- Email: [email protected]
Influences of geometrical parameters on the heat transfer characteristics through symmetry trapezoidal-corrugated channel using SiO2-water nanofluid
International Communications in Heat and Mass Transfer 101 (2019) 1–9
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Influences of geometrical parameters on the heat transfer characteristics through symmetry trapezoidal-corrugated channel using SiO2-water nanofluid
T
⁎
Raheem K. Ajeela,b, , W.S.-I.W. Salima, Khalid Hasnana a b
Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia, 86400, Parit Raja, Batu Pahat, Johor, Malaysia Department of Mechanical Engineering, College of Engineering, University of Babylon, Babylon, Iraq
A R T I C LE I N FO
A B S T R A C T
Keywords: Turbulent flow Symmetry trapezoidal-corrugated channel Height –to-width ratio Pitch-to-length ratio Nanofluids Finite volume method
Enhancing the geometrical parameters design of thermal devices leads to promote the thermal performance and boost design plan of these devices and make it more compact. In the current study, heat transfer and flow characteristics of the symmetry trapezoidal-corrugated channel with silicon dioxide (SiO2) - water as nanofluid was performed numerically over Reynolds number ranges of 10,000–30,000. The influence of geometrical parameters including height-to-width ratio (h/W) and pitch-to-length ratio (p/L) on the thermal and hydraulic characteristics are evaluated. A numerical simulation covers nanofluid with SiO2 volume fractions 8% and carried out by employing the finite volume method (FVM) and SIMPLE algorithm for discretization of the governing equations and coupling of the pressure-velocity system while the k−ε turbulence model was employed to compute the turbulent flow. The outcomes revealed that the (h/W) ratio has a more influence on the promotion of heat transfer compared with the (p/L) ratio. At Reynolds number 30000, there is 16.63% increment in Nuav due to a decrease of the (p/L) ratio from 0.175 to 0.075, while the increment about 99.45% due to an increase of the (h/W) ratio from 0.0 to 0.05. The numerical results indicate that the h/W of 0.05 with a p/L of 0.075 are the optimum parameters and have shown significant improvement in thermal performance factor. Furthermore, new correlations for Nusselt number and friction factor are developed and reported.
1. Introduction Nowadays, the urgent need to achieve high thermal performance and reduce weight and cost, push many industries to look for new ways and procedures to promote heat transfer. In this regard, the corrugated surface has emerged as one way to increase thermal performance and minimize the thermal boundary layer thickness of the heat exchangers surfaces. The main objective of the corrugated surface is to boost the blending of the fluids via form the secondary flow nearby the trough of the corrugated surfaces and then maximize the heat transfer exchange. On the other hand, traditional fluids have poor thermal properties especially thermal conductivity which can be considered a major obstacle to achieving high thermal performance. Therefore, employing nanofluids as a cooling medium in such channels instead of classic liquids can improve the thermophysical properties of the base liquids and thereby a further refinement in thermal efficiency of heat exchangers. Many investigators have focused in their studies on the use of classical
liquids through the corrugated channels numerically and experimentally [1–10]. Esmaeili et al. [11] tested the Al2O3-water nanofluid flow in a sinusoidal wavy channel by employing a finite volume technique. The outcomes indicated that the heat transfer significantly increased due to effect of the nanoparticles. Moreover, Nusselt number increased with increased Reynolds number. Vanaki et al. [12] conducted another numerical investigation in terms of nanoparticle shapes impact on heat transfer and flow fields over a wavy wall channels by implementing SiO2-ethylene glycol nanofluids. They reported that the platelets nanoparticle shape offered the best results in terms of heat transfer enhancement. Pandey and Nema [13] experimentally conducted on the convective heat transfer and flow characteristics in wavy-plate heat exchanger using Al2O3–water nanofluid. It was found that the enhancement in heat transfer increases with increasing in Reynolds number and Peclet number. In addition, the pumping power increases with increasing in volume fraction of nanoparticles. Akbarinia and Laur
⁎ Corresponding author at: Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia, 86400, Parit Raja, Batu Pahat, Johor, Malaysia. E-mail address: [email protected] (R.K. Ajeel).
https://doi.org/10.1016/j.icheatmasstransfer.2018.12.016
0735-1933/ © 2019 Elsevier Ltd. All rights reserved.
International Communications in Heat and Mass Transfer 101 (2019) 1–9
R.K. Ajeel et al.
Fig. 1. Schematic diagram (a) Computation domain, (b) Test section (corrugated wall).
trapezoidal channel; symmetry and zigzag configurations. The outcomes proved that the symmetry profile is superior to the zigzag profile in terms of thermal performance and the silicon dioxide -water nanofluid was the best rate of PEC. Based on the literature discussion, it can be inferred that the influences of design parameters, when a nanofluid is as working liquid and through corrugated channels, has not been totally investigated previously. Also, most of the previous investigations tested a 2-D turbulent convective heat transfer. Additionally, the SiO2-water nanofluid and the symmetry trapezoidal-corrugated channel were not combined previously to study the parameters design in such channels. In fact, this lack of knowledge motivates the present research. Accordingly, the present investigation considers turbulent forced convective flow of SiO2 -water nanofluid in 3-D corrugated channel. The influences of different design parameters with flowing of SiO2-water nanofluid over Re in the range of 10,000 ≤ Re ≤30,000 were discussed. Results of interests including average Nusselt number (Nuav), pressure drop (Δp), Nusselt number enhancement ratio (Nuer), and thermal performance factor (PEC) for turbulent forced convective of nanofluids in a symmetry trapezoidal -corrugated channel are reported to show the effect of corrugated channel and nanofluid on these parameters.
[14] have done a numerical study to investigate the impact of nanoparticle's diameter on flow in a tube having a circular cross-section. The authors claimed that the Nusselt number has affected by the diameter of the nanoparticle where it increased when the diameter of nanoparticles decreases. Khoshvaght-Aliabadi et al. [15] experimentally tested the impact of various kinds of nanofluid on the heat transfer performance in a corrugated channel. The test was done under constant wall temperature condition and covered volume fractions from 0.1 to 0.4%. The results showed that the HTC increased with increasing volume fraction of nanoparticles. Laminar forced convection of copper–water nanofluid in straight channel was numerically studied by Santra et al. [16]. The governing equations were discretized using finite volume approach and solved iteratively using the SIMPLER algorithm. Results indicated that the heat transfer rate increased as Reynolds number and nanoparticles volume friction increase. Fotukian and Nasr Esfahany [17] experimentally conducted on the turbulent forced convection of γ-Al2O3/ Water nanofluid in a circular tube. Their results showed that the addition of small amounts of solid particles to the base fluid enhanced the heat transfer, but accompanied by increasing the pressure drop. Using symmetry form of semicircle corrugated channel and Al2O3- water nanofluid, Ajeel and Salim [18] performed a numerical study on heat transfer performance. The authors claimed that the heat transfer improved by increasing the volume fraction of nanoparticles, but the pressure drop was also increased. Raisi et al. [19] numerically studied the laminar forced convection of copper–water nanofluid flow in a microchannel. Results showed that the coefficient of slip velocity and nanoparticle volume fraction had great influence on the rate of heat transfer at high Reynolds numbers. The laminar forced convection flow of nanofluid in a sinusoidal-wavy channel was numerically studied by Heidary and Kermani [20] using finite volume method. Results displayed that the heat transfer rate increased with amplitude of the wavy channel, nanoparticles volume fraction and Reynolds number. A numerical study on the forced convection of Al2O3 -water nanofluid in ribbed channel has been conducted by Manca et al. [21]. It was found that the heat transfer rate enhanced with the concentration of nanoparticles as well as Reynolds number. But this enhancement in heat transfer was accompanied by increasing the pressure drop penalty. Ahmed et al. [22] investigated numerically of the laminar forced convection flow in triangular-corrugated channel using copper–water nanofluid. It was observed that the average Nusselt number increases with Reynolds number and the volume fraction of nanoparticles. Recently, Ajeel et al. [23] carried out a numerical investigation to test the influences of nanofluids flow through two types of the
2. Problem description and assumptions Fig. 1 illustrated the 2-dimensional geometrical model of the present study (a), and (b) geometry of the symmetry trapezoidal- corrugated channel (test section). Plainly, the geometry of the current study is consists of upper walls and lower walls as well as side walls that are straight and not heated. In another way, the channel is composed of three parts; upstream part, corrugated part, and a downstream part, just the corrugated part was heated. The length of the upstream part is 4times of the downstream part while the total length of the corrugated wall is double length of the downstream wall. The height of the channel (H) is 10 mm while the channel width (W) is (5H). The corrugated height and the longitudinal pitch are (h) and (p), respectively. The geometrical and design parameters are listed in Table 1.Furthermore; several assumptions are made in the current study: i. Regarding the flow, steady-state, turbulent, fully developed, and 3D. ii. Nanofluid in single phase, Newtonian fluid, and incompressible. iii. Regarding the walls material, stainless steel, and the thermal conductivity does not change with temperature. 2
International Communications in Heat and Mass Transfer 101 (2019) 1–9
R.K. Ajeel et al.
