Heat transfer enhancement of turbulent nanofluid flow over various types of internally corrugated channels

Powder Technology 286 (2015) 332–341

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Heat transfer enhancement of turbulent nanofluid flow over various types of internally corrugated channels A.S. Navaei a,⁎, H.A. Mohammed b,⁎, K.M. Munisamy a, Hooman Yarmand c,⁎, Samira Gharehkhani c a b c

Department of Mechanical Engineering, College of Engineering, Universiti Tenaga Nasional, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysia Department of Thermofluids, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor Bahru, Malaysia Department of Mechanical Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia

a r t i c l e

i n f o

Article history: Received 5 March 2015 Received in revised form 13 May 2015 Accepted 1 June 2015 Available online 6 June 2015 Keywords: Nanofluids Turbulent flow Heat transfer Grooved channel

a b s t r a c t A numerical study is carried out to investigate the effects of different geometrical parameters and various nanofluids on the thermal performance of rib–grooved channels under uniform heat flux. The continuity, momentum and energy equations are solved by using the finite volume method (FVM). Three different rib– groove shapes are studied (rectangular, semi-circular and trapezoidal). Four different types of nanoparticles, Al2O3, CuO, SiO2 and ZnO with different volume fractions in the range of 1% to 4% and different nanoparticle diameters in the range of 20 nm to 60 nm, are dispersed in the base fluids such as water, glycerin and ethylene glycol. The Reynolds number varies from 5000 to 25,000. To optimize the shape of rib–groove channels different rib–groove heights from 0.1Dh (4 mm) to 0.2Dh (8 mm) and rib–groove pitch from 5e (20 mm) to 7e (56 mm) are examined. Simulation results reveal that the semi-circular rib–groove with height of 0.2Dh (8 mm) and pitch equals to 6e (48 mm) has the highest Nusselt number. The nanofluid containing SiO2 has the highest Nusselt number compared with other types. The Nusselt number rises as volume fraction increases, and it declines as the nanoparticle diameter increases. The glycerin–SiO2 nanofluid has the best heat transfer compared to other base fluids. It is also observed that in the case of using nanofluid by changing parameters such as nanoparticle diameter, volume fraction and base fluids the skin friction factor has no significant changes. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Forced convection heat transfer in a rib–groove channel has recently grabbed lots of researchers' attention. There are demands of improvement in convective heat transfer in engineering thermal systems in order to moderate size, weight and cost of heat exchangers. Numerous efforts have been made to enhance the heat transfer in the heat exchangers by using roughen surfaces or turbulators such as rib, groove and helical rib in disturbing the flow and in providing transverse/ longitudinal vortices or three dimensional mixing. Several geometric shapes of the rib–groove channel including rectangular, triangular, square, and circular had been studied in the past decades considering various combinations of the imposed temperature gradients and cavity configurations. All these types of rib–groove channel were used in many engineering applications such as cross-flow heat exchanger, gas turbine airfoil cooling design, solar air heater blade cooling system, and gas cooled nuclear reactor [1]. Employing of nanofluids can be considered as a way to enhance the heat transfer in rib–groove channels. Nanofluids are fluids that contain suspended nanoparticles such as ⁎ Corresponding authors. Tel.: +60 7 55 34716; fax: +60 7 55 66159. E-mail addresses: [email protected] (A.S. Navaei), [email protected] (H.A. Mohammed), [email protected] (H. Yarmand).

http://dx.doi.org/10.1016/j.powtec.2015.06.009 0032-5910/© 2015 Elsevier B.V. All rights reserved.

