated channel which leads to improve the blending of the fluid and consequently maximize the heat transfer exchange. On the coolant side, the poor thermal conductivity of the conventional fluid is the main impediment to improve the efficiency of heat exchangers. In order to cope with these limitations, the introduction of nanoparticles in a conventional fluid can be considered to jack up heat transfer abilities of these fluids. The component that produces (nanofluids) will have improved heat transfer capabilities, even with a small particle percentage. Many studies have detected that

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the thermal performance of nanofluids is much better than the conventional fluids [1–5]. Many studies, both numerical and experimental, have been conducted to examine the heat transfer performance of conventional fluids in corrugated channels under various flow regimes. Asako et al. [6] numerically determined the influence of using a corrugated duct with rounded corners on heat transfer and pressure drop. The parameters adopted in this investigation include three assigned corrugation angles (15°, 30°, and 45°), Pr =0.7 and Re =100-1000. Under identical mass flow rate and pumping power, they indicated that the corrugated duct with round corners has a great impact compared to the plain duct in terms of heat transfer progress. To compare the heat transfer performance and flow field between a straight channel and a corrugated channel, a numerical study was conducted under laminar condition by Fabbri [7]. The corrugated channel in this study consists of a smooth surface and a corrugated surface. For the corrugated channel, the adiabatic wall and constant heat flux conditions were applied for the smooth and corrugated surfaces, respectively. The finite element scheme was employed to analyze both velocity and temperature fields. The performance of heat transfer for the straight channel was 30% less than that in the corrugated channel while a 10% drop in pressure drop was observed, which the author attributed to the impact of Reynolds and Prandtl numbers. Another numerical investigation about heat transfer and flow field of the wavy channel was performed by Bahaidarah et al. [8]. The investigation was carried out across 24 to 400 Reynolds numbers and Prandtl number was 0.7. The study was carried out by using the sinusoidal and arc-shaped as a geometric parameter. Both channel configurations showed that the Nu was found to increase with the increase in Re. Also, the arc-shaped channel was highest in the ∆p compared to the sinusoidal channel. The impacts of the corrugation aspect ratio on the heat transfer enhancement were numerically conducted by Metwally and Manglik [9]. Laminar flow and sinusoidal corrugatedplate channels were adopted in this examination. The numerical results revealed that the aspect ratio of the corrugated channel has a significant impact in terms of heat transfer improvement. Naphon [10-12] conducted numerically and experimentally the forced convective flow in corrugated channels. The computational model was simulated by the commercial CFD program and the k-ε model. The results proved that the corrugated surface had a significant effect on heat transfer enhancement. The impacts of the entrance region in terms of heat transfer enhancement and flow behavior through asymmetric wavy-channel was numerically conducted by Mohamed et al. [13]. The amplitude of the surface was a range of 0-0.5, while Reynolds number rated between 1001500. They indicated that the Nusselt number and the shear stress increase by increasing the Re and highest values appearing in the entrance zone. Two-dimensional numerical study of parallel plate microchannels was focused on the impact of triangular roughness on the heat transfer conducted by Turgay and Yazicioglu [14]. The study results clarified that the heat transfer has been reduced with increased surface roughness while the Nu increased with rising roughness height. The impact of corrugated channel in terms of heat transfer enhancement and air flow behavior through a triangular corrugated shape channel was experimentally studied by Islamoglu and Parmaksizoglu [15]. Over a Reynolds number range of 1200-4000 with air as working fluid, the HTC and were evaluated for channel heights of 5 and 10 mm with the angle of the corrugation maintained at 20°. The results show that the corrugated channel has a great impact on HTC and and the increase in height of channel led to a rise in the Nu and the .

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In order to study heat transfer enhancement of corrugated channels, Ali and Ramadhyani [16] conducted an experimental study. The experimental study showed that the performance evaluation for both the corrugated channels is superior to the parallel-plate channel under design constraints. Hong et al. [17] studied numerically the gas flow at different temperatures, 373 K, 323 K, and 273 K in a microchannel having a straight rectangular cross-section. They employed the direct simulation Monte Carlo to simulate and compare between 3and 2-D cases. The results indicated that the comparison between 3-D cases and 2-D case shows that when the aspect ratio <3, the two extra side-walls in the 3-D case have significant effects on the heat transfer and flow properties. Zhang and Che [18] numerically studied the effect of different cross-corrugated plates on heat and flow characteristics. The study tested different types of corrugation profile such as trapezoidal, isosceles triangular, elliptic, rectangular and sinusoidal and their effect on thermal and hydraulic characteristics of the flow. The results indicated that Nusselt number and friction factor are about 1–4 times higher for the trapezoidal channel than for the elliptic channel. Elshafei et al. [19] performed an experimental study to investigate the turbulent flow characteristics and heat transfer through corrugated channels. The study utilized constant temperature condition over Re range of 3220–9420. The results of corrugated channels flow showed a significant heat transfer enhancement accompanied by increased pressure drop penalty. On the other hand, the convective heat transfer of nanofluids in straight channels has been numerically and experimentally investigated by many researchers. Xuan and Li [20-21] conducted experimental studies of turbulent convective heat transfer and thermal conductivity of Cu–water nanofluid through a tube. The studies discussed the influences of HTC and in terms of the flow and heat transfer features. They demonstrated that the nanofluids appeared better than traditional fluid utilized to increase the magnitude of the thermal conductivities. Also, the increase in the Nu was 39% using Cu-water nanofluid . Mohammed et al. [22] numerically tested the effects of different nanofluids (Al2O3, TiO2, SiO2 and Ag -water) on the thermal and hydraulic characteristics in a square-shaped microchannel heat exchange over Reynolds number ranges from 100 to 800. Water and nanoparticles with concentrations of 2%, 5%, and 10% were used in the simulation and (FVM) employed to deal with the governing equations. The results obtained exhibited an increase of the thermal performance in a microchannel due to the influence of using nanofluid as a base fluid. Rostamani et al. [23] presented the numerical investigation of the flow and heat transfer characteristics of nanofluids in a straight channel. Three different types of nanofluids (CuO, Al2O3, and TiO2–water) have been examined. Reynolds number range of 20,000–100,000 and nanoparticles volume fraction of 0–6% were considered. The average Nusselt number for CuO– water nanofluid was higher than the Al2O3 and TiO2–water but the shear stress was higher as well. Abu-Nada [24] presented another numerical investigation in terms of heat transfer over a backward facing step by implementing various kinds of nanofluids. The investigation was carried out across 200 to 600 Reynolds number while the nanoparticles ?? was 0-0.02. They reported that Nu increased with an increased in ?? of nanoparticles and Re. In addition, within recirculation regions, TiO2 having low thermal conductivity lead to better enhancement on heat transfer. Laminar flow of copper-water nanofluid in a rectangular duct having isothermal the top and bottom walls at Reynolds number of 5-1500 has been numerically examined by Santra et al. [25]. The said study revealed that the increase in ?? as well as the flow rate will produce a greater heat transfer rate. Kalteh et al. [26] numerically investigated the laminar forced convection heat