Table 1 Design parameters employed in the current study.
μt , m = ρm Cμ = 1.3
Parameter
Terminology
Value
Channel height Test section length Pitch-to-length ratio Height-to-width ratio
H L p/L h/W
10 mm 4W 0.075,0.125,and 0.175 0.0,0.03,0.04, and 0.05
The boundary conditions for the computational domains of the symmetry trapezoidal- corrugated channel have been adopted. There was constant heat flux and no-slip condition at the corrugated walls, whereas thermally insulated conditions utilized for the flat walls. Furthermore, the velocity inlet condition and temperature of 300 K is adapted at the inlet, whereas the pressure outlet condition is employed at outlet. Eventually, the boundary conditions for the complex flow through a symmetry trapezoidal -corrugated channel can be stated as follows: At the inlet:
Table 2 Values of β for SiO2 nanoparticles. Nanoparticles type
β -
1.9526(100ϕ)
SiO2
Concentration (%)
Temperature (K)
1% ≤ φ ≤ 10%
298 K ≤ T ≤ 363 K
1.4594
u = uin, v = w = 0, Tin = 300 k
kin =
Table 3 Thermo-physical properties of nanofluids with dp = 20 nm and ϕ=0.08. Thermo-physical properties Density ρ (kg/m3) Dynamic viscosity, μ(Ns/m2) Thermal conductivity, k(w/m.K) Specific heat, cp (J/kg.K)
∂Tƒ
SiO2
∂x 1094.344 0.004795 0.643072 3622.483
= 0,
∂u ∂v ∂w ∂k ∂ε = = = 0, and = =0 ∂x ∂x ∂x ∂x ∂x
At the wall:
u = v = w = 0, q = qwall In order to expound the outcomes and characteristics of flow and heat transfer in the tested channel, some of the variables should be computed and presented: Average Nusselt number can be defined as follows:
Grid number
Average Nusselt number
Relative error%
162,632 267,696 329,668 413,520 544,235
126.1311 126.1546 126.1789 126.1896 126.1971
– 0.018628 0.019258 0.008479 0.005943
ln = q″.
uin =
(1)
(2)
Dh =
Energy equation:
(7) (8)
R eμ ρDh
(9)
4A cross P
(10)
From definition of Fanning friction factor as: (3)
Cfx =
The present study used the k − ε turbulence model suggested by Launder and Spalding [24]. The influence of mean velocity gradients has been taking into consideration in this model which produces turbulent kinetic energy and can designate G as shown below:
2τs 2 ρ uin
(11)
And friction factor is defined [22,25] as follows:
ƒ = 4Cfx
(12)
Based on the friction factor, the pressure drop can also be obtained as follows: [22,25]:
⎟
(4)
∆p = f
μt , m
ε ∇ . (ρm Vε ) = ∇ . ⎛ ∇ε ⎞ + (C1 Gm − C2 ρm ε ) σ k ⎝ ε ⎠
)
(Tw − Tm,in) − (Tw − Tm,out )
In this investigation, the hydraulic diameter of corrugated part is calculated depending on cross section area (Across) and the perimeter of wetted (P) as [22,25]:
Momentum equation:
μt , m ∇ . (ρm Vk ) = ∇ . ⎛ ∇k ⎞ + Gm − ρm ε ⎝ σk ⎠
Tw − Tm,in Tw − Tm,out
where A is the surface area of corrugated part while Tm,in, Tm,out are the average temperatures of the working media at inlet and outlet. Additionally, can obtain the inlet velocity depending on the Reynolds number as below:
The governing equations of the flow problem are solved for threedimensional flow as follows: Continuity equations:
∇ . (ρf VCp, f T ) = ∇ . (kf ∇T − Cp, f ρf vt)
(
q″ = ṁ Cp (Tm, in − Tm, out )/ A
3. Governing equations and boundary conditions
∇ . (ρf VV ) = −∇p + ∇ . τ
(6)
And, average heat transfer coefficient as:
iv. Both the base fluid and nanoparticles of SiO2 is homogenous and in the thermal equilibrium state.
∇ . (ρf V ) = 0
hDh kƒ
Nuav =
hav
⎜
3 K 3/2 (Iuin )2, εin = Cμ3/4 2 Lt .
Outlet boundary:
Table 4 Grid independence test.
⎜
K2 , C1 = 1.44, C2 = 1.92, Cμ = 0.09 = 0.09, σk = 1.0, σε ε
⎟
(5)
2 ρLcorr uin 2Dh
(13)
Lastly, in order to assess the system of the current study compared to the reference system which is a smooth channel, the thermal
where: 3
International Communications in Heat and Mass Transfer 101 (2019) 1–9
R.K. Ajeel et al.
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. [9], (d) Naphon [6].
performance factor was adopted. The thermal performance factor (PEC) is specified by [21] as follow:
PEC =
(
Nuav
Nuav, o
( ) f
f0
(knp + 2kf ) − 2ϕ (kf − knp ) ⎤ kstatic = kf ⎡ ⎢ (knp + 2kf ) + ϕ (kf − knp ) ⎥ ⎦ ⎣
)
1/3
kBrownian = 5 ∗ 10 4β ϕρf Cp, f
(14)
KT f (T , ϕ) 2
(20)
where: Boltzmann constant: k = 1.3807*10–23 J/K. Modeling, f(T, ϕ)
4. Calculations of nanofluid properties In current study, the thermophysical properties of SiO2–water nanofluid are given as follows:
T f (T , ϕ) = (2.8217 × 10−2ϕ + 3.917 × 10−3) ⎛ ⎞ ⎝ T0 ⎠ + (−3.0669 × 10−2ϕ − 3.391123 × 10−3) ⎜
i. Density and heat capacity: The nanofluid density and it heat capacity can be calculated as follow: [21]:
ρnf = (1 − ϕ) + ϕρnp
(15)
(ρCP )nf = (1 − ϕ)(ρCP )f + ϕ (ρCP )np
(16)
⎟
(21)
iii. Dynamic viscosity: Lastly, the effective dynamic viscosity of nanofluid is given as: [26]:
μeff = μf ii. Thermal conductivity:
⎛ 1 ∗ ϕ−1.03 ∗ ⎜ dp ⎜ ⎜ 1 − 34.87 d f ⎝
−0.3
()
⎞ ⎟ ⎟ ⎟ ⎠
(22)
Equivalent diameter of based molecule:
To compute the effective thermal conductivity, the empirical correlation has been adopted which takes into account the influence of Brownian motion as shown below: [26]:
keff = kstatic + kBrownian
(19)
⎡ 6M ⎤ 1/3 df = ⎢ Nπρf 0 ⎥ ⎦ ⎣
(18) 4
(23)
International Communications in Heat and Mass Transfer 101 (2019) 1–9
R.K. Ajeel et al.
Fig. 3. The impact of various values of pitch –to-length ratio (p/L) of symmetry trapezoidal- corrugated channel on (A) Nu, (B) Δp, (C) Nuer, and (D) PEC.
water as working liquid, five groups of grid sizes are examined on the symmetry trapezoidal- corrugated channel. At the present investigation, the grid sizes have been involved 162,632, 267,696, 329,668, 413,520 and 544,235 elements, respectively. By comparing the outcomes in terms of Nuav to study the effect of grid size, it is detected that the mesh size of 413,520 elements can achieve and confirm grid independence solution as shown in Table 4. At this grid, the solution can achieve a reasonable compromise between the results accuracy and the computational time.
Table 2 displays the value of β for SiO2 particles employed in the present investigation while thermophysical properties of SiO2-water nanofluid with dp = 20 nm and ϕ=0.08 at T = 300 K illustrated in Table 3. 5. Numerical procedure 5.1. Implementation of numerical solution A numerical simulation out on the tested channel has been applied using nanofluids to examine and deal with complex fluid flow and heat transfer models. CFD commercial software ANSYS-FLUENT-V16.1 with finite volume method is utilized to discretize the governing equations. To deal with pressure-velocity fields and convective terms, the SIMPLE algorithm and 2nd order upwind scheme is adopted, respectively. Furthermore, the diffusion term in the governing equations is approximated by 2nd order upwind while the standard wall function for the k−ε turbulent model was selected. After 100 iterations, the solutions achieved a steady-state condition according to the monitor of velocity and temperature. The solutions converged when they obtained a 10−5 for the residues for momentum, continuity and turbulence equations and when 10−10 was reached for the energy equation.
6. Results and discussions Turbulent forced convection flow of SiO2–water nanofluid in symmetry trapezoidal-corrugated channel has been numerically investigated over Re ranges of 10,000–30,000 and volume fractions of 0–8%. Four values of height-to-width ratio (h/W = 0, 0.03, 0.04 and 0.05) and three values of pitch-to-length ratio (p/L = 0.075, 0.125 and 0.175) have been considered in the present study.
