- Email: [email protected]
Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models
ICHMT-03246; No of Pages 8 International Communications in Heat and Mass Transfer xxx (2015) xxx–xxx
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Q13Q3
F
2
Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models☆ Z. Yari Ghale, M. Haghshenasfard, M. Nasr Esfahany Department of Chemical Engineering, Isfahan University of Technology, Isfahan 8415683111, Iran
6
a r t i c l e
7 8
Available online xxxx
9 10 11 12
Keywords: Nanofluid Heat transfer Ribbed microchannel heat sink
i n f o
R O
4 5
a b s t r a c t
D
P
In this paper, laminar forced convective heat transfer of water/alumina nanofluids in a straight microchannel is studied numerically using CFD modeling. In the first part, single-phase and two-phase mixture models have been used for prediction of hydrodynamics and heat transfer parameters of nanofluids in a simple microchannel heat sink. The CFD predictions were compared to the experimental data and it was concluded that the two-phase approach gives better predictions compared to the single-phase model. The effects of ribs turbulators on the fluid flow and heat transfer performance of microchannel were investigated in the second part. The effects of geometrical characteristics of the ribs were studied, and the results showed that the Nusselt number and friction coefficient of nanofluids in the ribbed microchannel are higher than those of simple microchannel, and this enhancement increased with increasing the width of the ribs. © 2015 Elsevier Ltd. All rights reserved.
36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
C
E
R
R
34 35
Recent development in nanotechnology for improving cooling technology in the electronic devices have made possible production of efficient and compact cooling modules to provide reliable system operation [1]. Because of fast growth in miniaturization of electronics devices and large amount of the heat generated in these devices, a single-layered microchannel heat sink (MCHS) that was first introduced by Tuckerman and Pease [2] in 1981 has become inadequate. Thus, improving the system of MCHS is necessary. An MCHS contains a coolant flowing through the channels and carrying away the heat generated by electronic devices. Therefore, improving thermal behavior of coolant is an effective way to enhance the thermal performance of MCHSs. Nanofluid is a new class of fluids that first has been used by Choi et al. [3]. A nanofluid is a fluid containing nanosized particles suspended into a base fluid such as water, ethylene glycol, and engine oil. Metal oxide or metal nanoparticles have a much higher thermal conductivity than fluids, therefore suspending these particles can enhance the thermal conductivity of the base fluids and use of nanofluids does enhance the heat transfer performance of an MCHS. In recent years, many numerical and experimental studies have been made in the field of thermal behavior of nanofluids [4–13]. Two-phase and single-phase (homogeneous) approaches can be used for CFD analysis of heat transfer in nanofluids [14]. Most of the numerical studies have been carried out using the single-phase approach. In the homogeneous modeling, the base fluid and nanoparticles are assumed to be in thermal equilibrium. In the two-phase approach, the Eeulerian or
N C O
32 33
1. Introduction
U
30 31
T
26 24 23
28 29
13 14 15 16 17 18 19 20 21
E
22 25 27
O
1
☆ Communicated by W.J. Minkowycz. E-mail address: [email protected] (M. Haghshenasfard).
Lagrangian frameworks can be implemented for the base fluid and nanoparticles as two different liquid and solid phases [15]. Behzadmehr et al. [16] numerically investigated turbulent forced convection heat transfer of a Cu/water nanofluid in a circular tube using the two-phase mixture model. The results of two-phase model were compared to the single-phase predictions and experimental data, and they found that the mixture model is more accurate than the single- phase model. Haghshenasfard et al. [17] studied both single-phase and two-phase CFD models for prediction of heat transfer coefficient of Cu/water nanofluids in a tube with constant wall temperature. The effects of nanoparticle type, nanoparticle concentration, and nanofluid Peclet number on pressure drop, temperature profile, and heat transfer rate were studied. Their results showed that the heat transfer coefficient increases by increasing the nanoparticle concentration and Peclet number, and the two-phase model showed better agreement with the experimental measurements. Manay et al. [18] numerically studied the heat transfer and hydraulic characteristics of aqueous CuO/water and Al2O3/water nanofluids inside a microchannel with square duct using the mixture model. The predictions showed that the nanofluids enhance the heat transfer rate while the concentration and Reynolds number of nanofluids are increasing. Kalteh et al. [19] studied numerically laminar forced convection heat transfer of a Cu/water nanofluid in a microchannel with constant wall temperature. The Eulerian–Eulerian model has been used to calculate heat transfer and pressure drop parameters. They found that increasing in Reynolds number and nanofluid volume fraction increase the heat transfer rate. They also reported that heat transfer coefficients predicted by the two-phase model are higher than single-phase predictions.
http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.012 0735-1933/© 2015 Elsevier Ltd. All rights reserved.
Please cite this article as: Z.Y. Ghale, et al., Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models, Int. Commun. Heat Mass Transf. (2015), http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.012
53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82
94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114
116 117
Laminar forced convection of water and Al2O3/water nanofluids with volume fraction of 1 and 2 vol% in a rectangular microchannel with uniform heat flux was numerically investigated. The microchannel was designed with length, width, and height of 44.8 mm, 0.215 mm, and 0.821 mm, respectively. The dimensions are listed in Table 1. The heat flux for unit cell was 228586 W/m2, and the heat flux for a channel can be calculated using the following relation [24]:
E
R
R
O
q″eff W cell W ch þ 2H ch
C
125
q″p ¼
t1:4
The physical properties, density, viscosity, thermal conductivity, and specific heat capacity of Al2O3/water nanofluids were calculated using 126 Eqs. (2)–(5) [4] and are presented in Table 2: 127 ρn f ¼ ð1−φÞρb f þ φρP
ð1Þ
ð2Þ
where φ is volumetric concentration of nanoparticles; μnf ¼ 123ϕ2 þ 7:3ϕ þ 1 μbf kn f
kP þ ðn−1Þkb f −ðn−1Þφðkb f −kP Þ kb f ¼ kp þ ðn−1Þkb f þ φðkb f −kP Þ
129
ð3Þ
130 131
ð4Þ
where knf, kbf, and kP are the thermal conductivities of the nanofluid, 133 base fluid, and solid particles, respectively, and n is solid particle shape factor (n = 3 for spherical particles); 134 C p;n f ¼ ð1−φÞC P;b f þ φC p;P
ð5Þ 136
The friction factor and the local heat transfer coefficients of nanofluids were calculated using following relations [4,25]: 137 f ¼
ΔP ch Dh 2Lρ f u2
q″ ½T w ðxÞ−T m ðxÞ
ð6Þ
140
where q″, Tw and Tm are heat flux, local temperature of bottom wall and balk temperature of fluid. In order to evaluate the performance of microchannel with ribs, the thermal enhancement factor were measured using the following equation [25]: Nu
η¼
142 143 144 145
Nu0
f
139
ð7Þ
1 =3
ð8Þ
f0
where Nu and f are the parameters of microchannel without rib, and 0 147 index refers to the ribbed channel.