carbon based materials and metal oxides [2–4]. These nano-scale particles keep suspended in the base fluid. Thus, it does not cause an increase in pressure drop in the flow field. Past studies showed that not only nanofluids exhibit enhanced thermal properties, such as higher thermal conductivity and convective heat transfer coefficients, but also caused a lesser pressure drop in the flow field compared to the base fluid [5–9]. Investigations on heat transfer coefficient and pressure loss for different rib–groove channel configurations by both experimental and numerical works have been carried out by many researchers [10–24]. Karmare and Tikekar [10] presented an experimental investigation of heat transfer of the airflow in a rectangular duct. The top wall surface was made rough with metal ribs. It was found that the Nusselt number and friction factor can be enhanced up to 187% and 213%, respectively, by increasing the relative roughness height of grid (e/Dh) and relative length of grid (l/s). Tanda [11] investigated the effect of four different pitch-to-height ratios (p/e) including 6.66, 10.0, 13.33, and 20.0, on heat transfer in a rectangular channel with one-ribbed wall and tworibbed wall. Results showed that p/e = 13.33 was slightly preferable for the 1RW case (especially at the highest Re values) while a smaller p/e value (p/e = 6.66–10) gave the best performance for the 2RW case. Chiang et al. [12] investigated the effect of length-to-gap (L/B) ratio on heat transfer enhancement in a ribbed rectangular channel. The spatially averaged Nusselt number over the rib roughened fin surface

A.S. Navaei et al. / Powder Technology 286 (2015) 332–341

Nomenclature Cp e f f0 H h k L0 L1 L2 L3 N Nu Nu0 P Pr q Re T u

specific heat at constant pressure, J kg−1 K−1 height of rib, mm friction factor = ΔP/(ρu2/2)(L/D) friction factor of plain channel height of the channel, mm heat transfer coefficient, Wm−2 K−1 thermal conductivity of fluid, Wm−1 K−1 length of the channel, mm fully developed region, mm length of the grooved channel, mm length of the smooth channel, mm Avogadro number Nusselt number = hD/k Nusselt number of plain channel pitch of rib–groove, mm Prandtl number = Cpμ/k heat flux density, Wm−2 Reynolds number = ρuD/μ temperature, K flow velocity, ms−1

Greek symbols Β coefficient of thermal expansion, 1/K Μ dynamic viscosity, kg/ms ν kinematic viscosity, m2/s Γ molecular diffusivity Ρ mass density, kg/m3 Φ nanoparticle volume fraction Δ difference

consistently increased with the decrease of L/B ratio and the increase of Reynolds number. The effect of rib angle of attack (α) and pitch-to-rib height (p/e) to achieve an optimal design was investigated by Kim et al. [13]. As a result of the optimization, the high regions of heat transfer and thermal performance induced by two design variables (α and p/e) appeared in ranges of 50 ≤ α ≤ 60. and 6.0 ≤ p/e ≤ 7.0. Bilen et al. [14] presented an experimental study on heat transfer and friction characteristics of a turbulent air flow in a tube with three different groove shapes. Among all grooved tubes, heat transfer enhancement was obtained up to 63% for circular groove, 58% for trapezoidal groove and 47% for rectangular groove, in comparison with the smooth tube. A computer code to study the heat transfer in a square duct with various rib shapes including square, triangular, trapezoidal with decreasing height in the flow direction, and trapezoidal with increasing height in the flow direction, was developed by Kamali and Binesh [15]. The results show that the trapezoidal ribs with decreasing height in the flow direction provide higher heat transfer enhancement and pressure drop than other shapes. Promvonge and Thianpong [16] performed experiments to estimate the heat transfer rate of air flow in a steady heat flux channel with different shapes of ribs including triangular, wedge and rectangular shapes. The results showed that triangular rib with staggered array showed better thermal performance than other ribs. Eiamsa-ard and Promvonge [17] carried out an experimental research to study the integrated effects of rib–grooved turbulators on the heat transfer properties in a rectangular duct with three types of rib–grooved orders including rectangular-rib and triangular groove (RR–TG), triangular-rib and rectangular groove (TR–RG) and triangular-rib with triangular groove (TR TG). Results show that ducts with RR–TG order create the highest heat transfer rate and friction factor than others. Liu and Gao [18] examined the heat transfer in