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transfer of copper–water nanofluid inside an isothermally heated microchannel. They reported that the heat transfer enhancement increases with the increase in Reynolds number and nanoparticle volume concentration, while the pressure drop increases only slightly. Akbarinia and Laur [27] numerically examined the impact of nanoparticles on laminar mixed convection heat transfer of Al2O3-water nanofluid through a circular curved tube by implementing 3-d elliptic governing equations. The authors claimed that the increase in particle diameter causes no change in the flow behaviors when the particles are regular nano meter. Wongcharee and Eiamsa-ard [28] experimentally examined the effects of the copper oxide -water nanofluid on the thermal and hydraulic characteristics by implementing a laminar regime through the circular tube with twisted tape. Reynolds number ranged from 830 to 1990 while the concentration of nanofluid was varied from 0.3 to 0.7%. The results obtained showed that maximum PEC was 5.53 when the concentration of nanofluid was 0.7%. In addition, they inferred that the Nu was 13.8 times higher than those of a straight tube. Recently, Ajeel and Salim [29] examined the impact of Al2O3- water nanofluid on the heat transfer and friction factor in semi-circular corrugated channel numerically. Symmetry configuration for corrugation profile of semicircle has been employed. They reported from the obtained results that adopted geometry of semicircle corrugated profile with nanofluid can contribute to improving the efficiency of heat transfer devices. In addition, the outcomes of study showed that the increased ratio in Nusselt number was 2.07 at Re= 30000 and volume fraction 6%. Abed et al. [30] investigated the Al2O3, CuO, SiO2, and ZnO nanofluid effects numerically as a heat transfer fluid on thermal and hydraulic characteristics in a corrugated plate having Vshaped. Under uniform heat flux over a range of Re (8000-20000), the study was tested. They reported from the obtained results, that adopted geometry of V-shaped with nanofluid can contribute to improving the efficiency of heat transfer devices and make them more compact, which can be inferred from the enhanced Nusselt number results. Depending on the mentioned literature, it can be inferred that the forced convective heat transfer in a trapezoidal -corrugated channel with symmetry and zigzag configurations and using nanofluids has never been reported. Additionally, most of the past studies examined a 2D turbulent convective heat transfer. Accordingly, this lack of knowledge represents the prime motivation behind conducting the current research. Thus, the current study considers turbulent forced convective flow in three-dimensional trapezoidal-corrugated channels over Re in the range of 10,000≤ Re ≤30,000 under constant heat flux condition. Four kinds of nanofluids were utilized in this investigation. The influence of various values of nanoparticle volume fractions and nanoparticle diameters were discussed. Lastly, Nu, ∆P, Nuer and the PEC for a trapezoidal corrugated channel represent the results reviewed by the study to show the effect of trapezoidal corrugated channel and nanofluid on these parameters as well as the thermal and flow fields.

2. Geometrical model The 2-dimensional geometry of the trapezoidal- corrugated channel is illustrated in Fig. 1. The details of Fig. 1 are given as (A) which represents the geometrical model, (B) represents the trapezoidal symmetry- corrugated channel, and (C) represents the trapezoidal zigzag- corrugated channel. Generally, the corrugations are placed at the top and bottom walls and the sides of the channel are maintained flat. The flow domain is comprised of three parts; the test section with

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the corrugations which are heated from the upper and lower surfaces, downstream and upstream sections, with smooth, flat surfaces, which are treated as adiabatic surfaces. The overall length of the channel is 700 mm with the upstream, entrance section with length L1 = 400mm, the test section (L2 = 200mm) and the downstream section (L3). The entrance section is provided to ensure fully developed flow entering the test section while the downstream section of the test section is provided to prevent reverse flow from affecting the results. The height of channel (H) is 10 mm while the width of the channel is (W . The pitch of corrugation is (p=1.5H) while the width and height of corrugation are (w=H/2), (h=H/4), respectively. The corrugated walls for test section are subjected to a constant heat flux of =10 kW/m2 while the left and right sides represent the velocity inlet and pressure outlet, respectively.

2.1 Governing equations The governing equations are solved for three-dimensional flow and temperature fields with several assumptions: (i) The flow is steady; (ii) The working fluid mixture is uniform and is incompressible without phase-change; (iii) The thermo-physical properties of the fluid and channel material are independent of temperature change; and (iv) The Reynolds number is sufficiently high to induce turbulence. This type of flow is represented by the following governing equations [31]. Continuity equation: (1) Momentum equation: )

(2)

Energy equation: (

̅)

)

(3)

The current study used k − ε turbulence model suggested by Launder and Spalding [32], which was adjusted by Behzadmehr et al. [33] and Hejazian and Moraveji [34] so as to insert the nanoparticles effect. The model takes into account the impact of mean velocity gradients which lead to generate turbulent kinetic energy and can be symbolized as ‘G’. It can be illustrated by the equations below [31] ( ( Where:

) )

(4) (5)