6.1. Result validation First code validation has been done according to the empirical correlations of Gnielinski [27] and Petukov [28], respectively. The results of the current study for straight channel in terms of Nusselt number and friction factor are compared with these empirical correlations as shown in Fig. 2a–b.
5.2. Grid testing The accuracy of the results obtained by the numerical methods depends mainly on the optimum grid test. For this purpose and by using 5
International Communications in Heat and Mass Transfer 101 (2019) 1–9
R.K. Ajeel et al.
(24)
10,000–30,000 while that for p/L = 0.175, the increment of Nuav over the same range of Re is 61.33%. Additionally, there is 15.29% increment in Nuav due to a decrease of the channel ratio (p/L) from 0.175 to 0.075 at Re = 30,000. The reason behind that is the growth in flow disturbance that occur when the pitch –to-length ratio decreases. The symmetry trapezoidal-corrugated channel with lower ratio (p/L) provides the highest values of Nuav over the evaluated Re range. This can be observed from the velocity and isotherm contours shown in Fig. 4. The velocity contours indicate strong recirculation zones around the corrugations. At the upper surface, flow separations and recirculation take place at the edge of the cavity whereas at the bottom surface, most of the flow separation occurs at the roof peaks and rear edges. The effect of this on the temperature contour can be viewed from the isotherm contours. It is observed that larger zones of temperature change are present in channels with smaller pitch corrugations at the above mentioned areas. The influence of corrugation ratio (p/L) on pressure drop (Δp) is shown in Fig. 3b via comparison of the friction factor (f). It can be that f increases with raising Re for each value of p/L ratio. This indicates that the consequent pressure drop will be higher in channels with higher ratio of p/L. This is due to the change in flat length of corrugated channel with the increase in the longitudinal pitch at the same Re in addition to the effect of recirculation zones. Fig. 4 for streamlines indicates that the pressure changes are more apparent in the center area for high ratio of p/L subsequently leading to more pressure loss. Fig. 3c presents the ratio of the Nuav of SiO2 -water nanofluid in the tested channel to the Nuav of pure water in the flat channel with different value of p/L ratio. It is seen that Nu enhancement decreases as Reynolds number increases for all cases of p/L with the smallest ratio p/ L offering highest enhancement ratio. The symmetry trapezoidal- corrugated channel with a small ratio of p/L produces stronger turbulence and greater fluid mixing than that for the large ratio of p/L as observed in Fig. 5. Fig. 3d shows the variation of PEC against Reynolds number with different p/L ratio for the tested channel. The results show that PEC drops equally with increasing Re for all cases. For example, 9.22%, 8.788%, and 8.71% reductions in PEC are seen for p/L = 0.075, p/ L = 0.125, and p/L = 0.175, respectively at Re between 10,000 and 30,000. The PEC is seen to be better at low ratio of p/L with the highest value found to be approximately 2.9 at Re = 10,000. It can be suggested that for this particular corrugation geometry, the lowest ratio of p/L arrangement offers optimum PEC.
(25)
6.3. Effect of corrugation ratio height –to-width (h/W)
Fig. 4. Streamlines (left) and isotherms (right) contours for SiO2-water nonofluids flow in symmetry trapezoidal –corrugated channel with different pitchto-length ratio (p/L).
Nuav =
(f /8)(Re −1000) Pr
(
2
)
1 + 12.7(f /8)0.5 Pr 3 − 1
f = (0.79 ln(Re ) − 1.64)−2
Based on the experimental study of Elshafei et al. [9] for flowing air in straight and corrugated channels at turbulent regime, the second code validation has done. The results of comparison uncovered reasonable agreement in regard to the Nuavas shown in Fig. 2c. The last code validation has been done based on experimental work for air flow in a corrugated channel by Naphon [6] as shown in Fig. 2d. The outcome has been displayed in term Nuav and it was with a good agreement.
The impact of different height –to-width ratio of the tested channel on the flow and thermal fields has been considered at the best value of p/L ratio (0.075), and ϕ=8%. The corrugation height defined as the overall height of the corrugation (h) while (W) is the channel width. In this investigation, the non-dimensional corrugation ratio (h/W) varies from 0.0 to 0.05. Fig. 5a shows the average Nusselt number for different (h/W) ratio. The Nuav increases with Reynolds number for all corrugation ratio of h/ W. Furthermore, at a specific Reynolds number, the Nuav increases as the h/W ratio rises. There is 99.45% increment in Nuav due to a growth of the h/W ratio from 0.0 to 0.05 at Re = 30,000, which is represent the peak value. The symmetry trapezoidal-corrugated channel with higher ratio (h/W = 0.05) provides the highest values of Nuav at all values of Re. This can be attributed to the increased amount of mixing in the flow and can be observed in Fig. 6. The temperature contours in the figure show that a higher degree of temperature changes across the channel from the walls towards the main flow. This is primarily due to flow mixing taking place around the corrugation region in the channel. The pressure drop against Reynolds number with different values of h/W ratio is shown in Fig. 5 (b). Generally, the pressure drop rises with rising Re for all values of height –to-width ratio. Furthermore, the flat
6.2. Effect of corrugation ratio pitch –to-length (p/L) Fig.3a illustrates the variation of average Nusselt number with Reynolds number for the various symmetry trapezoidal-corrugated channel pitch –to-length ratio. The non-dimensional corrugation ratio (p/L) varies from 0.075 to 0.175 while the height to width ratio is constant (h/W = 0.05).The Nuav increases as the Reynolds number increases for all cases considered. In addition, the decrease in p/L ratio results in an increase in Nuav. Over the test section, Nuav increases from 548 to 631 at Re = 30,000. It is also observed that small ratio of p/L result in greater increment of Nuav as Re is increased. For example, the Nuav for case where p/L = 0.075 increase by 64.94% from Re range of 6
International Communications in Heat and Mass Transfer 101 (2019) 1–9
R.K. Ajeel et al.
Fig. 5. The impact of various values of height –to-width ratio (h/W) of symmetry trapezoidal- corrugated channel on (A) Nu, (B) Δp, (C) Nuer, and (D) PEC.
channel (h/W = 0) provides the lowest pressure drop due to the flow in this channel is regular (no secondary flow zones). By comparison, the channel with higher height –to-width ratio produced pressure drop is dramatically higher than that the same channel with lower ratio of h/ W. This could be due to the rise of fluid velocity which leads to boost the shear stress nearby corrugated walls, subsequently leading to growth the Δp as well as increase the intensity of recirculation zones to the major flow. It is noted in the velocity contours that the mainstream flow is less affected by the presence of the corrugation at low h/W ratio. As h/W is increased, recirculation zones are seen to develop in the cavity (top wall). In addition, flow separation is clearly seen at the rear section of the individual corrugation at the bottom wall. The separation line extends towards the next subsequent corrugation in the case of h/ W = 0.05. In short, it can be said that the recirculation zones and fluid mixing in cases h/W = 0.04,0.03 is less than that for the high value of h/W = 0.05, which also explains the thermal characteristics explained earlier. The Nusselt number enhancement ratio for the channel with different height-to-width ratio is presented in Fig. 5c. Clearly from the figure, it can be seen that changing the h/W ratio have a great impact on the Nuer. The Nuer is seen to be greater at lower Re and the effect of Re is slightly more dominant for higher height-to-width ratio. The highest enhancement of Nu is obtained at Re = 10,000 for h/W = 0.05 where Nu is increased by a factor of 3 compared to smooth surfaces with pure water as working liquid. The calculation of PEC also seems to follow this trend with h/W = 0.05 case having highest PEC over the
entire range of Re as shown in Fig. 5d. PEC is also observed to drop gradually as the Re is increased. For instance, 1.82%, 9.11%, 8.66%, and 9.22% reductions in PEC are seen for h/W = 0, 0.03, 0.04, and 0.05, respectively at Reynolds number between 10,000 and 30,000. Therefore, the symmetry trapezoidal-corrugated channel with a high ratio of h/W (0.05) can provide the best PEC with the highest heat transfer enhancement for a given pressure drop enabling a more compact design for a given heat load. 6.4. Correlations of Nusselt number and friction factor The obtained numerical data for flowing SiO2-water nanofluid through symmetry trapezoidal-corrugated channel have been employed to generate new correlations for Nu and f. The new correlations were derived based on the least square method of regression analysis by using SPSS Statistical Software package as shown below:
p −0.168 ⎛ h ⎞0.442 Nu = 0.192Re 0.952Pr −0.481 (1 − φ)−9.149 ⎛ ⎞ ⎝L⎠ ⎝W ⎠
(26)
p −0.071 ⎛ h ⎞0.476 f = 12.182Re−0.175Pr −1.299 (1 − φ)−14.723 ⎛ ⎞ ⎝L⎠ ⎝W ⎠
(27)
The development of new correlations was in good agreement with the numerical data; it was able to predict the Nusselt number and friction factor at the specific limitations with a maximum deviation of ± 10.2%, 12.3% respectively. The above developed correlations are 7
International Communications in Heat and Mass Transfer 101 (2019) 1–9
R.K. Ajeel et al.