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two-dimensional channels with different ribs. The results showed that the resistance co-efficient and average Nusselt number in the channel with triangular ribs were the largest ones compared with others. Manca et al. [19] analyzed a ribbed channel with different geometric ratios and heights under constant heat flux with relative roughness pitch (p/e) ratio equal to 6, 8, and 10, for triangular, square, rectangular and trapezoidal ribs, respectively. The results showed that the Nusselt number increased as relative roughness height (e/d) increases and the best thermal performance was provided by triangular ribs with relative roughness width (w/e) = 2.0 and p/e = 6. Peng et al. [20] showed that among different V-shaped ribs the 45° V-shaped continuous ribs have the best thermal/hydraulic performance. Promvonge et al. [21] conducted a numerical work to investigate heat transfer characteristics in a square-duct with inline 60° V-shaped ribs placed on two opposite heated walls. It was found that the maximum thermal performance was around 1.8 for the rib with BR = 0.0725 where the heat transfer rate was about 4.0 times above the smooth duct at lower Reynolds number. Chandra et al. [22] reported an experimental study of surface heat transfer characteristics of a fully developed turbulent air flow in a square channel with transverse ribs on one, two, three, and four walls. The channel with two opposite ribbed walls showed a 6% increase in heat transfer over the one ribbed wall case. The three ribbed wall case showed a 5% increase over two ribbed wall case and the four ribbed wall case showed an increase of 7% over the three ribbed wall case. Wang et al. [23] done PIV measurement in a channel with regular rib on one wall. The highest Reynolds shear stresses happened at the leading edge of the rib. They did a quadrant analysis and found that ejection motions played a major role in the Reynolds shear stress in this region. Liu and Wang [24] presented a novel design of ribbed channel which was called semi-attached rib-design. The ribs were perforated at the rib corners to form two rectangular holes, so a portion of the fluid can pass through the holes. Five different structures of the rib (width ratios of the channel to hole) and two positions (transverse rib and 45° angled ribs) were analyzed. The numerical results show that the semi-attached ribs with 45° angle of attack can achieve a higher efficiency of synthetically heat transfer than that of the fully attached and detached rib channels. A study on heat transfer distributions for straight and tapered twopass channels with and without ribs for three Reynolds numbers was done by Ekkad et al. [25] Results showed that the tapered channel with ribs provided 1.5–2.0 times higher Nusselt number ratios over the tapered smooth channel in the first pass. In the after-turn region of the second pass, the ribbed and smooth channels provided similar Nusselt number ratios. Saha and Acharya [26] found that among ducts with various aspect ratios of 1:1, 4:1 and 1:4, heat transfer was maximum for the 4:1 AR case. Zhu et al. [27] presented that the combination of rib roughness and winglets produced appreciable heat transfer enhancement. More than 450% enhancement of the Nusselt number was possible. Saha [28] found out that the transverse ribs in contact with wire–coil inserts perform better than when they were acting alone. Lu and Jiang [29] did a study on the effect of various rib angles (i.e., 90°, 60°, 45°, 30°, 20°, 10° and 0°) on heat transfer of air in a rectangular channel. The results showed that the channel with 60° ribs had the best heat transfer performance, the channel with 0° ribs had the least pressure drop, and the channel with 20° ribs had the best thermal/hydraulic performance. Singh et al. [30] carried out an investigation on the effect of flow-attack-angle (α) on thermo-hydraulic performance of rectangular ducts roughened with a new configuration of ‘V-down rib having gap’ on one wide wall. The results showed the best flow-attack-angle (α) was from 30° to 75°. Smulsky et al. [31] conducted an experimental work on the effect of the angle of rib orientation relative to the flow of the coordinates varying from 50° to 90°. The local heat transfer maximum for the angle of 50° is approximately 40% higher, than for the angle of 90°.