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,

,

,

= 0.09,

2.2 Boundary conditions Computational domains and boundary conditions were applied at the trapezoidal- corrugated channel which included velocity inlet condition and temperature of 300 , pressure outlet condition while slip velocity was ignored. Additionally, there was uniform heat flux on the corrugated walls whereas adiabatic condition is applied on the remaining straight walls. The specific thermal conditions for the complex flow field as well as the boundary conditions can be illustrated as below: The boundary conditions at the inlet: ,v

= w = 0, Tin = 300 K

= (I

)2 ,

=

Outlet boundary: In the current study, fully developed for the properties are assumed at the outlet. ,

, and

At the wall: u = v= w = 0, q = To represent the results and characterize the heat transfer and flow in the trapezoidal corrugated channels, the following variables and parameters are presented. The average Nusselt number can be defined as below: ̅̅̅̅ =

̅

(6)

The average heat transfer coefficient as: ̅= =

.(

)

(7) (8)

where are the average inlet and outlet temperatures of the working fluid while A is the corrugated surface area. Additionally, the inlet velocity can be obtained based on the required Reynolds number as below:

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(9) In the corrugated channel, the hydraulic diameter is computed based on cross-section area (Across) and the perimeter of wetted (P) as [35, 36]: Dh =

(10)

The Fanning friction factor as: (11) The friction factor is defined [35, 36]: ƒ=

(12)

The pressure drop can also be obtained as [35, 36]: (13)

For a better evaluation system, the thermal performance factor was computed based on the ratio between the heat transfer enhancements into the increase in friction factor. The thermal performance factor is given by [37]: ̅̅̅̅ ⁄̅̅̅̅̅̅ ( ⁄ )

(14)

3. Numerical Implementation 3.1 Numerical computation A numerical simulation for a trapezoidal- corrugated channel was performed by employing nanofluid in order to probe the characteristics of heat transfer and flow fluid. The finite volume method is used to solve the governing equations with corresponding boundary conditions by employing the CFD commercial software ANSYS-FLUENT-V16.1. The SIMPLE algorithm is employed to joint the pressure-velocity system and a 2nd order upwind scheme was also adopted for the convective terms. The k- turbulent model with standard wall function was selected while the diffusion term in the momentum and energy equations is approximated by 2nd order upwind. In the current investigation, the convergence criterion is considered as 10-5 for continuity, momentum and turbulence equations while 10-10 for energy equation.

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3.2 Grid convergence index Uniform measure of convergence for the grid refinement studies was provided by Grid Convergence Index (GCI) [38]. This measure is based on the estimated fractional error that was derived from the generalization of the extrapolation of Richardson [39]. The GCI values represent the resolution levels and the extent to which the solution approach the asymptotic values. In other words, the GCI represents the criteria of solution changing with a further refinement of the grid, the solution would be within the asymptotic range if indicated a small value. In order to determine the optimum grids, four grids were examined at the same boundary conditions, coarse, medium, fine and finer. The grid independence index GCI for grids 1, 2, 3 and 4 as shown in the equation below.

(15) }

where SF is the safety factor, P is the fractional error, R is the refinement ratio and n is the order of convergence while the numbers 1, 2, 3, 4…… represent coarse, medium, fine, finer and….etc., grid respectively. The safety factor SF value is said to be 1.25 for comparisons above 2 grids and the value 3.0 for comparisons between 2 grids according to Wilcox [40]. The grid independence index GCI for grids 1, 2, 3 and 4 was found to be 1.009, which close to the range of as shown in Fig. 1-D and Table 1. Based on this, the third finest grid of 1.0 mesh space was chosen as an optimum one between the computational time and the results accuracy.

4. Thermophysical properties of nanofluids The effective thermophysical properties of nanofluids to execute the simulations of the nanofluids as a working fluid should be obtained. In this regard, four kinds of nanoparticles, namely, Al2O3, CuO, SiO2, and ZnO were utilized and by applying the mixing theory, the required properties for simulations can be obtained as explained below: The density [37]: (16) The effective heat capacity [37]: (17) In order to compute the ( by using nanoparticles in corrugated channel, the effect of Brownian motion will be taken into consideration by utilizing the empirical correlation below [41] :

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keff = kstatic + kBrownian (

kstatic = kf [ (

(18)

)

(19)

)

√

(20)

where: Boltzmann constant: κ = 1.3807 10-23 J/k and Table 2 shows the values of β for particles used in the current study. Modeling, ( ) (21) Another property of nanofluid is effective viscosity [41]: )

(22)

Equivalent diameter of based molecule: (

)

⁄

(23)

Table 3 illustrates the thermo-physical properties of water-based nanofluids with dp = 20 nm and at T=300K.

5. Code validation In order to gain a better comprehension of the competences and restrictions and validated numerical codes with other previous work, code validation is a very essential procedure in any numerical work. Likewise, lower error values mean higher accuracy of the simulation and preparedness for numerical runs. First, the outcomes of the present study for straight channel in terms of Nusselt number (Nu) and friction factor (f) are compared with the empirical correlations of Dittus–Boelter and Petukov, respectively [42], as displayed in Fig.2a-b.

(25)