N
123
t1:3
5.637 mm
U
121 122
C
1.1. Model formulation and numerical procedure
120
Hw2 (mm)
0.821
hðxÞ ¼
115
118 119
Hch (mm)
12.700
F
92 93
Hw1 (mm)
0.215
O
90 91
Wch (mm)
0.125
R O
89
Ww (mm)
P
87 88
t1:1 t1:2
Table 1 Dimensions of unit cell microchannel.
D
85 86
O. Manca et al. [20] proposed a single-phase model to study the nanofluids heat transfer in a 2-D ribbed channel. The results showed that heat transfer enhancement increases with the nanofluid concentration, but it is accompanied by enhancing the pumping power. The effects of the ribs on the heat transfer performance have been studied under different pitches and Reynolds numbers. They found that the rectangular turbulators with rib width/rib height = 0.5 shows the highest thermal performances and highest losses. The single-phase model also has been used by Maiga et al. [21], Akbarnia and Behzadmehr [22], and Nambura et al. [23], for the investigation of convective heat transfer of various nanofluids inside the circular tubes. According to their results, the single-phase model gives the reasonable data for dilute nanofluids. The aim of present study is to compare the single-phase and the two-phase approaches for modeling laminar forced convective heat transfer of alumina/water nanofluids in a rectangular microchannel with uniformly heated walls. In addition, the modeling was extended to consider the effects of ribbed microchannel on the heat transfer performance. The results of this modeling have some benefits for prediction of operating conditions, which maximize the heat transfer rate and minimize the pressure drop through an MCHS. The CFD results have been compared to experimental data reported by Lee and Mudawar [4]. Lee and Mudawar [4] were performed some experiments to investigate the heat transfer of nanofluids in a microchannel. The experimental apparatus consists of a reservoir tank equipped with heater, constant temperature bath, and microchannel test module. The nanoparticles used in their work were Al2O3 and two volumetric concentrations of water/Al2O3 nanofluid, 1% and 2%, had been used in the test facility. The microchannel test module and the ribbed channel are shown in Fig. 1. The test facility include rectangular 215 mm wide by 821 mm deep grooves milled into the copper block. Heat is supplied to the test section by 12 cartridge heaters.
T
83 84
Z.Y. Ghale et al. / International Communications in Heat and Mass Transfer xxx (2015) xxx–xxx
E
2
Fig. 1. Schematic and computational domain of rectangular microchannel.
Please cite this article as: Z.Y. Ghale, et al., Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models, Int. Commun. Heat Mass Transf. (2015), http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.012
Z.Y. Ghale et al. / International Communications in Heat and Mass Transfer xxx (2015) xxx–xxx
t2:3
Properties
φ = 0%
φ = 1%
φ = 2%
t2:4 t2:5 t2:6 t2:7
k nf (W/m K) ρ nf (kg/m3) μ nf (kj/kg K) Cpnf (kj/kg °C))
0.603 995.7 0.0008977 4.183
0.62 1021.7 0.0008177 4.149
0.638 1047.7 0.0008376 4.115
152
Single-phase and two-phase flows of nanofluids through an MCHS are governed by the conservation equations for phase continuity, momentum, and energy transport. The governing equations in the single-phase model are given by the following:
153
- Continuity equation:
148 149 150 151
F
Table 2 Properties of alumina/water nanofluids at 100 kPa and 30 °C.
Fig. 3. Friction factor versus Reynolds number for nanofluid with different concentrations.
∇ ðρn f V m Þ ¼ 0
- Momentum:
ð9Þ
155
T ∇ ðρm vm vm Þ ¼ −∇p þ ∇ μ m ∇vm þ ∇v !m n X þ ∇: φm ρm vdr;k vdr;k
R O
- Momentum equation: ∇ ðρn f V m V m Þ ¼ −∇P þ ∇ ðμ n f ∇V m Þ
ð10Þ
- Energy equation:
ρm ¼
ρm
n X φk ρ k k¼1
P
177
vdr,k is the drift velocity for the secondary phase k.
vdr;k ¼ vk −vm
ð17Þ
ð13Þ
179
- Energy: " # n X ∇ ðρk ck Þφk V k T ¼ ∇ ðkeff ∇T Þ
ð18Þ
k¼1
181
- Volume fraction: ð14Þ
∇ ðφP ρP V m Þ ¼ −∇ φP ρP V dr;P
ð19Þ
αk is mole fraction of phase k.
U
171
R
169
φk ρk vk
N C O
168
k¼1
R
Xn
E
where Vm and ρm are mean velocity and density of the mixture, respectively, and define as follows: vm ¼
ð16Þ
k¼1
ð12Þ
C
∇ ðρm V m Þ ¼ 0 166
D
Continuity:
n X φk μ k
175
E
164
162
μm ¼
T
163
In the two-phase mixture model, equations of continuity, momentum, and energy solve for the mixture and a volume fraction equation uses for the secondary phases, as well as a correlation uses to calculate the relative velocity between the phases.
ð15Þ
where n, F, and μm are number of phase, body force, and viscosity of 174 mixture, respectively.
ð11Þ
159
160 161
172
k¼1
157
∇ ðρn f C V m T Þ ¼ ∇ ðkn f ∇T Þ
O
t2:1 t2:2
3
Fig. 2. Pressure drop versus Reynolds number for nanofluid with different concentrations.
Fig. 4. Experimental and predicted heat transfer coefficient for Al2O3/water nanofluid with 1% volume fraction.