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Insufficient studies on forced convective heat transfer in a grooved channel with different shaped ribs utilizing nanofluids in the past have motivated the present study. A 2D study on turbulent forced convective flow in a grooved channel with different shaped ribs by using different types of nanofluids, different nanoparticle volume fractions, and different nanoparticle diameters, is dispersed in different base fluids (water, glycerin, ethylene glycol) over Reynolds number in the range of 5000 ≤ Re ≤ 25,000, and different rib–groove heights from 0.1Dh (4 mm) to 0.2Dh (8 mm) and rib–groove pitch from 5e (20 mm) to 7e (56 mm) have been carried out in the present study. Results of interests including Nusselt number and skin friction coefficient are reported to show the effects of rib–groove shape and nanofluids on these parameters.

2. Numerical model 2.1. Physical model Schematic diagrams of rib–groove channel for geometrical model and three cases are shown in Fig. 1a–d. The first case is square rib– square groove shown in Fig. 1b and the second case, semi-circle rib– semi-circular groove is shown in Fig. 1c and the third case is trapezoidal rib–trapezoidal groove shown in Fig. 1d. A horizontal plane channel having five ribs and five grooves with a test section length of L2 = 200 mm (11H) is considered as shown in Fig. 1a–d. The channel height is set to be H = 40 mm while the channel rib & groove height (e) is equal to 0.1H, 0.15H and 0.2H, and channel rib & groove width (w) is equal to

Fig. 1. Schematic diagram of rib–groove channel, (a) geometrical model, (b) square rib–square groove, (c) semi-circular rib–semi-circular groove, and (d) trapezoidal rib–trapezoidal groove.

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the channel rib & groove height (e) except for the semi-circular which is equal to 2e. Both the height and length of the rib–groove channel are fixed and the shapes of rib and groove were interchanged with constant aspect ratio. To ensure a fully developed flow, a smooth entrance section was installed with the test section having a length of L1 = 400 mm, and an exit was also proceeded with a length of L3 = 100 mm. The left side of the channel is assigned as velocity inlet based on Reynolds number, the exit side of the channel is subjected to pressure outlet, and the top and bottom walls are subjected to uniform heat flux.

Similarly the dissipation rate of TKE, ε is given by the following equation: ∂ ∂ ðρεui Þ ¼ ∂xi ∂x j

The phenomenon under consideration is governed by the steady 2-dimensional form of the continuity, the time-averaged incompressible Navier–Stokes equations and energy equation. In the Cartesian tensor system these equations can be written as [32]: Continuity equation: ∂ ðρui Þ ¼ 0: ∂xi

"

#  ut ∂ε ε ε2 þ C 1 Gk −C 2ε ρ μþ k σ k ∂x j k

ð8Þ

where Gk is the rate of generation of the TKE while ρε is its destruction rate. Gk is written as:

Gk ¼ −

2.2. Governing equations

335

  l u  j ∂; u j ρu : ∂xi

ð9Þ

The Reynolds number, the Nusselt number, the friction factor, and the thermal enhancement factor are expressed by the following relations [17]. Re ¼

U av  Dh ν

ð10Þ

ð1Þ

Momentum equation: " ∂ðρui u j Þ ∂p ∂ ¼− þ μ ∂xi ∂x j ∂xi

∂ui ∂u j þ ∂x j ∂xi

!# þ

 ∂  l u j : −ρu ∂x J

ð2Þ

Energy equation: ∂ ∂ ðρui T Þ ¼ ∂xi ∂x j

ðΓ þ Γt Þ

∂T ∂x j

! ð3Þ

where Γ and Γt are molecular thermal diffusivity and turbulent thermal diffusivity, respectively and are given by Γ¼

μ μ ; and Γt ¼ t : Pr P rt

ð4Þ

The Reynolds-averaged approach to turbulence modeling requires   l u  j in Eq. (2) needs to be modeled. that the Reynolds stresses −ρu For closure of the equations, the k–ε turbulence model was chosen. A common method employs the Boussinesq hypothesis to relate the Reynolds stresses to the mean velocity gradients: l u  j ¼ μt −ρu

! ∂ui ∂u j þ : ∂x j ∂xi

ð5Þ

The turbulent viscosity term μt is to be computed from an appropriate turbulence model. The expression for the turbulent viscosity is given as 2

μ t ¼ ρC μ

k : ε

ð6Þ

The modeled equation of the turbulent kinetic energy (k) is written as: ∂ ∂ ðρkui Þ ¼ ∂xi ∂x j

" μþ

#  ut ∂k þ Gk −ρε: σ k ∂x j

ð7Þ

Fig. 2. Comparison of the present work with the results of the Eiamsa-ard and Promvonge [32], (a) Nusselt number and (b) friction factor.