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Another code validation was also carried out depended on the experimental work of Elshafei et al. [6] for turbulent air flow in straight and corrugated channels. The outcomes of comparison display a good agreement with regard to the as shown in Fig. 2c. 6. Results and discussions The influences of utilizing trapezoidal- corrugated channel with symmetry and zigzag configurations, types of nanofluid, diameter and volume fraction of the particles, Reynolds number on the hydrodynamics and flow fields in terms of the , , ∆p and PEC, have been reported and debated in this section. 6.1 The impact of different shapes of trapezoidal-corrugated channel The computed number allocation versus Re number for symmetry and zigzag configurations of trapezoidal- corrugated channel is shown in Fig.3a. It is clear that the increase of Nu seemed directly linked to the increase in Re number. Enhanced heat transfer is associated with the trouble of flow and latter is associated with increases in velocity. Thus, increasing Re number leads to strengthening the heat transfer. The overall trend is that straight channel flow recorded the lowest values of Nu number compared to the corrugated channel flow. The corrugated surface flows due to the creation of high recirculation flow and thin boundary layer. Generally, trapezoidal- corrugated channel flows were better in Nusselt number rates, and the symmetry corrugated channel was the highest at all Reynolds numbers. The impact of different designs of trapezoidal- corrugated channel on the ∆P is shown in Fig.3b. As indicated by this figure, the pressure obviously drops extensively, and incrementally, with growing Reynolds number for every case. Likewise, all geometries of corrugated channel give the greater elevated pressure drop than that for the straight channel. The reasons for that are the drag force generated by the corrugated surface and also created turbulence enlargement and rotational stream. In addition, the symmetry shape of trapezoidal-corrugated channel recorded the largest ∆P compared to the zigzag-shaped. Fig.3c demonstrates the ratio of the of trapezoidal- corrugated channels to that of the pure water flow in the straight channel. It be noted that the upgrade in Nu ratio diminishes with a rise in Re for all cases of corrugated channel. The explanation behind this is the fact that the blending of the working liquid in corrugated channel turns out to be better with the higher Re and leads to progress the heat transfer. Moreover, it can be observed that the symmetry shaped channel recorded the most significant ratio compared with zigzag shaped and it achieved highest the value of 1.77 at Reynolds number 10000. Fig.3d shows PEC against Re number for the configurations of trapezoidal-corrugated channel. Generally, the PEC fell in tandem with the rise of the Re number for both shapes of the channel. In contrast, the zigzag shape has a lower performance when compared to the symmetry shape. The symmetry shape of trapezoidal- corrugated channel was the best and had its highest performance of 1.74 at Re=10000. Fig.3 (e and f) exhibits the velocity distribution and isotherm contours for the configurations of trapezoidal- corrugated channel at Re=15000. Indeed, the velocity in the wrinkle of the corrugated walls appeared to be connected with the ascent in Reynolds number. Therefore, the adverse flow occurs in the wrinkle close to the troughs of the corrugated channel where the flow is the converse direction of the major flow. An increase in converse flow velocity

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means it had become more troubled and it can be said that the severity of the minor flow has expanded at the expense of the major flow. As per the temperature contours, the temperature gradient increment rises with Reynolds number and this is due to the creation of an opposite flow in the corrugated basin of the walls. Accordingly, blending the cold fluid in the center with the hot fluid nearby the corrugated walls rises with increased Reynolds number. This is identical to the numerical study of Naphon [11]. 6.2 Nanoparticles type effect Fig. 4a shows the outcomes of the Nuav which are obtained from the simulation of the different nanofluids kinds compared with using pure water as a heat transfer fluid in symmetry configuration of trapezoidal- corrugated channel. The outcomes show that every one of the nanofluids gives larger Nuav values than pure water. Clearly, the pure water has the lowest Nuav because of poor thermal conductivity of this fluid, whereas the nanofluid with SiO2 nanoparticles has the highest ratings of Nuav. As a result, the nanofluid with SiO2 nanoparticles is followed by Al2O3, ZnO, CuO, respectively. High velocity is a major reason for this rise due to the effect of the lowest density of SiO2– water nanofluid which correlates to the increase of the HTC. What is more, the intensity effect of the converse regions is also very important to achieve the trouble that stems from an increase in the velocity of SiO2-water nanofluid. In this way, the temperature gradient on the walls of the channel increases, which accordingly increases the heat transfer rate between the fluid and wall of channel. The outcomes are in agreement with results of Mohammed et al. [1]. The pressure drop against Reynolds number with various types of nanofluids is displayed in Fig.4 (b). It is worth noting that the pure water has a lower rate of a pressure drop than pressure drop in all types of nanofluids. This could be due to the higher viscosity and density of nanofluid when compared to pure water. Similarly, the high velocity makes SiO2-water nanofluid the most elevated pressure drop among the other types of nanofluid. Thus, the shear stress will increase nearby corrugated walls, subsequently leading to increase the pressure drop penalty. Fig.4(c) demonstrates the ratio of the Nuav of trapezoidal symmetry- corrugated channel with various types of nanofluids to that of the pure water flow in straight channel. Although there was a fall in tandem with increases in Reynolds number in the enhancement ratio for all types of the fluids, the nanofluids type recorded the highest enhancement ratio compared with the base fluid. Additionally, the SiO2–water nanofluid was rated best since it achieved the highest enhancement ratio among different kinds of nanofluid followed by Al2O3, ZnO, and CuO–water nanofluids for reasons explained previously. Fig.4 (d) delineates the impact of various types of nanofluids on thermal performance factor. All the types of nanofluids give higher performance factor compared with the base fluid. While it is true that SiO2–water nanofluid displays the highest value of the pressure drop, it recorded the largest enhancement in heat transfer. As a result, with 2.50 at Re=10000 SiO2–water nanofluid offered the maximum value of PEC among the other kinds of nanofluids. Fig. 4 (e,f,g, and h) shows the velocity distribution and isotherm contours for pure water and nanofluid flow at nanoparticle diameter of 20 nm, and Re = 15000 for the various kinds of nanoparticles. The velocity contours display that the most striking finding was the firmer converse flow regions in the case of SiO2–water nanofluid followed by Al2O3, ZnO, CuO– water nanofluid and then the pure water. According to inverse proportionality between density and velocity, the low density of SiO2-water plays a significant role to jack up the velocity rate at