seen for h/W = 0.0, 0.03, 0.04, and 0.05, respectively at Reynolds number between 10,000 and 30,000. 5. Over the design parameters investigated, the h/W ratio of 0.05 with a corrugation ratio p/L of 0.075 is the optimum parameters and they have a great influence on the PEC. 6. The new correlations for the Nusselt number and friction factor are developed using nanofluid through the corrugated channel. Finally, it can be proposed the present investigation as a useful reference to design more compact heat exchangers with an optimum thermal efficiency. Nomenclature A area, mm2 c1ε, c2ε, Cμ, σK, σε Model constants 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, μm h corrugated height, mm HTC heat transfer coefficient, (W/m2.K) H height of channel, mm Ι turbulent intensity k turbulent kinetic energy, (m2/s2) ṁ Mass flow rate, kg/s Nu Nusselt number p corrugated pitch, mm Δp Pressure drop(pa) Pr Prandtl number, Pr = cp μ k p/L Pitch-to-length ratio 2 q heat flux, (W/m ) h/W Height-to-width ratio Re Reynolds number, Re = ρ ui Dh μ SiO2 silicon dioxide T temperature, K u,v,w velocity component, (m/s) W width of corrugated channel, mm
Fig. 6. Streamlines (left) and isotherms (right) contours for SiO2-water nonofluids flow in symmetry trapezoidal –corrugated channel with different height –to-width ratio (h/W).
valid for the turbulent flow regime with 10,000 ≤ Re ≤ 30,000 with volume fraction ≤8% through symmetry trapezoidal –corrugated channel.
Greek symbols μ ρ ε τ σk ϕ
7. Conclusion In the current study, turbulent flow of SiO2– water nanofluid in symmetry trapezoidal-corrugated channel has been numerically investigated using the finite volume method. The range of Reynolds number is 10,000–30,000 and nanoparticle volume fraction varying from 0 to 0.08. The influences of Reynolds number, pitch-to-length ratio and the height-to-width ratio of the tested channel on the average Nusselt number, pressure drop, enhancement ratio, and thermal performance factor are presented and discussed. The highlights of the current study are given below:
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 o er nf in av out nf np w
1. The outcomes detect that the average Nusselt number has improved with increasing of Reynolds number and corrugated height –towidth ratio of the tested channel, but the pressure drop will also growth. 2. Also, when the pitch-to-length ratio of the corrugated channel rises, the average Nusselt number declines, and the pressure drop will growth. 3. The ratio of h/W is more effect than p/L ratio in term of thermal performance factor. 4. There are 1.82%, 9.11%, 8.66%, and 9.22% reductions in PEC are
Straight channel Enhancement ratio nanofluid inlet average outlet nanofluid nanoparticles wall
Acknowledgement The authors wish to acknowledge that this paper and the work was funded by the Fundamental Research Grant Scheme (FRGS 1589), 8
International Communications in Heat and Mass Transfer 101 (2019) 1–9
R.K. Ajeel et al.
Universiti Tun Hussein Onn Malaysia.
[15] M. Khoshvaght-Aliabadi, A. Zamzamian, F. Hormozi, Wavy channel and different nanofluids effects on performance of plate-fin heat exchangers, J. Thermophys. Heat Transf. 28 (3) (2014 Mar 21) 474–484. [16] A.K. Santra, S. Sen, N. Chakraborty, Study of heat transfer due to laminar flow of copper–water nanofluid through two isothermally heated parallel plates, Int. J. Therm. Sci. 48 (2) (2009 Feb 1) 391–400. [17] S.M. Fotukian, M.N. Esfahany, Experimental investigation of turbulent convective heat transfer of dilute γ-Al2O3/water nanofluid inside a circular tube, Int. J. Heat Fluid Flow 31 (4) (2010 Aug 1) 606–612. [18] R.K. Ajeel, W.S. Salim, A CFD study on turbulent forced convection flow of Al2O3water nanofluid in semi-circular corrugated channel, InIOP Conference Series: Materials Science and Engineering, Vol. 243(1) IOP Publishing, 2017 Sep, p. 012020. [19] A. Raisi, B. Ghasemi, S.M. Aminossadati, A numerical study on the forced convection of laminar nanofluid in a microchannel with both slip and no-slip conditions, Num. Heat Transf. A 59 (2) (2011 Jan 27) 114–129. [20] H. Heidary, M.J. Kermani, Effect of nano-particles on forced convection in sinusoidal-wall channel, Int. Commun. Heat Mass Transfer. 37 (10) (2010 Dec 1) 1520–1527. [21] O. Manca, S. Nardini, D. Ricci, A numerical study of nanofluid forced convection in ribbed channels, Appl. Therm. Eng. 37 (2012 May 1) 280–292. [22] M.A. Ahmed, N.H. Shuaib, M.Z. Yusoff, A.H. Al-Falahi, Numerical investigations of flow and heat transfer enhancement in a corrugated channel using nanofluid, Int. Commun. Heat Mass Transfer. 38 (10) (2011 Dec 1) 1368–1375. [23] R.K. Ajeel, W. Saiful-Islam, K.B. Hasnan, Thermal and hydraulic characteristics of turbulent nanofluids flow in trapezoidal-corrugated channel: symmetry and zigzag shaped, Case Stud. Therm. Eng. 12 (2018 Sep 1) 620–635. [24] B.E. Launder, D.B. Spalding, Mathematical Models of Turbulence, Academic Press, 1972. [25] H.A. Mohammed, A.M. Abed, M.A. Wahid, The effects of geometrical parameters of a corrugated channel with in out-of-phase arrangement, Int. Commun. Heat Mass Transfer. 40 (2013 Jan 1) 47–57. [26] 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. Heat Mass Transf. 53 (21−22) (2010 Oct 1) 4607–4618. [27] V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, Int. Chem. Eng. 16 (2) (1976) 359–368. [28] B.S. Petukhov, Heat transfer and friction in turbulent pipe flow with variable physical properties, Advances in Heat Transfer, Vol. 6 Elsevier, 1970 Jan 1, pp. 503–564.
References [1] G. Fabbri, Heat transfer optimization in corrugated wall channels, Int. J. Heat Mass Transf. 43 (23) (2000 Dec 1) 4299–4310. [2] M. Vasudevaiah, K. Balamurugan, Heat transfer of rarefied gases in a corrugated microchannel, Int. J. Therm. Sci. 40 (5) (2001 May 1) 454–468. [3] C.C. Wang, C.K. Chen, Forced convection in a wavy-wall channel, Int. J. Heat Mass Transf. 45 (12) (2002 Jun 30) 2587–2595. [4] M. Gradeck, B. Hoareau, M. Lebouche, Local analysis of heat transfer inside corrugated channel, Int. J. Heat Mass Transf. 48 (10) (2005 May 31) 1909–1915. [5] P. Naphon, Laminar convective heat transfer and pressure drop in the corrugated channels, Int. Heat Mass Transfer. 34 (1) (2007 Jan 31) 62–71. [6] P. Naphon, Heat transfer characteristics and pressure drop in channel with V corrugated upper and lower plates, Energy Convers. Manag. 48 (5) (2007 May 31) 1516–1524. [7] P. Naphon, Effect of corrugated plates in an in-phase arrangement on the heat transfer and flow developments, Int. J. Heat Mass Transf. 51 (15) (2008 Jul 15) 3963–3971. [8] P. Naphon, Effect of wavy plate geometry configurations on the temperature and flow distributions, Int. Commun. Heat Mass Transfer. 36 (9) (2009 Nov 30) 942–946. [9] E.A. Elshafei, M.M. Awad, E. El-Negiry, A.G. Ali, Heat transfer and pressure drop in corrugated channels, Energy 35 (1) (2010 Jan 1) 101–110. [10] H.A. Mohammed, P. Gunnasegaran, N.H. Shuaib, Numerical simulation of heat transfer enhancement in wavy microchannel heat sink, Int. Heat Mass Transfer. 38 (1) (2011 Jan 1) 63–68. [11] M. Esmaeili, K. Sadeghy, M. Moghaddami, Heat transfer enhancement of wavy channels using Al2O3 nanoparticles, J. Enhanc. Heat Transf. 17 (2) (2010) 139. [12] S.M. Vanaki, H.A. Mohammed, A. Abdollahi, M.A. Wahid, Effect of nanoparticle shapes on the heat transfer enhancement in a wavy channel with different phase shifts, J. Mol. Liq. 196 (2014 Aug 1) 32–42. [13] S.D. Pandey, V.K. Nema, Experimental analysis of heat transfer and friction factor of nanofluid as a coolant in a corrugated plate heat exchanger, Exp. Thermal Fluid Sci. 38 (2012 Apr 1) 248–256. [14] A. Akbarinia, R. Laur, Investigating the diameter of solid particles effects on a laminar nanofluid flow in a curved tube using a two phase approach, Int. J. Heat Fluid Flow 30 (4) (2009 Aug 1) 706–714.