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Table 1 The values of β for different particles. Type of particles

β

Concentration (%)

Temperature (K)

Al2O3 CuO SiO2 ZnO

8.4407(100ϕ)−1.07304 [35] 9.881(100ϕ)−0.9446 [35] 1.9526(100ϕ)−1.4594 [35] 8.4407(100ϕ)−1.07304 [35]

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

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

Nu ¼

f ¼

h  Dh k

2Δp   L

ð11Þ

:

Dh ρ  U av 2

! :

ð12Þ

determine the velocity components. The pressure is updated using the continuity equation. Even though the continuity equation does not contain any pressure, it can be transformed easily into a pressure correction equation [34]. The turbulence intensity was kept at 1% at the inlet. The solutions are considered to be converged when the normalized residual values reach 10−5 for all variables. 2.5. Thermophysical properties of nanofluids The thermophysical properties of nanofluids used in this study were obtained using the following equations. The density of nanofluid, ρnf can be obtained from the following Eq. (1): ρn f ¼ ð1−ϕÞρ f þ ϕρnp

ð13Þ

where ρf and ρnp are the mass densities of the based fluid and the solid nanoparticles, respectively. The effective heat capacity at constant pressure of nanofluid, (ρCp)nf can be calculated from the following Eq. (1):

2.3. Grid testing and code validation A grid independence test was performed to evaluate the effects of grid sizes on the results. In this study, nine mesh faces are considered, which are 31,480, 125,762, 165,563, 182,203, 187,271, 199,834, 201,832, 208,202 and 238,325 at Re = 25,000. The discretization grid is structured and uniform. All nine grid mesh faces have almost similar results of Nusselt number. Thus, a domain with mesh faces of 199,834 is used to reduce the computational time. The code validation was done based on the geometry and boundary conditions which were used by Eiamsa-ard and Promvonge [32]. They studied the thermal characteristics of turbulent rib groove channel flows with constant heat flux boundary condition. The comparison between obtaining a Nusselt number and friction factor from this study and results of Eiamsa-ard and Promvonge [32] are presented in Fig. 2a and b. As it can be seen in these figures a good agreement is achieved between them. 2.4. Numerical parameters and procedures The numerical computations were carried out by solving the governing conservation equations (Eqs. (1)–(4)) along with the boundary conditions. The standard k–e turbulence model and the renormalized group (RNG) k–e turbulence model were selected. The discretization of time-independent incompressible Navier– Stokes governing equations and the turbulence model analysis in the fluid and solid regions were done using the finite-volume method (FVM). The diffusion term in the momentum and energy equations is approximated by first-order central difference which gives a stable solution. In addition, a first-order upwind differencing scheme is adopted for the convective terms. The numerical model was developed in the physical domain, and dimensionless parameters were calculated from the computed velocity and temperature distributions. The flow field was solved using the SIMPLE algorithm [33]. This is an iterative solution procedure where the computation is initialized by guessing the pressure field. Then, the momentum equation is solved to



ρ Cp

 nf

    ¼ ð1−ϕÞ ρ C p f þ ϕ ρC p np

ð14Þ

where (ρCp)f and (ρCp)np are heat capacities of the based fluid and the solid nanoparticles, respectively. By using Brownian motion of nanoparticles in rib–groove channel, the effective thermal conductivity can be obtained by using the following mean empirical correlation [35]: keff ¼ kstatic þ kBrownian