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the same Re. Therefore, SiO2–water nanofluid has the largest velocity among the other nanofluids. On the other hand, the isotherm contours demonstrate the thermal boundary layer thickness for all types of nanofluid. Due to the high values of Prandtl number for SiO 2–water nanofluids, the thermal boundary layer thickness in this case is not as much as that for other nanofluids. In addition, the better refinement in the fluid blending in the case of SiO 2–water nanofluid is due to the intensity of converse flow regions. This makes the SiO2–water nanofluid the highest augmentation in terms of heat transfer among the other types of nanofluids. 6.3 Nanoparticles volume fraction effect The Nuav against Re with various types of volume fractions is displayed in Fig.5 (a). As predicted, the Nuav rises in tandem with Re increases, depending on volume fraction. In other words, it is clear there was a significant effect of nanoparticles volume fraction to jack up the Nu rate at a certain Re. Regarding the nanoparticles, the Brownian motion and strong improvement of thermal conductivity could explain the increase of the Nuav. The results are consistent with the numerical results of Rostamani et al. [23]. Fig. 5(b) indicates the style of pressure drop against Reynolds number with numerous volume fractions of SiO2–water nanofluid in trapezoidal symmetry-corrugated channel. The most striking finding was that the pressure drop has been significantly boosted with the raising of ?? as well as Re. To understand why, we should be the first look at the properties of nanofluid, specifically viscosity, where high volume fraction means high viscosity, and the high velocity gradient of mixing at the walls of channel which is associated with the re-circulation flow of corrugated channel. Abed et al. [24] and Mohammed et al. [1] previously found comparable outcomes. The obtained results of the enhancement in Nu ratio of SiO2–water nanofluid with various volume fractions in symmetry shaped of trapezoidal-corrugated channel are elaborated in Fig.5(c). Although there were falls in tandem with the increase in Re in terms of enhancement ratio for all volume fractions of the fluids, the nanofluid types recorded the highest enhancement ratio compared with the base fluid. Plainly, the SiO2–water nanofluid with 8% volume fraction offered the highest enhancement ratio compared with the others. This is because of the higher thermal conductivity and viscosity for the working fluid which leads to improve the converse flow nearby the corrugated walls. Fig. 5(d) demonstrates the variation of PEC against Reynolds number with various volume fractions of SiO2–water nanofluid. Evidently, the values of PEC of nanofluids at different volume fraction over Reynolds number range were greater than pure water. This is because thermal performance factor depends on the heat transfer enhancement which can be deduced from enhanced Nu results. Also, the results indicated that PEC fell in tandem with increasing Reynolds number for all types of fluid. In other words, this means the heat gained or heat transfer enhancement is much less than pressure loss. However, SiO2–water nanofluid with 8% volume fraction gives the best PEC recorded at 2.50 at Re=10000. Fig. 5(e,f,g, and h) plotted the streamwise velocity and isotherm contours for different volume fraction of SiO2 at Re=15000 and dp =20 nm. The figure gives a decent image of the progress of the flow as well as the converse flow of fluid and increases recirculation zones due to the increase in the ??. The recirculation zones seemed linked to the highest ??, in this way, the irregular motion of nanoparticles will increment and therefore increment the intensity of

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recirculation zones. This is compatible and consistent with the numerical studies of Ahmed et al. [36] and Mohammed et al. [1]. On the other hand, the temperature contours demonstrate the effect of corrugated surface alongside with volume fraction on the temperature gradient near the top and bottom walls due to enhancement in the working fluid via mixing the converse flow which is in contact with channel walls with the main flow in the center of channel. Additionally, increasing leads to increase the irregular motions of nanoparticles which inferred to enhanced heat transfer and the rates of energy exchange. 6.4 Nanoparticles diameter effect SiO2-water nanofluid at volume fraction 8% has been utilized to examine the impact of nanoparticle diameter on Nuav under nanoparticles diameter ranges from 20 nm to 80 nm. As shown in Fig. 6(a), the Nuav rose in tandem with decreasing diameter of nanoparticle and increasing of Re. The major cause of this increase is the strength of Brownian motion that has a great influence on thermal conductivity and enhances it. The other reason is an increase in the specific area due to a decrease in nanoparticle diameter. Therefore, the thermal conductivity increases not only by Brownian motion but also by an increase in the specific area and this mechanism was adduced in a previous study by Mohammed et al. [1] and Abed et al. [24]. Fig. 6(b) displayed the impact of particle diameter for SiO2–water nanofluid on the pressure drop at ϕ = 8% and different Reynolds number. As shown, as the diameter of nanoparticle decreases, the ∆p increases due to the rise in viscosity of nanofluids, which is the same result obtained by Abed et al. [24], in addition to the effect of reverse flow zone, which is smaller in cases of large diameter than small. This implies that the strength of reverse flow will increase and cause more friction between the nanofluid and corrugated walls, leading to an increase in the penalty. Fig. 6(c) illustrated the obtained results of the Nuer of SiO2–water nanofluid with various diameter of nanoparticle in the trapezoidal symmetry-corrugated channel to that for the pure water in the straight channel. Although there were falls in tandem with increases Reynolds number in the enhancement ratio for all diameter of the nanoparticles, the nanofluid types recorded the highest enhancement ratio compared with the base fluid. Clearly, the SiO2–water nanofluid with 20 nm diameter offered highest enhancement ratio compared with the others. This is because of the higher thermal conductivity and viscosity for the heat transfer medium which leads to improve the inverse flow near the corrugated walls. Thermal performance factor of trapezoidal symmetry- corrugated channel at volume fraction 8% and under a different range of Reynolds number was accomplished and displayed in Fig.6 (d). Evidently, the values of PEC of nanofluids at various diameters of nanoparticles over Reynolds number range were greater than pure water. As mentioned earlier, this is because thermal performance factor depends on the heat transfer enhancement which can be deduced from enhanced Nu results. Also, the results indicated that PEC fell in tandem with increasing Reynolds number for all types of fluid. In other words, this means the pressure loss is much greater than heat gained or heat transfer enhancement. However, SiO2–water nanofluid with 20 nm diameter gives the best PEC, recorded at 2.50 at Re=10000. For a better comprehension of the flow and heat transfer characteristics, the streamwise velocity and isotherm contours for different nanoparticle diameter of SiO2 at Re=15000 and dp =20 nm are shown in Fig 6(e, f, g, and h). The figure gives a decent image of the progress of the flow as well as the reverse flow of fluid and increases recirculation zones due to a decrease in the