9
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Influences of geometrical parameters on the heat transfer characteristics through symmetry trapezoidal-corrugated channel using SiO2-water nanofluid
T
⁎
Raheem K. Ajeela,b, , W.S.-I.W. Salima, Khalid Hasnana a b
Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia, 86400, Parit Raja, Batu Pahat, Johor, Malaysia Department of Mechanical Engineering, College of Engineering, University of Babylon, Babylon, Iraq
A R T I C LE I N FO
A B S T R A C T
Keywords: Turbulent flow Symmetry trapezoidal-corrugated channel Height –to-width ratio Pitch-to-length ratio Nanofluids Finite volume method
Enhancing the geometrical parameters design of thermal devices leads to promote the thermal performance and boost design plan of these devices and make it more compact. In the current study, heat transfer and flow characteristics of the symmetry trapezoidal-corrugated channel with silicon dioxide (SiO2) - water as nanofluid was performed numerically over Reynolds number ranges of 10,000–30,000. The influence of geometrical parameters including height-to-width ratio (h/W) and pitch-to-length ratio (p/L) on the thermal and hydraulic characteristics are evaluated. A numerical simulation covers nanofluid with SiO2 volume fractions 8% and carried out by employing the finite volume method (FVM) and SIMPLE algorithm for discretization of the governing equations and coupling of the pressure-velocity system while the k−ε turbulence model was employed to compute the turbulent flow. The outcomes revealed that the (h/W) ratio has a more influence on the promotion of heat transfer compared with the (p/L) ratio. At Reynolds number 30000, there is 16.63% increment in Nuav due to a decrease of the (p/L) ratio from 0.175 to 0.075, while the increment about 99.45% due to an increase of the (h/W) ratio from 0.0 to 0.05. The numerical results indicate that the h/W of 0.05 with a p/L of 0.075 are the optimum parameters and have shown significant improvement in thermal performance factor. Furthermore, new correlations for Nusselt number and friction factor are developed and reported.
1. Introduction Nowadays, the urgent need to achieve high thermal performance and reduce weight and cost, push many industries to look for new ways and procedures to promote heat transfer. In this regard, the corrugated surface has emerged as one way to increase thermal performance and minimize the thermal boundary layer thickness of the heat exchangers surfaces. The main objective of the corrugated surface is to boost the blending of the fluids via form the secondary flow nearby the trough of the corrugated surfaces and then maximize the heat transfer exchange. On the other hand, traditional fluids have poor thermal properties especially thermal conductivity which can be considered a major obstacle to achieving high thermal performance. Therefore, employing nanofluids as a cooling medium in such channels instead of classic liquids can improve the thermophysical properties of the base liquids and thereby a further refinement in thermal efficiency of heat exchangers. Many investigators have focused in their studies on the use of classical
liquids through the corrugated channels numerically and experimentally [1–10]. Esmaeili et al. [11] tested the Al2O3-water nanofluid flow in a sinusoidal wavy channel by employing a finite volume technique. The outcomes indicated that the heat transfer significantly increased due to effect of the nanoparticles. Moreover, Nusselt number increased with increased Reynolds number. Vanaki et al. [12] conducted another numerical investigation in terms of nanoparticle shapes impact on heat transfer and flow fields over a wavy wall channels by implementing SiO2-ethylene glycol nanofluids. They reported that the platelets nanoparticle shape offered the best results in terms of heat transfer enhancement. Pandey and Nema [13] experimentally conducted on the convective heat transfer and flow characteristics in wavy-plate heat exchanger using Al2O3–water nanofluid. It was found that the enhancement in heat transfer increases with increasing in Reynolds number and Peclet number. In addition, the pumping power increases with increasing in volume fraction of nanoparticles. Akbarinia and Laur
⁎ Corresponding author at: Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia, 86400, Parit Raja, Batu Pahat, Johor, Malaysia. E-mail address: [email protected] (R.K. Ajeel).
https://doi.org/10.1016/j.icheatmasstransfer.2018.12.016
0735-1933/ © 2019 Elsevier Ltd. All rights reserved.
International Communications in Heat and Mass Transfer 101 (2019) 1–9
R.K. Ajeel et al.
Fig. 1. Schematic diagram (a) Computation domain, (b) Test section (corrugated wall).
trapezoidal channel; symmetry and zigzag configurations. The outcomes proved that the symmetry profile is superior to the zigzag profile in terms of thermal performance and the silicon dioxide -water nanofluid was the best rate of PEC. Based on the literature discussion, it can be inferred that the influences of design parameters, when a nanofluid is as working liquid and through corrugated channels, has not been totally investigated previously. Also, most of the previous investigations tested a 2-D turbulent convective heat transfer. Additionally, the SiO2-water nanofluid and the symmetry trapezoidal-corrugated channel were not combined previously to study the parameters design in such channels. In fact, this lack of knowledge motivates the present research. Accordingly, the present investigation considers turbulent forced convective flow of SiO2 -water nanofluid in 3-D corrugated channel. The influences of different design parameters with flowing of SiO2-water nanofluid over Re in the range of 10,000 ≤ Re ≤30,000 were discussed. Results of interests including average Nusselt number (Nuav), pressure drop (Δp), Nusselt number enhancement ratio (Nuer), and thermal performance factor (PEC) for turbulent forced convective of nanofluids in a symmetry trapezoidal -corrugated channel are reported to show the effect of corrugated channel and nanofluid on these parameters.
[14] have done a numerical study to investigate the impact of nanoparticle's diameter on flow in a tube having a circular cross-section. The authors claimed that the Nusselt number has affected by the diameter of the nanoparticle where it increased when the diameter of nanoparticles decreases. Khoshvaght-Aliabadi et al. [15] experimentally tested the impact of various kinds of nanofluid on the heat transfer performance in a corrugated channel. The test was done under constant wall temperature condition and covered volume fractions from 0.1 to 0.4%. The results showed that the HTC increased with increasing volume fraction of nanoparticles. Laminar forced convection of copper–water nanofluid in straight channel was numerically studied by Santra et al. [16]. The governing equations were discretized using finite volume approach and solved iteratively using the SIMPLER algorithm. Results indicated that the heat transfer rate increased as Reynolds number and nanoparticles volume friction increase. Fotukian and Nasr Esfahany [17] experimentally conducted on the turbulent forced convection of γ-Al2O3/ Water nanofluid in a circular tube. Their results showed that the addition of small amounts of solid particles to the base fluid enhanced the heat transfer, but accompanied by increasing the pressure drop. Using symmetry form of semicircle corrugated channel and Al2O3- water nanofluid, Ajeel and Salim [18] performed a numerical study on heat transfer performance. The authors claimed that the heat transfer improved by increasing the volume fraction of nanoparticles, but the pressure drop was also increased. Raisi et al. [19] numerically studied the laminar forced convection of copper–water nanofluid flow in a microchannel. Results showed that the coefficient of slip velocity and nanoparticle volume fraction had great influence on the rate of heat transfer at high Reynolds numbers. The laminar forced convection flow of nanofluid in a sinusoidal-wavy channel was numerically studied by Heidary and Kermani [20] using finite volume method. Results displayed that the heat transfer rate increased with amplitude of the wavy channel, nanoparticles volume fraction and Reynolds number. A numerical study on the forced convection of Al2O3 -water nanofluid in ribbed channel has been conducted by Manca et al. [21]. It was found that the heat transfer rate enhanced with the concentration of nanoparticles as well as Reynolds number. But this enhancement in heat transfer was accompanied by increasing the pressure drop penalty. Ahmed et al. [22] investigated numerically of the laminar forced convection flow in triangular-corrugated channel using copper–water nanofluid. It was observed that the average Nusselt number increases with Reynolds number and the volume fraction of nanoparticles. Recently, Ajeel et al. [23] carried out a numerical investigation to test the influences of nanofluids flow through two types of the
2. Problem description and assumptions Fig. 1 illustrated the 2-dimensional geometrical model of the present study (a), and (b) geometry of the symmetry trapezoidal- corrugated channel (test section). Plainly, the geometry of the current study is consists of upper walls and lower walls as well as side walls that are straight and not heated. In another way, the channel is composed of three parts; upstream part, corrugated part, and a downstream part, just the corrugated part was heated. The length of the upstream part is 4times of the downstream part while the total length of the corrugated wall is double length of the downstream wall. The height of the channel (H) is 10 mm while the channel width (W) is (5H). The corrugated height and the longitudinal pitch are (h) and (p), respectively. The geometrical and design parameters are listed in Table 1.Furthermore; several assumptions are made in the current study: i. Regarding the flow, steady-state, turbulent, fully developed, and 3D. ii. Nanofluid in single phase, Newtonian fluid, and incompressible. iii. Regarding the walls material, stainless steel, and the thermal conductivity does not change with temperature. 2
International Communications in Heat and Mass Transfer 101 (2019) 1–9
R.K. Ajeel et al.