Please cite this article as: Z.Y. Ghale, et al., Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models, Int. Commun. Heat Mass Transf. (2015), http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.012
Z.Y. Ghale et al. / International Communications in Heat and Mass Transfer xxx (2015) xxx–xxx
F
4
Vm ¼
k¼1
φk ρ k V k
ð20Þ
ρeff
184
190
f drag ¼
192
ρp
2. Results and discussion
T
189
18μ f drag
ρp −ρm
! α
ð21Þ
C
! v pq ¼
2 ρP dP
Re≤1000 1 þ 0:15Re0:687 ; 0:0183Re; Re N1000
E
187
The relative velocity is determined from relation proposed by Manninen et al. [20], which is used to calculate the drag function fdrag from Eq. (22):
R
185 186
R O
Xn
P
where
D
183
The flow pattern and temperature distribution through an MCHS were simulated using a commercial CFD package, Ansys Fluent version 14. As shown in Fig. 1, the velocity inlet boundary condition was applied to the channel inlet. The velocity, the temperature, and the volume fraction of each phase were specified in this boundary. Pressure outlet boundary condition was applied to the channel outlet, and no-slip boundary condition was defined for the walls. The heated wall is under the constant heat flux. The geometry was meshed using tetrahedral type structured meshes with a cluster near the wall. Mesh independence test was performed to note that the results are independent of grid size.
E
Fig. 5. Experimental and predicted heat transfer coefficient for Al2O3/water nanofluid with 2% volume fraction.
O
Fig. 7. Variation of Nu/Nu0 in 1% Al2O3/water nanofluid in the MCHS for different values of “w.”
where
R
! ∂vm ! ! ! ! α ¼ g − v m ∇ v m− ∂t
O
and
C
! ! ! v pq ¼ v p − v q
ð23Þ
ð24Þ
196 197 198 199 200 201 202 203
204
2.1. Investigation of fluid flow and heat transfer in a straight microchannel 205 In this section, heat transfer and hydrodynamic parameters of water/ alumina nanofluids with different concentrations were studied and the CFD predictions were validated and compared with the experimental data [4]. The results of single-phase and two-phase mixture models were compared and validated using the experimental data reported by Lee and Mudawar [4] to obtain the accuracy of both simulations. Results are depicted in Figs. 2 and 3. As shown in the figures, for all of fluids by increasing Reynolds number, the pressure drop increased and friction factor decreased. There are two noticeable issues, one that the pressure drop and friction factor for both single- and two-phase models are almost identical, and other point is the fact that increasing concentration of particles has no significant effect on the friction factor.
U
N
194
ð22Þ
195
Fig. 6. Velocity contours of pure water in a plan at the center of microchannel under Reynolds number of 560.
Please cite this article as: Z.Y. Ghale, et al., Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models, Int. Commun. Heat Mass Transf. (2015), http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.012
206 207 208 209 210 211 212 213 214 215 216 217
5
O
F
Z.Y. Ghale et al. / International Communications in Heat and Mass Transfer xxx (2015) xxx–xxx
Fig. 10. Variation of Nu/Nu0 in 1% Al2O3/water nanofluid in the MCHS for different values of “l.”
231
2.3. Investigation of fluid flow and heat transfer in a ribbed microchannel
232
Ribs can be used to enhance the heat transfer rate from heated surface by adding contact surface area and flow turbulency. In this section, the results are reported in terms of Nusselt number and friction coefficient, as a function of Reynolds number, nanofluid concentration, height of the ribs (l), and width of the ribs (w). A sample of velocity contours of pure water in a plan at the center of microchannel equipped with a rib with w = 0.1 mm under Reynolds number of 560 is shown in Fig. 6. It can be found that as the fluid passes over the rib, the flow direction changes and the transverse velocity increases and leads to better fluid mixing. Therefore, it is expected that the heat transfer performance in
233 234 235 236 237 238 239 240 241
C
E
228 229
R
226 227
R
224 225
N C O
222 223
U
220 221
P
230
Comparison of the predicted heat transfer coefficients using both single- and two-phase models for 1% and 2% nanofluids at power input of 100 W under different Reynolds numbers are shown in Figs. 4, 5. As shown in this figure, results of the mixture model are more precise than the single-phase model, and there is a good agreement between the experimental results and CFD predictions. The average relative error between the experimental data and the CFD results based on the single-phase model is 32.6% and 37.4% for 1% and 2% nanofluid, respectively, while the average relative error based on the two-phase model for 1% and 2% nanofluids is 11.39% and 2%, respectively.
D
219
a ribbed channel is higher than performance of straight microchannel without rib. For evaluation of thermal and hydraulic performance of MCHS, (Nu/ Nu0), (f/f0), and η were analyzed. The variations of Nu/Nu0 and f/f0 of 1% Al2O3/water nanofluid in the MCHS with l = 0.4 mm as a function of w, for different Reynolds numbers, are plotted in Figs. 7 and 8. The width of the ribs is in the range of 0.1, 0.12, and 0.14 mm. It is clear that in the ribbed microchannel, both friction coefficients and Nusselt numbers are higher than those in a channel without rib. By increasing the channel width, the heat transfer performance increases; in fact, bigger turbulators cause to higher Nusselt numbers. In a channel with bigger ribs, the available surface area for fluid flow decreases; therefore, the transverse velocity and turbulency increases and leads to better heat transfer rate. The heat transfer performance of the ribbed channel with w = 0.14 mm is about 31% higher than ribbed channel with w = 0.10 mm. While the heat transfer performance increases, the pressure drop and friction factor also increases. For the investigation of the effects of both friction factor and Nusselt number, thermal enhancement factor, η, was defined using Eq. (8). In fact, η shows the enhancement of Nusselt number against enhancement of friction factor. Fig. 9 shows the variation of η versus Reynolds number under different values of rib width. It is clear that by increasing the Reynolds number, the thermal enhancement factor increases. This enhancement is higher for the wider ribs, and the dependence of η to the w in Re N 560 is more remarkable. The effects of the rib height, l, on the Nusselt number, friction factor, and thermal enhancement factor are shown in Figs. 10–12, and it can be found that unlike the effect of rib width, by increasing the rib height, the thermal
E
2.2. Heat transfer coefficient
T
218
R O
Fig. 8. Variation of f/f0 in 1% Al2O3/water nanofluid in the MCHS for different values of “w.”
Fig. 9. Variation of η with Re for different values of “w.”