14

diameter of nanoparticles. The recirculation zones seemed linked to the lowest diameter of nanoparticles. As previously stated, the irregular motions of nanoparticles will increment and therefore increment the intensity of recirculation zones. Abed et al. [24] obtained the same result. From temperature contours, the effect of the corrugated surface can be seen alongside with decrease in the diameter of nanoparticles on the temperature gradient near the top and bottom walls due to the enhancement of the working fluid via mixing the reserve flow, which is in contact with channel walls with the main flow in the center of channel. Additionally, a decrease in nanoparticle diameter leads to increase the irregular motions of nanoparticles which infer enhanced heat transfer and the rates of energy exchange. 7. Conclusion In this paper, turbulent forced convective of four nanofluids types Al2O3, CuO, SiO2, and ZnO flowing in trapezoidal-corrugated channels over Reynolds number in the range of 10,000≤ Re ≤30,000 are numerically conducted. Regarding the nanofluid, the impact of different values of nanoparticle volume fractions with ranges of 0-8% and nanoparticle diameters with ranges of 2080 nm was discussed. The major conclusion of this numerical study is that the utilization of nanofluid in corrugated channels can be offered as an appropriate way to get best thermal performance, which can prompt design plan of heat exchangers and make it more compact. Also, other conclusions that can be drawn from the current study include: 1. The corrugation profile of trapezoidal –corrugated channel had a great impact on the thermal performance compared with a straight profile. 2. The adopted geometry of trapezoidal symmetry- corrugated channel can progress heat transfer enhancement at the rate of 1.6-2.88 times that of straight channel. 3. For all channel shapes, the Nuav and ∆p increases with increasing ?? and Re and decreases with decreasing nanoparticle diameter. 4. The PEC was consistent with the Nuav and ∆p with respect to the effect of ??, but Re had the opposite effect as PEC decreased when the Re increased. 5. For all studied cases of trapezoidal- corrugated channel, the symmetry shaped recorded the highest heat transfer, followed by zigzag configuration. 6. Among the four types of nanoparticles which are tested, SiO2-water recorded the best heat transfer enhancement followed by Al2O3, ZnO, and CuO–water nanofluids. 7. Over the range investigated (Re=10000-30000), the symmetry shaped trapezoidalcorrugated channel achieved the maximum PEC of 2.50 at volume fraction 0.08 and Re = 10000.

15 Nomenclature List of symbols

A

area, mm2

Al2O3

aluminum oxide

C1 , C2 ,

closure coefficients

CuO

copper oxide

Cp

specific heat capacity (J/kg.k)

CFD

computational fluid dynamic

Cf

skin friction coefficient

Dh

hydraulic diameter, mm

dp

diameter of nanofluid particles, nm

df

equivalent diameter of a base fluid molecule,??m

G

generation of turbulent kinetic energy (kg/ms3)

h

corrugated height, mm

HTC

heat transfer coefficient, (W/m2.k)

H

height of channel, mm

L1

upstream length, mm

L2

length of the corrugated section, mm

L3

length of exit section, mm turbulent intensity

k

turbulent kinetic energy, (m2/s2)

16

k

thermal conductivity, (w/m.k)

M

Molecular weight of base fluid

N

Avogadro number (6.022× 10+23 mol-1)

Nu

Nusselt number

p

corrugated pitch, mm

∆p

Pressure drop(pa)

Pr

Prandtl number, pr =

q

heat flux, (w/m2)

Re

Reynolds number, Re =

SiO2

silicon dioixide

T

temperature, k

u,v,w

velocity component, (m/s)

w

width of corrugated channel, mm

X

distance along the x-coordinate

ZnO

zinc oxide

17

Greek symbols Fraction of liquid volume traveling with a particle

Dynamic viscosity of the fluid, (kg/m.s) Density, (kg/m3) Turbulent kinetic dissipation (m2/s2) Wall shear stress (pa) diffusion Prandtl number for k Nanoparticle volume fraction

Subscripts 0 bf corr eff er f in av out nf p w

Straight channel base fluid Corrugated channel effective Enhancement ratio fluid inlet average outlet nanofluid particles wall

Conflict of interest The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgment: The authors wish to acknowledge that this paper and the work was funded by the Fundamental Research Grant Scheme (FRGS 1589), Universiti Tun Hussein Onn Malaysia.

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References [1] Mohammed, H.A., Al-Shamani, A.N. and Sheriff, J.M., 2012. Thermal and hydraulic characteristics of turbulent nanofluids flow in a rib–groove channel. International Communications in Heat and Mass Transfer, 39(10), pp.1584-1594.Wang G, Vanka SP. [2] Hussein, A.M., Dawood, H.K., Bakara, R.A. and Kadirgamaa, K., 2017. Numerical study on turbulent forced convective heat transfer using nanofluids TiO2 in an automotive cooling system. Case Studies in Thermal Engineering, 9, pp.72-78. [3] Murshed, S.M.S., Leong, K.C. and Yang, C., 2005. Enhanced thermal conductivity of TiO2—water based nanofluids. International Journal of Thermal Sciences, 44(4), pp.367-373. [4] Hussein, A.M., 2016. Adaptive Neuro-Fuzzy Inference System of friction factor and heat transfer nanofluid turbulent flow in a heated tube. Case Studies in Thermal Engineering, 8, pp.94-104. [5] Bianco, V., Manca, O. and Nardini, S., 2011. Numerical investigation on nanofluids turbulent convection heat transfer inside a circular tube. International Journal of Thermal Sciences, 50(3), pp.341-349. [6] Yutaka, A., Hiroshi, N. and Faghri, M., 1988. Heat transfer and pressure drop characteristics in a corrugated duct with rounded corners. International Journal of Heat and Mass Transfer, 31(6), pp.1237-1245. [7] Fabbri G. Heat transfer optimization in corrugated wall channels. Int J Heat Mass Transf 2000; 43(23):4299–310. [8] Bahaidarah, H.M., Anand, N.K. and Chen, H.C., 2005. Numerical study of heat and momentum transfer in channels with wavy walls. Numerical Heat Transfer, Part A, 47(5), pp.417-439. [9] Metwally, H.M. and Manglik, R.M., 2004. Enhanced heat transfer due to curvatureinduced lateral vortices in laminar flows in sinusoidal corrugated-plate channels. International Journal of Heat and Mass Transfer, 47(10), pp.2283-2292. [10] Naphon, P., 2007. Laminar convective heat transfer and pressure drop in the corrugated channels. International communications in heat and mass transfer, 34(1), pp.62-71. [11] Naphon, P., 2008. Effect of corrugated plates in an in-phase arrangement on the heat transfer and flow developments. International Journal of Heat and Mass Transfer, 51(15), pp.3963-3971. [12] Naphon, P., 2009. Effect of wavy plate geometry configurations on the temperature and flow distributions. International Communications in Heat and Mass Transfer, 36(9), pp.942-946. [13] Mohamed, N., Khedidja, B., Abdelkader, S. and Belkacem, Z., 2007. Heat transfer and flow field in the entrance region of a symmetric wavy-channel with constant wall heat flux density. Int. J. Dyn. Fluid, 3(1), pp.63-79. [14] Turgay, M.B. and Yazicioglu, A.G., 2009. Effect of surface roughness in parallel-plate microchannels on heat transfer. Numerical Heat Transfer, Part A: Applications, 56(6), pp.497514. [15] Islamoglu Y, Parmaksizoglu C. The effect of channel height on the enhanced heat transfer characteristics in a corrugated heat exchanger channel. Appl Therm Eng 2003; 23(8):979–87. [16] ALI, M., RAMADHYANI S., 1992. Experiments on Convective Heat Transfer in Corrugated Channels. Experimental Heat Transfer, 5.175–93.