ð15Þ

"   # knp þ 2k f −2ϕ k f −knp    kstatic¼ k f  knp þ 2k f þ ϕ k f þ knp

kBrownian

ð15:1Þ

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi KT ¼ 5  10 β ϕ ρ f C p; f f ðT; ϕÞ 2 ρnp Rnp 4

ð15:2Þ

where:Boltzmann constant: k = 1.3807 ∗ 10−23 J/K. Values of β for different particles are listed in Table 1. Modeling, f(T,ϕ)   T  f ðT; ϕÞ ¼ 2:8217  10−2 ϕ þ 3:917  10−3 T0   þ −3:0669  10−2 ϕ−3:3:91123  10−3 :

For 1% ≤ ϕ ≤ 4% and 300 K b T b 325 K.

Table 2 The thermo-physical properties of water and different nanoparticles at T = 300 K. Thermo-physical properties

Water [42]

EG [43]

Al2O3 [35]

CuO [35]

SiO2 [44]

ZnO [35]

Density, ρ (kg/m3) Specific heat, Cp (J/kg K) Thermal conductivity, K (W/m K) Dynamic viscosity, μ (Ns/m2)

998.2 4182 0.6 0.001003

1111.4 2415 0.252 0.0157

3970 765 40 0

6500 535.6 20 0

2200 703 1.2 0

5600 495.2 13 0

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The effective viscosity can be obtained by using the following mean empirical correlation [36]: 1  μ eff ¼ μ f    −0:3 =d  ϕ1:03 1−34:87 d p f " #1=3 6M df ¼ Nπρ f o

ð16Þ ð16:1Þ

where: M is the molecular weight of base fluid, N is the Avogadro number = 6.022 ∗ 1023 mol−1, ρf0 is the mass density of the based fluid calculated at temperature T0 = 293 K. Table 2 shows the thermophysical properties of water and nanoparticle.

3. Results and discussion The effects of different rib–groove shapes, rib–groove aspect ratio, different nanofluid types, its concentration and particle diameter, Reynolds number and different base fluids on the thermal and flow fields are analyzed and discussed in this section.

Fig. 3. The effect of different rib–groove shapes at different Reynolds numbers, (a) Nusselt number and (b) friction factor.

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3.1. The effect of different rib–groove shapes In this section, four different rib–groove shapes which (square rib– groove, trapezoidal rib–groove, and semi-circular rib–groove) are considered to investigate their effects on the thermal and flow fields. The variation of Nusselt number with Reynolds number for different rib–groove shapes is presented in Fig. 3a. It can be seen that the Nusselt number increases with the increase of Reynolds number. This can be explained by the strong turbulence intensity of the presence of the rib–groove turbulator leading to rapid mixing between the core and the wall of the channel. It is observed that the semi-circular rib–groove channel provided the highest heat transfer enhancement among the aforementioned shapes. This is because of a strong mixing of the fluid induced form turbulent flow and the appearance of reverse flow between the adjacent rib–groove elements, leading to higher temperature gradients [37]. Fig. 3b shows the variation of friction factor with Reynolds number along the channel. It is seen that the friction factor is high at lower Reynolds number and then it tends to reduce when the Reynolds number increases. The friction factor using the rib–groove turbulator is observed to be higher than that for the smooth channel [38].

Fig. 4. Variation of (a) Nusselt number and (b) skin friction coefficient via Reynolds number for channel with semi-circular rib–groove shapes (e/d = 0.15).