Fig. 11. Variation of f/f0 in 1% Al2O3/water nanofluid in the MCHS for different values of “l.”
Please cite this article as: Z.Y. Ghale, et al., Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models, Int. Commun. Heat Mass Transf. (2015), http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.012
242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269
Z.Y. Ghale et al. / International Communications in Heat and Mass Transfer xxx (2015) xxx–xxx
F
6
O
Fig. 14. Nusselt number for Al2O3/water nanofluid at different concentrations versus Re number.
276 277 278 279
α ¼ l=w
ð25Þ
292
R
R
E
Variation of thermal enhancement factor for the ribbed channel with α = 2, 2.857, 3.33, 4, and 6 is presented in Fig. 13. As shown in Fig. 13, under the low Reynolds numbers (Re˂360), the dimensions of the rib have not a large impact on the thermal enhancement. Under the higher Reynolds numbers, the ribbed channel with aspect ratio of 2.875 has the best thermal and hydrodynamics performance. The width and height of this rib are 0.14 mm and 4 mm, respectively. The effects of volume fraction of nanofluid on the Nusselt number and friction factor of the MCHS with aspect ratio of 2.875 are shown in Figs. 14 and 15. By increasing the nanofluid concentration, heat transfer performance of the MCHS enhances, while the friction factor is not significant change. The results clearly show that the heat transfer
O
290 291
3. Conclusion
309
Computational fluid dynamics analysis was developed to predict the Nusselt number and friction factor of Al2O3/water nanofluids in a straight and ribbed microchannel heat sink, MCHS. In the present work, all of the simulations were performed under steady conditions using the software Ansys Fluent 14, which is based on the finite volume approach.
310
R O
301 302
C
288 289
Figs. 16, 17, and 18 show the effects of numbers of ribs on the thermal performance and friction factor. Three microchannels equipped with 3, 5, and 9 ribs were investigated. Increasing number of the ribs has two opposing effects. According to Figs. 16 and 17, by increasing number of the ribs, thermal performance of the MCHS increases, while the hydraulics performance decreases. As shown in Fig. 18, an MCHS equipped with five ribs has the optimum thermal and hydraulics performance.
N
286 287
300
U
284 285
C
281 282 283
2.4. Effects of rib number on hydrodynamics and thermal performance
P
274 275
D
272 273
performance of the channel decreases. By comparison of Fig. 9 with Fig. 12, it can be found that the effects of the rib width on the thermal performance of MCHS are more remarkable than the effects of the rib height. With a 28% increase in the rib width, the heat transfer performance increases 31%, while a 66% increase in the rib height cause to 15% enhancement in thermal performance. Because according to Fig. 1, the height of the channel is about four times greater than the channel width; therefore, change in the rib width is more effective on reduction of the flow area. For evaluation of the best dimension for a rib, an aspect ratio was defined as follow:
293
T
270 271
performance of the nanofluid is higher than the base fluid, distilled water. The Nusselt number of 2% Al2O3/water is about 16.1% and 34.7% higher than 1% nanofluid and pure water respectively. The nanoparticles provide higher heat transfer rate due to the larger thermal conductivity of nanofluids and large energy exchange resulting from the chaotic movement of nanoparticles. This behavior is more significant as Reynolds number and volume fraction increases.
E
Fig. 12. Variation of η with Re for different values of “l.”
Fig. 13. Variation of η with Re for different values of “α .”
Fig. 15. Friction factor for Al2O3/water nanofluid at different concentrations versus Re number.
Please cite this article as: Z.Y. Ghale, et al., Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models, Int. Commun. Heat Mass Transf. (2015), http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.012
294 295 296 297 298 299
303 304 305 306 307 308
311 312 313 314 315
Fig. 18. Variation of η in the ribbed MCHS with different ribs number.
333 334 335 336 337 338 339 340 341
Fig. 17. Variation of f/f0 in the ribbed MCHS with different ribs number.
R O
P
[26]
342 Q2 343
References
344
D
331 332
4. Uncited reference
345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395
[1] H.A. Mohammed, P. Gunnasegaran, N.H. Shuaib, Influence of various base nanofluids and substrate materials on heat transfer in trapezoidal microchannel heat sinks, Int. Commun. Heat Mass Transfer 38 (2) (2011) 194–201. [2] D.B. Tuckerman, R.F.W. Pease, High-performance heat sinking for VLSI, IEEE Electron Device Lett. 2 (5) (1981) 126–129. [3] S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, ASME Publ. Fed. 231 (1995) 99–106. [4] J. Lee, I. Mudawar, Assessment of the effectiveness of nanofluids for single-phase and two-phase heat transfer in micro-channels, Int. J. Heat Mass Transf. 50 (3) (2007) 452–463. [5] L. Asmaei, M. Haghshenasfard, M. Nasr Esfahany, Thermal performance analysis of nanofluids in a thermosyphon heat pipe using CFD modeling, Heat Mass Transf. 49 (5) (2013) 667–678. [6] M. Izadi, A. Behzadmehr, D. Jalali-Vahida, Numerical study of developing laminar forced convection of a nanofluid in an annulus, Int. J. Therm. Sci. 48 (11) (2009) 2119–2129. [7] M.A. Ahmed, M.Z. Yusoff, N.H. Shuaib, Effects of geometrical parameters on the flow and heat transfer characteristics in trapezoidal-corrugated channel using nanofluid, Int. Commun. Heat Mass Transfer 42 (2013) 69–74. [8] 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) 1368–1375. [9] S. Göktepe, K. Atalık, H. Ertürk, Comparison of single and two-phase models for nanofluid convection at the entrance of a uniformly heated tube, Int. J. Therm. Sci. 8 (2014) 83–92. [10] R. Chein, J. Chuang, Experimental microchannel heat sink performance studies using nanofluids, Int. J. Therm. Sci. 46 (1) (2007) 57–66. [11] C.J. Ho, L.C. Wei, Z.W. Li, An experimental investigation of forced convective cooling performance of a microchannel heat sink with Al2O3/water nanofluid, Appl. Therm. Eng. 30 (2) (2010) 96–103. [12] K. Anoop, R. Sadr, J. Yu, S. Kang, S. Jeon, D. Banerjee, Experimental study of forced convective heat transfer of nanofluids in a microchannel, Int. Commun. Heat Mass Transfer 39 (9) (2012) 1325–1330. [13] S. Zeinali Heris, T.H. Nassan, S.H. Noie, H. Sardarabadi, M. Sardarabadi, Laminar convective heat transfer of Al2O3/water nanofluid through square cross-sectional duct, Int. J. Heat Fluid Flow 44 (2013) 375–382. [14] M. Haghshenafard, M.R. Talaei, S. Nasr, Numerical and experimental investigation of heat transfer of ZnO/water nanofluid in the concentric tube and plate heat exchangers, Therm. Sci. 15 (1) (2011) 183–194. [15] M. Akhtari, M. Haghshenasfard, M.R. Talaie, Numerical and experimental investigation of heat transfer of α-Al2O3/water nanofluid in double pipe and shell and tube heat exchangers, Numer. Heat Transfer Part A Appl. 63 (12) (2013) 941–958. [16] A. Behzadmehr, M. Saffar-Avval, N. Galanis, Prediction of turbulent forced convection of a nanofluid in a tube with uniform heat flux using a two phase approach, Int. J. Heat Fluid Flow 28 (2) (2007) 211–219. [17] M. Haghshenas Fard, M.N. Esfahany, M.R. Talaie, Numerical study of convective heat transfer of nanofluids in a circular tube two-phase model versus single-phase model, Int. Commun. Heat Mass Transfer 37 (1) (2010) 91–97. [18] E. Manay, B. Sahin, M. Yilmaz, K. Gelis, Thermal performance analysis of nanofluids in microchannel heat sinks, World Academy of Science, Eng. Technol. 67 (2012).