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[17] Hong, Z.C., Zhen, C.E. and Yang, C.Y., 2008. Fluid dynamics and heat transfer analysis of three dimensional microchannel flows with microstructures. Numerical Heat Transfer, Part A: Applications, 54(3), pp.293-314. [18] Zhang, L. and Che, D., 2011. Influence of corrugation profile on the thermalhydraulic performance of cross-corrugated plates. Numerical Heat Transfer, Part A: Applications, 59(4), pp.267-296. [19] Elshafei EA, Awad MM, El-Negiry E, Ali AG. Heat transfer and pressure drop in corrugated channels. Energy. 2010 Jan 1;35(1):101-10. [20] Xuan, Y. and Li, Q., 2000. Heat transfer enhancement of nanofluids. International Journal of heat and fluid flow, 21(1), pp.58-64. [21] Li, Q., Xuan, Y. and Wang, J., 2003. Investigation on convective heat transfer and flow features of nanofluids. Journal of Heat transfer, 125(2003), pp.151-155. [22] Mohammed, H.A., Bhaskaran, G., Shuaib, N.H. and Abu-Mulaweh, H.I., 2011. Influence of nanofluids on parallel flow square microchannel heat exchanger performance. International Communications in Heat and Mass Transfer, 38(1), pp.1-9. [23] Rostamani, M., Hosseinizadeh, S.F., Gorji, M. and Khodadadi, J.M., 2010. Numerical study of turbulent forced convection flow of nanofluids in a long horizontal duct considering variable properties. International Communications in Heat and Mass Transfer, 37(10), pp.14261431. [24] Abu-Nada, E., 2008. Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step. International Journal of Heat and Fluid Flow, 29(1), pp.242-249. [25] Santra, A.K., Sen, S. and Chakraborty, N., 2009. Study of heat transfer due to laminar flow of copper–water nanofluid through two isothermally heated parallel plates. International Journal of Thermal Sciences, 48(2), pp.391-400. [26] Kalteh, M., Abbassi, A., Saffar-Avval, M. and Harting, J., 2011. Eulerian–Eulerian twophase numerical simulation of nanofluid laminar forced convection in a microchannel. International journal of heat and fluid flow, 32(1), pp.107-116. [27] Akbarinia, A. and Laur, R., 2009. Investigating the diameter of solid particles effects on a laminar nanofluid flow in a curved tube using a two phase approach. International Journal of Heat and Fluid Flow, 30(4), pp.706-714. [28] Wongcharee, K. and Eiamsa-Ard, S., 2011. Enhancement of heat transfer using CuO/water nanofluid and twisted tape with alternate axis. International Communications in Heat and Mass Transfer, 38(6), pp.742-748. [29] Ajeel, R.K. and Salim, W.S.I.W., 2017, September. A CFD study on turbulent forced convection flow of Al2O3-water nanofluid in semi-circular corrugated channel. In IOP Conference Series: Materials Science and Engineering (Vol. 243, No. 1, p. 012020). IOP Publishing. [30] Abed, A.M., Sopian, K., Mohammed, H.A., Alghoul, M.A., Ruslan, M.H., Mat, S. and Al-Shamani, A.N., 2015. Enhance heat transfer in the channel with V-shaped wavy lower plate using liquid nanofluids. Case Studies in Thermal Engineering, 5, pp.13-23. [31] Yang, Y.T., Tang, H.W., Zeng, B.Y. and Wu, C.H., 2015. Numerical simulation and optimization of turbulent nanofluids in a three-dimensional rectangular rib-grooved channel. International Communications in Heat and Mass Transfer, 66, pp.71-79.

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[32] B.E. Launder, D.B. Spalding, Lectures in Mathematical Models of Turbulence, Academic Press, London, England, 1972. [33] Behzadmehr, M. Saffar-Avval, N. Galanis, Prediction of turbulent forced convection of a nanofluid in a tube with uniform heat flux using a two phase approach, Int. J. Heat Fluid Flow 28 (2007) 211–219. [34] M. Hejazian, M.K. Moraveji, A comparative analysis of single and two-phase models of turbulent convective heat transfer in a tube for TiO2 nanofluid with CFD, Numer. Heat Transfer, Part A, Appl. 63 (2013) 795–806. [35] H. A. Mohammed, A.M. Abed, M. Wahid, The effects of geometrical parameters of a corrugated channel with in out-of-phase arrangement, Int. Commun. Heat Mass Transfer 40 (2013) 47–57. [36] M. Ahmed, N. Shuaib, M. Yusoff, A. Al-Falahi, Numerical investigations of flow and heat transfer enhancement in a corrugated channel using nanofluid, Int. Commun. Heat Mass Transfer 38 (2011) 1368–1375. [37] O. Manca, S. Nardini, D. Ricci, A numerical study of nanofluid forced convection in ribbed channels, Appl. Therm. Eng. 37 (2012) 280–292. [38] Roache, P.J, 1994. Perspective: a method for uniform reporting of grid refinement studies. J. Fluids Eng. 116 405-41. [39] Richardson, L.F., Gaunt, J.A., 1927. The deferred approach to the limit. Part I. Single lattice. Part II. Interpenetrating lattices. Philos. Trans. R. Soc. London 226, 299–361. [40] Wilcox, D.C., 2006. Turbulence Modeling for CFD, third ed. PratyushPeddireddi, California. [41] R. S. Vajjha, D. K. Das, D. P. Kulkarni, ―Development of new correlations for convective heat transfer and friction factor in turbulent regime for nanofluids‖ , Int. J. of Heat and Mass Transfer, vol. 53 ,2010,pp 4607–4618. [42] F.P. Incropera, P.D. DeWitt, T.L. Bergman, A.S. Lavine, Fundamentals of Heat and Mass Transfer, John-Wiley & Sons, 2006.