Table 1 Design parameters employed in the current study.
μt , m = ρm Cμ = 1.3
Parameter
Terminology
Value
Channel height Test section length Pitch-to-length ratio Height-to-width ratio
H L p/L h/W
10 mm 4W 0.075,0.125,and 0.175 0.0,0.03,0.04, and 0.05
The boundary conditions for the computational domains of the symmetry trapezoidal- corrugated channel have been adopted. There was constant heat flux and no-slip condition at the corrugated walls, whereas thermally insulated conditions utilized for the flat walls. Furthermore, the velocity inlet condition and temperature of 300 K is adapted at the inlet, whereas the pressure outlet condition is employed at outlet. Eventually, the boundary conditions for the complex flow through a symmetry trapezoidal -corrugated channel can be stated as follows: At the inlet:
Table 2 Values of β for SiO2 nanoparticles. Nanoparticles type
β -
1.9526(100ϕ)
SiO2
Concentration (%)
Temperature (K)
1% ≤ φ ≤ 10%
298 K ≤ T ≤ 363 K
1.4594
u = uin, v = w = 0, Tin = 300 k
kin =
Table 3 Thermo-physical properties of nanofluids with dp = 20 nm and ϕ=0.08. Thermo-physical properties Density ρ (kg/m3) Dynamic viscosity, μ(Ns/m2) Thermal conductivity, k(w/m.K) Specific heat, cp (J/kg.K)
∂Tƒ
SiO2
∂x 1094.344 0.004795 0.643072 3622.483
= 0,
∂u ∂v ∂w ∂k ∂ε = = = 0, and = =0 ∂x ∂x ∂x ∂x ∂x
At the wall:
u = v = w = 0, q = qwall In order to expound the outcomes and characteristics of flow and heat transfer in the tested channel, some of the variables should be computed and presented: Average Nusselt number can be defined as follows:
Grid number
Average Nusselt number
Relative error%
162,632 267,696 329,668 413,520 544,235
126.1311 126.1546 126.1789 126.1896 126.1971
– 0.018628 0.019258 0.008479 0.005943
ln = q″.
uin =
(1)
(2)
Dh =
Energy equation:
(7) (8)
R eμ ρDh
(9)
4A cross P
(10)
From definition of Fanning friction factor as: (3)
Cfx =
The present study used the k − ε turbulence model suggested by Launder and Spalding [24]. The influence of mean velocity gradients has been taking into consideration in this model which produces turbulent kinetic energy and can designate G as shown below:
2τs 2 ρ uin
(11)
And friction factor is defined [22,25] as follows:
ƒ = 4Cfx
(12)
Based on the friction factor, the pressure drop can also be obtained as follows: [22,25]:
⎟
(4)
∆p = f
μt , m
ε ∇ . (ρm Vε ) = ∇ . ⎛ ∇ε ⎞ + (C1 Gm − C2 ρm ε ) σ k ⎝ ε ⎠
)
(Tw − Tm,in) − (Tw − Tm,out )
In this investigation, the hydraulic diameter of corrugated part is calculated depending on cross section area (Across) and the perimeter of wetted (P) as [22,25]:
Momentum equation:
μt , m ∇ . (ρm Vk ) = ∇ . ⎛ ∇k ⎞ + Gm − ρm ε ⎝ σk ⎠
Tw − Tm,in Tw − Tm,out
where A is the surface area of corrugated part while Tm,in, Tm,out are the average temperatures of the working media at inlet and outlet. Additionally, can obtain the inlet velocity depending on the Reynolds number as below:
The governing equations of the flow problem are solved for threedimensional flow as follows: Continuity equations:
∇ . (ρf VCp, f T ) = ∇ . (kf ∇T − Cp, f ρf vt)
(
q″ = ṁ Cp (Tm, in − Tm, out )/ A
3. Governing equations and boundary conditions
∇ . (ρf VV ) = −∇p + ∇ . τ
(6)
And, average heat transfer coefficient as:
iv. Both the base fluid and nanoparticles of SiO2 is homogenous and in the thermal equilibrium state.
∇ . (ρf V ) = 0
hDh kƒ
Nuav =
hav
⎜
3 K 3/2 (Iuin )2, εin = Cμ3/4 2 Lt .
Outlet boundary:
Table 4 Grid independence test.
⎜
K2 , C1 = 1.44, C2 = 1.92, Cμ = 0.09 = 0.09, σk = 1.0, σε ε
⎟
(5)
2 ρLcorr uin 2Dh
(13)
Lastly, in order to assess the system of the current study compared to the reference system which is a smooth channel, the thermal
where: 3
International Communications in Heat and Mass Transfer 101 (2019) 1–9
R.K. Ajeel et al.
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. [9], (d) Naphon [6].
performance factor was adopted. The thermal performance factor (PEC) is specified by [21] as follow:
PEC =
(
Nuav
Nuav, o
( ) f
f0
(knp + 2kf ) − 2ϕ (kf − knp ) ⎤ kstatic = kf ⎡ ⎢ (knp + 2kf ) + ϕ (kf − knp ) ⎥ ⎦ ⎣
)
1/3
kBrownian = 5 ∗ 10 4β ϕρf Cp, f
(14)
KT f (T , ϕ) 2
(20)
where: Boltzmann constant: k = 1.3807*10–23 J/K. Modeling, f(T, ϕ)
4. Calculations of nanofluid properties In current study, the thermophysical properties of SiO2–water nanofluid are given as follows:
T f (T , ϕ) = (2.8217 × 10−2ϕ + 3.917 × 10−3) ⎛ ⎞ ⎝ T0 ⎠ + (−3.0669 × 10−2ϕ − 3.391123 × 10−3) ⎜
i. Density and heat capacity: The nanofluid density and it heat capacity can be calculated as follow: [21]:
ρnf = (1 − ϕ) + ϕρnp
(15)
(ρCP )nf = (1 − ϕ)(ρCP )f + ϕ (ρCP )np
(16)
⎟
(21)
iii. Dynamic viscosity: Lastly, the effective dynamic viscosity of nanofluid is given as: [26]:
μeff = μf ii. Thermal conductivity:
⎛ 1 ∗ ϕ−1.03 ∗ ⎜ dp ⎜ ⎜ 1 − 34.87 d f ⎝
−0.3
()
⎞ ⎟ ⎟ ⎟ ⎠
(22)
Equivalent diameter of based molecule:
To compute the effective thermal conductivity, the empirical correlation has been adopted which takes into account the influence of Brownian motion as shown below: [26]:
keff = kstatic + kBrownian
(19)
⎡ 6M ⎤ 1/3 df = ⎢ Nπρf 0 ⎥ ⎦ ⎣
(18) 4
(23)
International Communications in Heat and Mass Transfer 101 (2019) 1–9
R.K. Ajeel et al.
Fig. 3. The impact of various values of pitch –to-length ratio (p/L) of symmetry trapezoidal- corrugated channel on (A) Nu, (B) Δp, (C) Nuer, and (D) PEC.
water as working liquid, five groups of grid sizes are examined on the symmetry trapezoidal- corrugated channel. At the present investigation, the grid sizes have been involved 162,632, 267,696, 329,668, 413,520 and 544,235 elements, respectively. By comparing the outcomes in terms of Nuav to study the effect of grid size, it is detected that the mesh size of 413,520 elements can achieve and confirm grid independence solution as shown in Table 4. At this grid, the solution can achieve a reasonable compromise between the results accuracy and the computational time.
Table 2 displays the value of β for SiO2 particles employed in the present investigation while thermophysical properties of SiO2-water nanofluid with dp = 20 nm and ϕ=0.08 at T = 300 K illustrated in Table 3. 5. Numerical procedure 5.1. Implementation of numerical solution A numerical simulation out on the tested channel has been applied using nanofluids to examine and deal with complex fluid flow and heat transfer models. CFD commercial software ANSYS-FLUENT-V16.1 with finite volume method is utilized to discretize the governing equations. To deal with pressure-velocity fields and convective terms, the SIMPLE algorithm and 2nd order upwind scheme is adopted, respectively. Furthermore, the diffusion term in the governing equations is approximated by 2nd order upwind while the standard wall function for the k−ε turbulent model was selected. After 100 iterations, the solutions achieved a steady-state condition according to the monitor of velocity and temperature. The solutions converged when they obtained a 10−5 for the residues for momentum, continuity and turbulence equations and when 10−10 was reached for the energy equation.
6. Results and discussions Turbulent forced convection flow of SiO2–water nanofluid in symmetry trapezoidal-corrugated channel has been numerically investigated over Re ranges of 10,000–30,000 and volume fractions of 0–8%. Four values of height-to-width ratio (h/W = 0, 0.03, 0.04 and 0.05) and three values of pitch-to-length ratio (p/L = 0.075, 0.125 and 0.175) have been considered in the present study.