E
T
329 330
C
327 328
E
325 326
R
323 324
R
322
N C O
320 321
Single-phase and two-phase models were used for prediction of temperature profile and fluid flow distribution and calculation of friction factor and Nusselt number. The CFD predictions based on singlephase and mixture models were compared to the experimental data, and it was concluded that the two-phase model is more precise than the single-phase model. The average relative error between the experimental data and CFD results based on the single-phase model and the two-phase mixture model for 1% nanofluid is 32.6% and 11.39%, respectively. The heat transfer coefficient of nanofluids increases with increasing the volume fraction of nanofluids and Reynolds number. Increasing the nanofluid volume fraction from 1% to 2% results in 16.1% increase in the Nusselt number. For the investigation of the effects of the ribs on the thermal performance of an MCHS, a ribbed microchannel was considered, and the effects of the height, width, and number of the ribs on the hydraulics and thermal performance of an MCHS were studied. According to the CFD predictions, it was found that in the ribbed microchannel, both friction coefficients and Nusselt numbers are higher than those in a channel without rib. By increasing the channel width, the heat transfer performance increases, while by increasing the rib height, the thermal performance of the channel decreases. The variation of thermal enhancement factor for the ribbed channel with different aspect ratios was investigated, and the results showed that under the low Reynolds numbers, the dimensions of the rib have not important effects on the thermal enhancement. However, under the higher Reynolds numbers, the ribbed channel with aspect ratio of 2.875 showed the best performance.
U
318 319
O
Fig. 16. Variation of Nu/Nu0 in the ribbed MCHS with different ribs number.
316 317
7
F
Z.Y. Ghale et al. / International Communications in Heat and Mass Transfer xxx (2015) xxx–xxx
Please cite this article as: Z.Y. Ghale, et al., Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models, Int. Commun. Heat Mass Transf. (2015), http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.012
8
[23] P.K. Namburu, D.K. Das, K.M. Tanguturi, R.S. Vajjha, Numerical study of turbulent flow and heat transfer characteristics of nanofluids considering variable properties, Int. J. Therm. Sci. 48 (2009) 290–302. [24] W. Qu, I. Mudawar, Measurement and correlation of critical heat flux in two-phase micro-channel heat sinks, Int. J. Heat Mass Transf. 47 (10–11) (2004) 2045–2059. [25] L. Chai, G. Xia, M. Zhou, J. Li, J. Qi, Optimum thermal design of interrupted microchannel heat sink with rectangular ribs in the transverse microchambers, Appl. Therm. Eng. 51 (1-2) (2013) 880–889. [26] M. Manninen, V. Taivassalo, S. Kallio, On the mixture model for multiphase flow, VTT Publications 288Technical Research Centre of Finland, 1996.
N
C
O
R
R
E
C
T
E
D
P
R O
O
F
[19] M. Kalteh, A. Abbassi, M. Saffar-Avval, J. Harting, Eulerian–Eulerian two-phase numerical simulation of nanofluid laminar forced convection in a microchannel, Int. J. Heat Fluid Flow 32 (1) (2011) 107–116. [20] O. Manca, S. Nardini, D. Ricci, A numerical study of nanofluid forced convection in ribbed channels, Appl. Therm. Eng. 37 (2012) 280–292. [21] S.E.B. Maiga, C.T. Nguyen, N. Galanis, G. Roy, Heat transfer behavior of nanofluids in a uniformly heated tube, Superlattice. Microst. 35 (2004) 543–557. [22] A. Akbarnia, A. Behzadmehr, Numerical study of laminar mixed convection of a nanofluid in horizontal curved tube, Appl. Therm. Sci. 27 (2007) 1327–1337.
U
396 397 398 399 400 401 402 403 404 405
Z.Y. Ghale et al. / International Communications in Heat and Mass Transfer xxx (2015) xxx–xxx
Please cite this article as: Z.Y. Ghale, et al., Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models, Int. Commun. Heat Mass Transf. (2015), http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.012
406 407 408 409 410 411 412 413
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Q13Q3
F
2
Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models☆ Z. Yari Ghale, M. Haghshenasfard, M. Nasr Esfahany Department of Chemical Engineering, Isfahan University of Technology, Isfahan 8415683111, Iran
6
a r t i c l e
7 8
Available online xxxx
9 10 11 12
Keywords: Nanofluid Heat transfer Ribbed microchannel heat sink
i n f o
R O
4 5
a b s t r a c t
D
P
In this paper, laminar forced convective heat transfer of water/alumina nanofluids in a straight microchannel is studied numerically using CFD modeling. In the first part, single-phase and two-phase mixture models have been used for prediction of hydrodynamics and heat transfer parameters of nanofluids in a simple microchannel heat sink. The CFD predictions were compared to the experimental data and it was concluded that the two-phase approach gives better predictions compared to the single-phase model. The effects of ribs turbulators on the fluid flow and heat transfer performance of microchannel were investigated in the second part. The effects of geometrical characteristics of the ribs were studied, and the results showed that the Nusselt number and friction coefficient of nanofluids in the ribbed microchannel are higher than those of simple microchannel, and this enhancement increased with increasing the width of the ribs. © 2015 Elsevier Ltd. All rights reserved.