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Caption of figures

Fig. 1. Schematic diagram of corrugated channel, (A) geometrical model, (B) trapezoidal symmetry-corrugated channel, (C) trapezoidal zigzag-corrugated channel, (D) Computational mesh domain. Fig. 2. Average Nusselt number (a) and friction factor (b) vs. Reynolds number, and comparison between the current work and the outcomes of (c) Rostamani et al. [23] and (d) Abed et al. [24]. .Fig. 3. The impact of different shapes of trapezoidal-corrugated channel on (a) Nu, (b) ∆P, (c) Nuer, (d) PEC and streamlines (right) and isotherm (left) contours for different configurations of trapezoidal-corrugated channel at Re = 15000 (e) symmetry, (f) zigzag. Fig. 4. The impact of various types of nanofluids of trapezoidal symmetry- corrugated channel on (a) Nu, (b) ∆p, (c) Nuer, (d) PEC and streamlines (right) and isotherm (left) contours for different types of nonofluids at Re=30000 : (e) CuO-water, (f) ZnO-water , (g) Al2O3-water, and (h) SiO2-water. Fig.5. The effect of nanoparticles volume fraction of on (a) Nu number, (b) ∆p, (c) number, (d) PEC, and streamlines (right) and isotherm (left) contours of -water for different nanoparticles volume fraction at Re=30000: (e) 0.02, (f) 0.04, (g) 0.06, and (h) 0.08. Fig. 6. The effect of nanoparticle diameter of SiO2 on (a) Nu, (b) ∆p, (c) Nuer, (d) PEC, and streamlines (right) and isotherm (left) contours of SiO2-water for different nanoparticles diameter at Re=30000: (e) 80 nm, (f) 60 nm, (g) 40 nm, and (h) 20 nm. Caption of tables Table 1. Grid optimization. Table 2. Values of β for different nanoparticles. Table 3. The thermo-physical properties of water –based nanofluids with dp = 20 nm and ?? = 0.02 at T=300K.

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(A)

(B)

(C)

(D)

Fig.1. Schematic diagram of corrugated channel, (A) geometrical model, (B) trapezoidal symmetry-corrugated channel, (C) trapezoidal zigzag-corrugated channel, (D) Computational mesh domain.

23

Fig. 2. Average Nusselt number (a) and friction factor (b) vs. Reynolds number, and comparison between the current work and the outcomes of (c) Elshafei et al. [6]

24

Fig. 3. The impact of different shapes of trapezoidal-corrugated channel on (a) Nu, (b) ∆P, (c) Nuer, (d) PEC and streamlines (right) and isotherm (left) contours for different configurations of trapezoidal-corrugated channel at Re = 15000 (e) symmetry, (f) zigzag.

25

Fig.4. The impact of various types of nanofluids of trapezoidal symmetry- corrugated channel on (a) Nu, (b) ∆p, (c) Nuer, (d) PEC and streamlines (right) and isotherm (left) contours for different types of nonofluids at Re=30000 : (e) CuO-water, (f) ZnO-water , (g) Al2O3-water, and (h) SiO2-water.

26

Fig.5. The effect of nanoparticles volume fraction of on (a) Nuav , (b) ∆p, (c) number, (d) PEC, and streamlines (right) and isotherm (left) contours of -water for different nanoparticles volume fraction at Re=30000: (e) 0.02, (f) 0.04, (g) 0.06, and (h) 0.08., (g) Al2O3-water, and (h) SiO2-water.

27

Fig. 6. The effect of nanoparticle diameter of SiO2 on (a) Nuav, (b) ∆p, (c) Nuer, (d) PEC, and streamlines (right) and isotherm (left) contours of SiO2-water for different nanoparticles diameter at Re=30000: (e) 80 nm, (f) 60 nm, (g) 40 nm, and (h) 20 nm.

28

Table 1: Grid optimization Grid normalize

Grid spacing

1 2 3 4

2 1.5 1 0.9

Bulk temperature recovery (x= 1 m) 305.836 305.032 304.971 304.963

Table 2: Values of β for different nanoparticles [28] Nanoparticles type Al2O3 CuO SiO2 ZnO

β

Concentration (%)

8.4407(100??)-1.07304 9.881(100??)-0.9446 1.9526(100??)-1.4594 8.4407(100??)-1.07304

Temperature(K)

1% ≤ φ ≤ 10% 1% ≤ φ ≤ 6% 1% ≤ φ ≤ 10% 1% ≤ φ ≤ 7%

298K ≤ T ≤ 363K 298K ≤ T ≤ 363K 298K ≤ T ≤ 363K 298K ≤ T ≤ 363K

Table 3: The thermo-physical properties of water-based nanofluids with dp = 20 nm and ?? = 0.02 at T=300K. Thermo-physical properties Density ?? (kg/m3) Dynamic viscosity, μ(Ns/m2) Thermal conductivity, k(W/m.K) Specific heat, Cp (J/kg.K)

Al2O3

SiO2

CuO

ZnO

1050.24 0.0012377 0.685 3947.74

1022.24 0.0012377 0.620 4032.25

1108.24 0.0012377 0.682 3754.26

1090.24 0.0012377 0.672 3803.26