6.1. Result validation First code validation has been done according to the empirical correlations of Gnielinski [27] and Petukov [28], respectively. The results of the current study for straight channel in terms of Nusselt number and friction factor are compared with these empirical correlations as shown in Fig. 2a–b.
5.2. Grid testing The accuracy of the results obtained by the numerical methods depends mainly on the optimum grid test. For this purpose and by using 5
International Communications in Heat and Mass Transfer 101 (2019) 1–9
R.K. Ajeel et al.
(24)
10,000–30,000 while that for p/L = 0.175, the increment of Nuav over the same range of Re is 61.33%. Additionally, there is 15.29% increment in Nuav due to a decrease of the channel ratio (p/L) from 0.175 to 0.075 at Re = 30,000. The reason behind that is the growth in flow disturbance that occur when the pitch –to-length ratio decreases. The symmetry trapezoidal-corrugated channel with lower ratio (p/L) provides the highest values of Nuav over the evaluated Re range. This can be observed from the velocity and isotherm contours shown in Fig. 4. The velocity contours indicate strong recirculation zones around the corrugations. At the upper surface, flow separations and recirculation take place at the edge of the cavity whereas at the bottom surface, most of the flow separation occurs at the roof peaks and rear edges. The effect of this on the temperature contour can be viewed from the isotherm contours. It is observed that larger zones of temperature change are present in channels with smaller pitch corrugations at the above mentioned areas. The influence of corrugation ratio (p/L) on pressure drop (Δp) is shown in Fig. 3b via comparison of the friction factor (f). It can be that f increases with raising Re for each value of p/L ratio. This indicates that the consequent pressure drop will be higher in channels with higher ratio of p/L. This is due to the change in flat length of corrugated channel with the increase in the longitudinal pitch at the same Re in addition to the effect of recirculation zones. Fig. 4 for streamlines indicates that the pressure changes are more apparent in the center area for high ratio of p/L subsequently leading to more pressure loss. Fig. 3c presents the ratio of the Nuav of SiO2 -water nanofluid in the tested channel to the Nuav of pure water in the flat channel with different value of p/L ratio. It is seen that Nu enhancement decreases as Reynolds number increases for all cases of p/L with the smallest ratio p/ L offering highest enhancement ratio. The symmetry trapezoidal- corrugated channel with a small ratio of p/L produces stronger turbulence and greater fluid mixing than that for the large ratio of p/L as observed in Fig. 5. Fig. 3d shows the variation of PEC against Reynolds number with different p/L ratio for the tested channel. The results show that PEC drops equally with increasing Re for all cases. For example, 9.22%, 8.788%, and 8.71% reductions in PEC are seen for p/L = 0.075, p/ L = 0.125, and p/L = 0.175, respectively at Re between 10,000 and 30,000. The PEC is seen to be better at low ratio of p/L with the highest value found to be approximately 2.9 at Re = 10,000. It can be suggested that for this particular corrugation geometry, the lowest ratio of p/L arrangement offers optimum PEC.
(25)
6.3. Effect of corrugation ratio height –to-width (h/W)
Fig. 4. Streamlines (left) and isotherms (right) contours for SiO2-water nonofluids flow in symmetry trapezoidal –corrugated channel with different pitchto-length ratio (p/L).
Nuav =
(f /8)(Re −1000) Pr
(
2
)
1 + 12.7(f /8)0.5 Pr 3 − 1
f = (0.79 ln(Re ) − 1.64)−2
Based on the experimental study of Elshafei et al. [9] for flowing air in straight and corrugated channels at turbulent regime, the second code validation has done. The results of comparison uncovered reasonable agreement in regard to the Nuavas shown in Fig. 2c. The last code validation has been done based on experimental work for air flow in a corrugated channel by Naphon [6] as shown in Fig. 2d. The outcome has been displayed in term Nuav and it was with a good agreement.
The impact of different height –to-width ratio of the tested channel on the flow and thermal fields has been considered at the best value of p/L ratio (0.075), and ϕ=8%. The corrugation height defined as the overall height of the corrugation (h) while (W) is the channel width. In this investigation, the non-dimensional corrugation ratio (h/W) varies from 0.0 to 0.05. Fig. 5a shows the average Nusselt number for different (h/W) ratio. The Nuav increases with Reynolds number for all corrugation ratio of h/ W. Furthermore, at a specific Reynolds number, the Nuav increases as the h/W ratio rises. There is 99.45% increment in Nuav due to a growth of the h/W ratio from 0.0 to 0.05 at Re = 30,000, which is represent the peak value. The symmetry trapezoidal-corrugated channel with higher ratio (h/W = 0.05) provides the highest values of Nuav at all values of Re. This can be attributed to the increased amount of mixing in the flow and can be observed in Fig. 6. The temperature contours in the figure show that a higher degree of temperature changes across the channel from the walls towards the main flow. This is primarily due to flow mixing taking place around the corrugation region in the channel. The pressure drop against Reynolds number with different values of h/W ratio is shown in Fig. 5 (b). Generally, the pressure drop rises with rising Re for all values of height –to-width ratio. Furthermore, the flat
6.2. Effect of corrugation ratio pitch –to-length (p/L) Fig.3a illustrates the variation of average Nusselt number with Reynolds number for the various symmetry trapezoidal-corrugated channel pitch –to-length ratio. The non-dimensional corrugation ratio (p/L) varies from 0.075 to 0.175 while the height to width ratio is constant (h/W = 0.05).The Nuav increases as the Reynolds number increases for all cases considered. In addition, the decrease in p/L ratio results in an increase in Nuav. Over the test section, Nuav increases from 548 to 631 at Re = 30,000. It is also observed that small ratio of p/L result in greater increment of Nuav as Re is increased. For example, the Nuav for case where p/L = 0.075 increase by 64.94% from Re range of 6
International Communications in Heat and Mass Transfer 101 (2019) 1–9
R.K. Ajeel et al.
Fig. 5. The impact of various values of height –to-width ratio (h/W) of symmetry trapezoidal- corrugated channel on (A) Nu, (B) Δp, (C) Nuer, and (D) PEC.
channel (h/W = 0) provides the lowest pressure drop due to the flow in this channel is regular (no secondary flow zones). By comparison, the channel with higher height –to-width ratio produced pressure drop is dramatically higher than that the same channel with lower ratio of h/ W. This could be due to the rise of fluid velocity which leads to boost the shear stress nearby corrugated walls, subsequently leading to growth the Δp as well as increase the intensity of recirculation zones to the major flow. It is noted in the velocity contours that the mainstream flow is less affected by the presence of the corrugation at low h/W ratio. As h/W is increased, recirculation zones are seen to develop in the cavity (top wall). In addition, flow separation is clearly seen at the rear section of the individual corrugation at the bottom wall. The separation line extends towards the next subsequent corrugation in the case of h/ W = 0.05. In short, it can be said that the recirculation zones and fluid mixing in cases h/W = 0.04,0.03 is less than that for the high value of h/W = 0.05, which also explains the thermal characteristics explained earlier. The Nusselt number enhancement ratio for the channel with different height-to-width ratio is presented in Fig. 5c. Clearly from the figure, it can be seen that changing the h/W ratio have a great impact on the Nuer. The Nuer is seen to be greater at lower Re and the effect of Re is slightly more dominant for higher height-to-width ratio. The highest enhancement of Nu is obtained at Re = 10,000 for h/W = 0.05 where Nu is increased by a factor of 3 compared to smooth surfaces with pure water as working liquid. The calculation of PEC also seems to follow this trend with h/W = 0.05 case having highest PEC over the
entire range of Re as shown in Fig. 5d. PEC is also observed to drop gradually as the Re is increased. For instance, 1.82%, 9.11%, 8.66%, and 9.22% reductions in PEC are seen for h/W = 0, 0.03, 0.04, and 0.05, respectively at Reynolds number between 10,000 and 30,000. Therefore, the symmetry trapezoidal-corrugated channel with a high ratio of h/W (0.05) can provide the best PEC with the highest heat transfer enhancement for a given pressure drop enabling a more compact design for a given heat load. 6.4. Correlations of Nusselt number and friction factor The obtained numerical data for flowing SiO2-water nanofluid through symmetry trapezoidal-corrugated channel have been employed to generate new correlations for Nu and f. The new correlations were derived based on the least square method of regression analysis by using SPSS Statistical Software package as shown below:
p −0.168 ⎛ h ⎞0.442 Nu = 0.192Re 0.952Pr −0.481 (1 − φ)−9.149 ⎛ ⎞ ⎝L⎠ ⎝W ⎠
(26)
p −0.071 ⎛ h ⎞0.476 f = 12.182Re−0.175Pr −1.299 (1 − φ)−14.723 ⎛ ⎞ ⎝L⎠ ⎝W ⎠
(27)
The development of new correlations was in good agreement with the numerical data; it was able to predict the Nusselt number and friction factor at the specific limitations with a maximum deviation of ± 10.2%, 12.3% respectively. The above developed correlations are 7
International Communications in Heat and Mass Transfer 101 (2019) 1–9
R.K. Ajeel et al.