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3.2. The effect of roughness pitch In this section, different geometrical parameters which height of ribs (e/d = 0.1, 0.15, 0.2) and the pitch of ribs (p/e = 5, 6, 7) were studied. In order to see the effect of different geometrical parameters on the heat transfer enhancement all other parameters of the system of heat transfer should be fixed. Fig. 4a shows the variation of Nusselt number via Reynolds number while the height of rib–groove was fixed at e = 6 and pitch of rib–groove was (p/e = 5, 6 and 7). It is clearly seen that the semi-circular with P/e = 6 has the highest Nusselt number in different Reynolds numbers because of the flow separation and reattachment are induced by these roughness. From the reattachment point the Nusselt number enhancement rapidly deteriorates due to the boundary layer growth and the flow separation in front of the next corrugation. It also provides periodic redevelopment of the boundary layers and causes a more effective heat transfer. It can be said that thermal boundary layers for roughed flow became thinner than the case of the smooth channel and secondary vortices inside the corrugations contributed to the enhancement of the heat transfer. Fig. 4b shows the effect of Reynolds number and rib–groove pitch on the skin friction factor in the range

Fig. 5. Variation of (a) Nusselt number and (b) skin friction coefficient via Reynolds number for channel with semi-circular rib–groove shapes (p/e = 6).

of Reynolds number investigated for a fixed value of roughness height. They show that the skin friction factor varied with the variation of rib–groove pitch in all cases as expected due to the suppression of viscous sub-layer and the introduction of the ribbed surface yields to higher friction factor as compared to that of the smooth surface. 3.3. The effect of roughness height In this case p/e was fixed at 6 as the result of last section showed it has the highest effect on heat transfer enhancement and thermofield, so the variation of different heights was studied in this section (e/d = 0.1, 0.15, 0.2) It can be seen from Fig. 5a that as the Reynolds number increases, the average Nusselt number also increases almost linearly. The large Reynolds number is attributed to the higher velocity which can lead to disturb the flow and thus, the heat transfer is strengthened. In all cases, the roughed channel flows gave higher values

Fig. 6. Variation of (a) Nusselt number and (b) skin friction factor via Reynolds number for channel with semi-circular rib–groove shapes with different types of nanofluids.

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of Nusselt number than that for smooth channel flow due to the induction of high re-circulation/reverse flow and thin boundary layer in the roughed tubes, leading to higher temperature gradients. On the other hand, as expected, these inner corrugations cause a significant pressure drop as well, in comparison with the smooth channel. The increase in Nusselt number results in an increase in pressure drop, the pressure drop increases with increasing roughness height due to the fact that increasing the height of roughness disturbs the entire flow field and causes more pressure drop. The average Nusselt number does not increase with additional rib–groove surface area; this suggests that the primary cause for the enhancement is the strong turbulent motion induced by the roughness. It is observed that the variation of Nusselt number with roughness height is insignificant at lower value of Reynolds number but at higher Reynolds number, the variation is substantial [39]. As shown in Fig. 5a the roughed tube with roughness height equal to 8 mm (e/d = 0.2) provides the highest average Nusselt number at all Reynolds numbers. The macro-vortex behind the rib–groove increases its dimension with the increase of Reynolds number, so there is an enhancement of the turbulent mixing and heat transfer.

Fig. 7. The effect of different volume fractions of nanoparticles at different Reynolds numbers. (a) Nusselt number and (b) skin friction factor.

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Fig. 5b shows the variation of skin friction factor via Reynolds number in a channel. It is clearly shown that the skin friction factor decreases while Reynolds number increases. In addition, to be in comparison the skin friction factor in rib–groove roughness with the height of 8 mm is the highest. In fact in comparing the different geometries, it can be noticed that the skin friction factor generally tends to increase as the roughness height increases for a fixed roughness pitch as shown in this figure.

3.4. The effect of different types of nanoparticles Four different types of nanoparticles such as Al2O3, CuO, Si2O and ZnO and pure water as a base fluid are used. The Nusselt number for different nanofluids and different values of Reynolds number are shown in Fig. 6a. It can be clearly seen that SiO2 nanofluid has the highest average Nusselt number, followed by Al2O3, ZnO, and CuO respectively. This is because SiO2 has the lowest thermal conductivity than other nanofluids, but higher than water and has the highest average velocity among other fluids due to its lowest density compared

Fig. 8. The effect of different nanoparticle diameters at different Reynolds numbers, (a) Nusselt number, and (b) skin friction factor.