36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
C
E
R
R
34 35
Recent development in nanotechnology for improving cooling technology in the electronic devices have made possible production of efficient and compact cooling modules to provide reliable system operation [1]. Because of fast growth in miniaturization of electronics devices and large amount of the heat generated in these devices, a single-layered microchannel heat sink (MCHS) that was first introduced by Tuckerman and Pease [2] in 1981 has become inadequate. Thus, improving the system of MCHS is necessary. An MCHS contains a coolant flowing through the channels and carrying away the heat generated by electronic devices. Therefore, improving thermal behavior of coolant is an effective way to enhance the thermal performance of MCHSs. Nanofluid is a new class of fluids that first has been used by Choi et al. [3]. A nanofluid is a fluid containing nanosized particles suspended into a base fluid such as water, ethylene glycol, and engine oil. Metal oxide or metal nanoparticles have a much higher thermal conductivity than fluids, therefore suspending these particles can enhance the thermal conductivity of the base fluids and use of nanofluids does enhance the heat transfer performance of an MCHS. In recent years, many numerical and experimental studies have been made in the field of thermal behavior of nanofluids [4–13]. Two-phase and single-phase (homogeneous) approaches can be used for CFD analysis of heat transfer in nanofluids [14]. Most of the numerical studies have been carried out using the single-phase approach. In the homogeneous modeling, the base fluid and nanoparticles are assumed to be in thermal equilibrium. In the two-phase approach, the Eeulerian or
N C O
32 33
1. Introduction
U
30 31
T
26 24 23
28 29
13 14 15 16 17 18 19 20 21
E
22 25 27
O
1
☆ Communicated by W.J. Minkowycz. E-mail address: [email protected] (M. Haghshenasfard).
Lagrangian frameworks can be implemented for the base fluid and nanoparticles as two different liquid and solid phases [15]. Behzadmehr et al. [16] numerically investigated turbulent forced convection heat transfer of a Cu/water nanofluid in a circular tube using the two-phase mixture model. The results of two-phase model were compared to the single-phase predictions and experimental data, and they found that the mixture model is more accurate than the single- phase model. Haghshenasfard et al. [17] studied both single-phase and two-phase CFD models for prediction of heat transfer coefficient of Cu/water nanofluids in a tube with constant wall temperature. The effects of nanoparticle type, nanoparticle concentration, and nanofluid Peclet number on pressure drop, temperature profile, and heat transfer rate were studied. Their results showed that the heat transfer coefficient increases by increasing the nanoparticle concentration and Peclet number, and the two-phase model showed better agreement with the experimental measurements. Manay et al. [18] numerically studied the heat transfer and hydraulic characteristics of aqueous CuO/water and Al2O3/water nanofluids inside a microchannel with square duct using the mixture model. The predictions showed that the nanofluids enhance the heat transfer rate while the concentration and Reynolds number of nanofluids are increasing. Kalteh et al. [19] studied numerically laminar forced convection heat transfer of a Cu/water nanofluid in a microchannel with constant wall temperature. The Eulerian–Eulerian model has been used to calculate heat transfer and pressure drop parameters. They found that increasing in Reynolds number and nanofluid volume fraction increase the heat transfer rate. They also reported that heat transfer coefficients predicted by the two-phase model are higher than single-phase predictions.
http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.012 0735-1933/© 2015 Elsevier Ltd. All rights reserved.
Please cite this article as: Z.Y. Ghale, et al., Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models, Int. Commun. Heat Mass Transf. (2015), http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.012
53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82
94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114
116 117
Laminar forced convection of water and Al2O3/water nanofluids with volume fraction of 1 and 2 vol% in a rectangular microchannel with uniform heat flux was numerically investigated. The microchannel was designed with length, width, and height of 44.8 mm, 0.215 mm, and 0.821 mm, respectively. The dimensions are listed in Table 1. The heat flux for unit cell was 228586 W/m2, and the heat flux for a channel can be calculated using the following relation [24]:
E
R
R
O
q″eff W cell W ch þ 2H ch
C
125
q″p ¼
t1:4
The physical properties, density, viscosity, thermal conductivity, and specific heat capacity of Al2O3/water nanofluids were calculated using 126 Eqs. (2)–(5) [4] and are presented in Table 2: 127 ρn f ¼ ð1−φÞρb f þ φρP
ð1Þ
ð2Þ
where φ is volumetric concentration of nanoparticles; μnf ¼ 123ϕ2 þ 7:3ϕ þ 1 μbf kn f
kP þ ðn−1Þkb f −ðn−1Þφðkb f −kP Þ kb f ¼ kp þ ðn−1Þkb f þ φðkb f −kP Þ
129
ð3Þ
130 131
ð4Þ
where knf, kbf, and kP are the thermal conductivities of the nanofluid, 133 base fluid, and solid particles, respectively, and n is solid particle shape factor (n = 3 for spherical particles); 134 C p;n f ¼ ð1−φÞC P;b f þ φC p;P
ð5Þ 136
The friction factor and the local heat transfer coefficients of nanofluids were calculated using following relations [4,25]: 137 f ¼
ΔP ch Dh 2Lρ f u2
q″ ½T w ðxÞ−T m ðxÞ
ð6Þ
140
where q″, Tw and Tm are heat flux, local temperature of bottom wall and balk temperature of fluid. In order to evaluate the performance of microchannel with ribs, the thermal enhancement factor were measured using the following equation [25]: Nu
η¼
142 143 144 145
Nu0
f
139
ð7Þ
1 =3
ð8Þ
f0
where Nu and f are the parameters of microchannel without rib, and 0 147 index refers to the ribbed channel.
N
123
t1:3
5.637 mm
U
121 122
C
1.1. Model formulation and numerical procedure
120
Hw2 (mm)
0.821
hðxÞ ¼
115
118 119
Hch (mm)
12.700
F
92 93
Hw1 (mm)
0.215
O
90 91
Wch (mm)
0.125
R O
89
Ww (mm)
P
87 88
t1:1 t1:2
Table 1 Dimensions of unit cell microchannel.