seen for h/W = 0.0, 0.03, 0.04, and 0.05, respectively at Reynolds number between 10,000 and 30,000. 5. Over the design parameters investigated, the h/W ratio of 0.05 with a corrugation ratio p/L of 0.075 is the optimum parameters and they have a great influence on the PEC. 6. The new correlations for the Nusselt number and friction factor are developed using nanofluid through the corrugated channel. Finally, it can be proposed the present investigation as a useful reference to design more compact heat exchangers with an optimum thermal efficiency. Nomenclature A area, mm2 c1ε, c2ε, Cμ, σK, σε Model constants 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, μm h corrugated height, mm HTC heat transfer coefficient, (W/m2.K) H height of channel, mm Ι turbulent intensity k turbulent kinetic energy, (m2/s2) ṁ Mass flow rate, kg/s Nu Nusselt number p corrugated pitch, mm Δp Pressure drop(pa) Pr Prandtl number, Pr = cp μ k p/L Pitch-to-length ratio 2 q heat flux, (W/m ) h/W Height-to-width ratio Re Reynolds number, Re = ρ ui Dh μ SiO2 silicon dioxide T temperature, K u,v,w velocity component, (m/s) W width of corrugated channel, mm
Fig. 6. Streamlines (left) and isotherms (right) contours for SiO2-water nonofluids flow in symmetry trapezoidal –corrugated channel with different height –to-width ratio (h/W).
valid for the turbulent flow regime with 10,000 ≤ Re ≤ 30,000 with volume fraction ≤8% through symmetry trapezoidal –corrugated channel.
Greek symbols μ ρ ε τ σk ϕ
7. Conclusion In the current study, turbulent flow of SiO2– water nanofluid in symmetry trapezoidal-corrugated channel has been numerically investigated using the finite volume method. The range of Reynolds number is 10,000–30,000 and nanoparticle volume fraction varying from 0 to 0.08. The influences of Reynolds number, pitch-to-length ratio and the height-to-width ratio of the tested channel on the average Nusselt number, pressure drop, enhancement ratio, and thermal performance factor are presented and discussed. The highlights of the current study are given below:
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 o er nf in av out nf np w
1. The outcomes detect that the average Nusselt number has improved with increasing of Reynolds number and corrugated height –towidth ratio of the tested channel, but the pressure drop will also growth. 2. Also, when the pitch-to-length ratio of the corrugated channel rises, the average Nusselt number declines, and the pressure drop will growth. 3. The ratio of h/W is more effect than p/L ratio in term of thermal performance factor. 4. There are 1.82%, 9.11%, 8.66%, and 9.22% reductions in PEC are
Straight channel Enhancement ratio nanofluid inlet average outlet nanofluid nanoparticles wall
Acknowledgement The authors wish to acknowledge that this paper and the work was funded by the Fundamental Research Grant Scheme (FRGS 1589), 8
International Communications in Heat and Mass Transfer 101 (2019) 1–9
R.K. Ajeel et al.
Universiti Tun Hussein Onn Malaysia.
[15] M. Khoshvaght-Aliabadi, A. Zamzamian, F. Hormozi, Wavy channel and different nanofluids effects on performance of plate-fin heat exchangers, J. Thermophys. Heat Transf. 28 (3) (2014 Mar 21) 474–484. [16] A.K. Santra, S. Sen, N. Chakraborty, Study of heat transfer due to laminar flow of copper–water nanofluid through two isothermally heated parallel plates, Int. J. Therm. Sci. 48 (2) (2009 Feb 1) 391–400. [17] S.M. Fotukian, M.N. Esfahany, Experimental investigation of turbulent convective heat transfer of dilute γ-Al2O3/water nanofluid inside a circular tube, Int. J. Heat Fluid Flow 31 (4) (2010 Aug 1) 606–612. [18] R.K. Ajeel, W.S. Salim, A CFD study on turbulent forced convection flow of Al2O3water nanofluid in semi-circular corrugated channel, InIOP Conference Series: Materials Science and Engineering, Vol. 243(1) IOP Publishing, 2017 Sep, p. 012020. [19] A. Raisi, B. Ghasemi, S.M. Aminossadati, A numerical study on the forced convection of laminar nanofluid in a microchannel with both slip and no-slip conditions, Num. Heat Transf. A 59 (2) (2011 Jan 27) 114–129. [20] H. Heidary, M.J. Kermani, Effect of nano-particles on forced convection in sinusoidal-wall channel, Int. Commun. Heat Mass Transfer. 37 (10) (2010 Dec 1) 1520–1527. [21] O. Manca, S. Nardini, D. Ricci, A numerical study of nanofluid forced convection in ribbed channels, Appl. Therm. Eng. 37 (2012 May 1) 280–292. [22] M.A. Ahmed, N.H. Shuaib, M.Z. Yusoff, A.H. Al-Falahi, Numerical investigations of flow and heat transfer enhancement in a corrugated channel using nanofluid, Int. Commun. Heat Mass Transfer. 38 (10) (2011 Dec 1) 1368–1375. [23] R.K. Ajeel, W. Saiful-Islam, K.B. Hasnan, Thermal and hydraulic characteristics of turbulent nanofluids flow in trapezoidal-corrugated channel: symmetry and zigzag shaped, Case Stud. Therm. Eng. 12 (2018 Sep 1) 620–635. [24] B.E. Launder, D.B. Spalding, Mathematical Models of Turbulence, Academic Press, 1972. [25] H.A. Mohammed, A.M. Abed, M.A. Wahid, The effects of geometrical parameters of a corrugated channel with in out-of-phase arrangement, Int. Commun. Heat Mass Transfer. 40 (2013 Jan 1) 47–57. [26] 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. Heat Mass Transf. 53 (21−22) (2010 Oct 1) 4607–4618. [27] V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, Int. Chem. Eng. 16 (2) (1976) 359–368. [28] B.S. Petukhov, Heat transfer and friction in turbulent pipe flow with variable physical properties, Advances in Heat Transfer, Vol. 6 Elsevier, 1970 Jan 1, pp. 503–564.
References [1] G. Fabbri, Heat transfer optimization in corrugated wall channels, Int. J. Heat Mass Transf. 43 (23) (2000 Dec 1) 4299–4310. [2] M. Vasudevaiah, K. Balamurugan, Heat transfer of rarefied gases in a corrugated microchannel, Int. J. Therm. Sci. 40 (5) (2001 May 1) 454–468. [3] C.C. Wang, C.K. Chen, Forced convection in a wavy-wall channel, Int. J. Heat Mass Transf. 45 (12) (2002 Jun 30) 2587–2595. [4] M. Gradeck, B. Hoareau, M. Lebouche, Local analysis of heat transfer inside corrugated channel, Int. J. Heat Mass Transf. 48 (10) (2005 May 31) 1909–1915. [5] P. Naphon, Laminar convective heat transfer and pressure drop in the corrugated channels, Int. Heat Mass Transfer. 34 (1) (2007 Jan 31) 62–71. [6] P. Naphon, Heat transfer characteristics and pressure drop in channel with V corrugated upper and lower plates, Energy Convers. Manag. 48 (5) (2007 May 31) 1516–1524. [7] P. Naphon, Effect of corrugated plates in an in-phase arrangement on the heat transfer and flow developments, Int. J. Heat Mass Transf. 51 (15) (2008 Jul 15) 3963–3971. [8] P. Naphon, Effect of wavy plate geometry configurations on the temperature and flow distributions, Int. Commun. Heat Mass Transfer. 36 (9) (2009 Nov 30) 942–946. [9] E.A. Elshafei, M.M. Awad, E. El-Negiry, A.G. Ali, Heat transfer and pressure drop in corrugated channels, Energy 35 (1) (2010 Jan 1) 101–110. [10] H.A. Mohammed, P. Gunnasegaran, N.H. Shuaib, Numerical simulation of heat transfer enhancement in wavy microchannel heat sink, Int. Heat Mass Transfer. 38 (1) (2011 Jan 1) 63–68. [11] M. Esmaeili, K. Sadeghy, M. Moghaddami, Heat transfer enhancement of wavy channels using Al2O3 nanoparticles, J. Enhanc. Heat Transf. 17 (2) (2010) 139. [12] S.M. Vanaki, H.A. Mohammed, A. Abdollahi, M.A. Wahid, Effect of nanoparticle shapes on the heat transfer enhancement in a wavy channel with different phase shifts, J. Mol. Liq. 196 (2014 Aug 1) 32–42. [13] S.D. Pandey, V.K. Nema, Experimental analysis of heat transfer and friction factor of nanofluid as a coolant in a corrugated plate heat exchanger, Exp. Thermal Fluid Sci. 38 (2012 Apr 1) 248–256. [14] A. Akbarinia, R. Laur, Investigating the diameter of solid particles effects on a laminar nanofluid flow in a curved tube using a two phase approach, Int. J. Heat Fluid Flow 30 (4) (2009 Aug 1) 706–714.
9