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with the others. The fluid velocity plays an important role on the heat transfer in the case of forced convection and it represents the main reason to give high heat transfer coefficient. As shown in Fig. 6b the friction factor decreases with the increase of the Reynolds number for different nanofluid types. 3.5. The effect of different nanoparticle volume fractions In this study the nanoparticle volume fraction in the range of 1–4% with different values of Reynolds number is investigated. As shown clearly in Fig. 7a, increasing nanoparticle volume fraction enhances the Nusselt number. The Nusselt number is not very sensitive to the volume fraction of nanoparticles at lower Reynolds number and in all cases with increasing the Reynolds number, the Nusselt number increases. This is because as the volume fraction increases, irregular and random movements of the particles increase the energy exchange rates in the fluid with penalty on the wall shear stress and consequently enhance the thermal dispersion of the flow. As shown in Fig. 7b the friction factor decreases with the increase of Reynolds number for different volume fractions of nanoparticles. 3.6. The effect of different nanoparticle diameters This study used SiO2 water as a working fluid with fixed other parameters such as volume fraction at 4% except that Reynolds number was in the range of 5000–25,000. The range of nanoparticle diameter is 25–60 nm. As illustrated in Fig. 8a, the results revealed that the nanofluid with smaller particle diameter has the higher Nusselt number. The effect of particle size may be attributed mainly to two reasons which are the high specific surface area of the nanoparticles and the Brownian motion [40]. As the particle size reduces, the surface area per unit volume increases, the heat transfer is being dependent on the surface area, and thus the effectiveness of nanoparticles in transferring heat to the base liquid increases [41]. However, reducing the particle size means increasing the Brownian motion velocity, which again adds up to the contribution by the nanoparticles to the total heat transfer by continuously creating additional paths for the heat flow in the fluid. As presented in this figure the nanofluid with 25 nm nanoparticle diameter has the highest Nusselt number, whereas, the nanoparticle with a diameter of 80 nm has the lowest Nusselt number. As shown in Fig. 8b the friction factor decreases with the increase of Reynolds number for different nanoparticle diameters. 3.7. The effect of different base fluids The effect of different types of base fluids on the Nusselt number versus the Reynolds number is presented in Fig. 9a. The results show that the maximum and minimum values of the Nusselt number are obtained for SiO2–glycerin and SiO2–water respectively. This trend is attributed to the nature of glycerin which has the highest dynamic viscosity compared to other base fluids. Consequently, SiO2 particles are mixed properly in glycerin which contributes to increase the thermal transport capacity of the mixture and the Nusselt number as well. It means the higher viscosity of glycerin results in a suspension with more homogeneous dispersion of the particles which has direct influence on increasing the thermal performance of the nanofluid [38]. As shown in Fig. 9b the friction factor decreases with increasing the Reynolds number for the different base fluids. 4. Conclusions Numerical simulations of turbulent forced convection heat transfer in a rib–groove channel subjected to uniform heat flux were carried out. The emphasis is given on the heat transfer enhancement resulting from various parameters, which include different shapes of rib–groove channel, the type of nanofluid, volume fraction of nanoparticle,

Fig. 9. The effect of different base fluids at different Reynolds numbers, (a) Nusselt number, and (b) friction factor.

nanoparticle diameter, roughness pitch and height, Reynolds number and base fluid type. The governing equations were solved utilizing finite volume method with the SIMPLE algorithm. The results show that semicircular rib–groove gives the highest Nusselt number and the best thermal enhancement factor. It is found that SiO2 nanofluid gives the highest Nusselt number followed by Al2O3, ZnO, and CuO respectively while pure water gives the lowest Nusselt number. The Nusselt number increased with the increase of nanoparticle volume fraction, roughness height and Reynolds number; however, it decreased with the increase of nanoparticle diameter. It was also shown that rib–groove channel with roughness pitch of 6 had the highest heat transfer. The results revealed that glycerin–SiO2 gives the highest Nusselt number followed by ethylene glycol–SiO2 while water–SiO2 gives the lowest Nusselt number.

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