D
85 86
O. Manca et al. [20] proposed a single-phase model to study the nanofluids heat transfer in a 2-D ribbed channel. The results showed that heat transfer enhancement increases with the nanofluid concentration, but it is accompanied by enhancing the pumping power. The effects of the ribs on the heat transfer performance have been studied under different pitches and Reynolds numbers. They found that the rectangular turbulators with rib width/rib height = 0.5 shows the highest thermal performances and highest losses. The single-phase model also has been used by Maiga et al. [21], Akbarnia and Behzadmehr [22], and Nambura et al. [23], for the investigation of convective heat transfer of various nanofluids inside the circular tubes. According to their results, the single-phase model gives the reasonable data for dilute nanofluids. The aim of present study is to compare the single-phase and the two-phase approaches for modeling laminar forced convective heat transfer of alumina/water nanofluids in a rectangular microchannel with uniformly heated walls. In addition, the modeling was extended to consider the effects of ribbed microchannel on the heat transfer performance. The results of this modeling have some benefits for prediction of operating conditions, which maximize the heat transfer rate and minimize the pressure drop through an MCHS. The CFD results have been compared to experimental data reported by Lee and Mudawar [4]. Lee and Mudawar [4] were performed some experiments to investigate the heat transfer of nanofluids in a microchannel. The experimental apparatus consists of a reservoir tank equipped with heater, constant temperature bath, and microchannel test module. The nanoparticles used in their work were Al2O3 and two volumetric concentrations of water/Al2O3 nanofluid, 1% and 2%, had been used in the test facility. The microchannel test module and the ribbed channel are shown in Fig. 1. The test facility include rectangular 215 mm wide by 821 mm deep grooves milled into the copper block. Heat is supplied to the test section by 12 cartridge heaters.
T
83 84
Z.Y. Ghale et al. / International Communications in Heat and Mass Transfer xxx (2015) xxx–xxx
E
2
Fig. 1. Schematic and computational domain of rectangular microchannel.
Please cite this article as: Z.Y. Ghale, et al., Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models, Int. Commun. Heat Mass Transf. (2015), http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.012
Z.Y. Ghale et al. / International Communications in Heat and Mass Transfer xxx (2015) xxx–xxx
t2:3
Properties
φ = 0%
φ = 1%
φ = 2%
t2:4 t2:5 t2:6 t2:7
k nf (W/m K) ρ nf (kg/m3) μ nf (kj/kg K) Cpnf (kj/kg °C))
0.603 995.7 0.0008977 4.183
0.62 1021.7 0.0008177 4.149
0.638 1047.7 0.0008376 4.115
152
Single-phase and two-phase flows of nanofluids through an MCHS are governed by the conservation equations for phase continuity, momentum, and energy transport. The governing equations in the single-phase model are given by the following:
153
- Continuity equation:
148 149 150 151
F
Table 2 Properties of alumina/water nanofluids at 100 kPa and 30 °C.
Fig. 3. Friction factor versus Reynolds number for nanofluid with different concentrations.
∇ ðρn f V m Þ ¼ 0
- Momentum:
ð9Þ
155
T ∇ ðρm vm vm Þ ¼ −∇p þ ∇ μ m ∇vm þ ∇v !m n X þ ∇: φm ρm vdr;k vdr;k
R O
- Momentum equation: ∇ ðρn f V m V m Þ ¼ −∇P þ ∇ ðμ n f ∇V m Þ
ð10Þ
- Energy equation:
ρm ¼
ρm
n X φk ρ k k¼1
P
177
vdr,k is the drift velocity for the secondary phase k.
vdr;k ¼ vk −vm
ð17Þ
ð13Þ
179
- Energy: " # n X ∇ ðρk ck Þφk V k T ¼ ∇ ðkeff ∇T Þ
ð18Þ
k¼1
181
- Volume fraction: ð14Þ
∇ ðφP ρP V m Þ ¼ −∇ φP ρP V dr;P
ð19Þ
αk is mole fraction of phase k.
U
171
R
169
φk ρk vk
N C O
168
k¼1
R
Xn
E
where Vm and ρm are mean velocity and density of the mixture, respectively, and define as follows: vm ¼
ð16Þ
k¼1
ð12Þ
C
∇ ðρm V m Þ ¼ 0 166
D
Continuity:
n X φk μ k
175
E
164
162
μm ¼
T
163
In the two-phase mixture model, equations of continuity, momentum, and energy solve for the mixture and a volume fraction equation uses for the secondary phases, as well as a correlation uses to calculate the relative velocity between the phases.
ð15Þ
where n, F, and μm are number of phase, body force, and viscosity of 174 mixture, respectively.
ð11Þ
159
160 161
172
k¼1
157
∇ ðρn f C V m T Þ ¼ ∇ ðkn f ∇T Þ
O
t2:1 t2:2
3
Fig. 2. Pressure drop versus Reynolds number for nanofluid with different concentrations.
Fig. 4. Experimental and predicted heat transfer coefficient for Al2O3/water nanofluid with 1% volume fraction.
Please cite this article as: Z.Y. Ghale, et al., Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models, Int. Commun. Heat Mass Transf. (2015), http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.012
Z.Y. Ghale et al. / International Communications in Heat and Mass Transfer xxx (2015) xxx–xxx
F
4
Vm ¼
k¼1
φk ρ k V k
ð20Þ
ρeff
184
190
f drag ¼
192
ρp
2. Results and discussion
T
189
18μ f drag
ρp −ρm
! α
ð21Þ
C
! v pq ¼
2 ρP dP
Re≤1000 1 þ 0:15Re0:687 ; 0:0183Re; Re N1000
E
187
The relative velocity is determined from relation proposed by Manninen et al. [20], which is used to calculate the drag function fdrag from Eq. (22):
R
185 186
R O
Xn
P
where
D
183
The flow pattern and temperature distribution through an MCHS were simulated using a commercial CFD package, Ansys Fluent version 14. As shown in Fig. 1, the velocity inlet boundary condition was applied to the channel inlet. The velocity, the temperature, and the volume fraction of each phase were specified in this boundary. Pressure outlet boundary condition was applied to the channel outlet, and no-slip boundary condition was defined for the walls. The heated wall is under the constant heat flux. The geometry was meshed using tetrahedral type structured meshes with a cluster near the wall. Mesh independence test was performed to note that the results are independent of grid size.
E
Fig. 5. Experimental and predicted heat transfer coefficient for Al2O3/water nanofluid with 2% volume fraction.
O
Fig. 7. Variation of Nu/Nu0 in 1% Al2O3/water nanofluid in the MCHS for different values of “w.”
where
R
! ∂vm ! ! ! ! α ¼ g − v m ∇ v m− ∂t
O
and
C
! ! ! v pq ¼ v p − v q
ð23Þ
ð24Þ
196 197 198 199 200 201 202 203
204
2.1. Investigation of fluid flow and heat transfer in a straight microchannel 205 In this section, heat transfer and hydrodynamic parameters of water/ alumina nanofluids with different concentrations were studied and the CFD predictions were validated and compared with the experimental data [4]. The results of single-phase and two-phase mixture models were compared and validated using the experimental data reported by Lee and Mudawar [4] to obtain the accuracy of both simulations. Results are depicted in Figs. 2 and 3. As shown in the figures, for all of fluids by increasing Reynolds number, the pressure drop increased and friction factor decreased. There are two noticeable issues, one that the pressure drop and friction factor for both single- and two-phase models are almost identical, and other point is the fact that increasing concentration of particles has no significant effect on the friction factor.
U
N
194
ð22Þ
195
Fig. 6. Velocity contours of pure water in a plan at the center of microchannel under Reynolds number of 560.
Please cite this article as: Z.Y. Ghale, et al., Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models, Int. Commun. Heat Mass Transf. (2015), http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.012
206 207 208 209 210 211 212 213 214 215 216 217
5
O
F
Z.Y. Ghale et al. / International Communications in Heat and Mass Transfer xxx (2015) xxx–xxx
Fig. 10. Variation of Nu/Nu0 in 1% Al2O3/water nanofluid in the MCHS for different values of “l.”
231
2.3. Investigation of fluid flow and heat transfer in a ribbed microchannel
232
Ribs can be used to enhance the heat transfer rate from heated surface by adding contact surface area and flow turbulency. In this section, the results are reported in terms of Nusselt number and friction coefficient, as a function of Reynolds number, nanofluid concentration, height of the ribs (l), and width of the ribs (w). A sample of velocity contours of pure water in a plan at the center of microchannel equipped with a rib with w = 0.1 mm under Reynolds number of 560 is shown in Fig. 6. It can be found that as the fluid passes over the rib, the flow direction changes and the transverse velocity increases and leads to better fluid mixing. Therefore, it is expected that the heat transfer performance in
233 234 235 236 237 238 239 240 241
C
E
228 229
R
226 227
R
224 225
N C O
222 223
U
220 221
P
230
Comparison of the predicted heat transfer coefficients using both single- and two-phase models for 1% and 2% nanofluids at power input of 100 W under different Reynolds numbers are shown in Figs. 4, 5. As shown in this figure, results of the mixture model are more precise than the single-phase model, and there is a good agreement between the experimental results and CFD predictions. The average relative error between the experimental data and the CFD results based on the single-phase model is 32.6% and 37.4% for 1% and 2% nanofluid, respectively, while the average relative error based on the two-phase model for 1% and 2% nanofluids is 11.39% and 2%, respectively.
D
219
a ribbed channel is higher than performance of straight microchannel without rib. For evaluation of thermal and hydraulic performance of MCHS, (Nu/ Nu0), (f/f0), and η were analyzed. The variations of Nu/Nu0 and f/f0 of 1% Al2O3/water nanofluid in the MCHS with l = 0.4 mm as a function of w, for different Reynolds numbers, are plotted in Figs. 7 and 8. The width of the ribs is in the range of 0.1, 0.12, and 0.14 mm. It is clear that in the ribbed microchannel, both friction coefficients and Nusselt numbers are higher than those in a channel without rib. By increasing the channel width, the heat transfer performance increases; in fact, bigger turbulators cause to higher Nusselt numbers. In a channel with bigger ribs, the available surface area for fluid flow decreases; therefore, the transverse velocity and turbulency increases and leads to better heat transfer rate. The heat transfer performance of the ribbed channel with w = 0.14 mm is about 31% higher than ribbed channel with w = 0.10 mm. While the heat transfer performance increases, the pressure drop and friction factor also increases. For the investigation of the effects of both friction factor and Nusselt number, thermal enhancement factor, η, was defined using Eq. (8). In fact, η shows the enhancement of Nusselt number against enhancement of friction factor. Fig. 9 shows the variation of η versus Reynolds number under different values of rib width. It is clear that by increasing the Reynolds number, the thermal enhancement factor increases. This enhancement is higher for the wider ribs, and the dependence of η to the w in Re N 560 is more remarkable. The effects of the rib height, l, on the Nusselt number, friction factor, and thermal enhancement factor are shown in Figs. 10–12, and it can be found that unlike the effect of rib width, by increasing the rib height, the thermal
E
2.2. Heat transfer coefficient
T
218
R O
Fig. 8. Variation of f/f0 in 1% Al2O3/water nanofluid in the MCHS for different values of “w.”
Fig. 9. Variation of η with Re for different values of “w.”
Fig. 11. Variation of f/f0 in 1% Al2O3/water nanofluid in the MCHS for different values of “l.”
Please cite this article as: Z.Y. Ghale, et al., Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models, Int. Commun. Heat Mass Transf. (2015), http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.012
242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269
Z.Y. Ghale et al. / International Communications in Heat and Mass Transfer xxx (2015) xxx–xxx
F
6
O
Fig. 14. Nusselt number for Al2O3/water nanofluid at different concentrations versus Re number.
276 277 278 279
α ¼ l=w
ð25Þ
292
R
R
E
Variation of thermal enhancement factor for the ribbed channel with α = 2, 2.857, 3.33, 4, and 6 is presented in Fig. 13. As shown in Fig. 13, under the low Reynolds numbers (Re˂360), the dimensions of the rib have not a large impact on the thermal enhancement. Under the higher Reynolds numbers, the ribbed channel with aspect ratio of 2.875 has the best thermal and hydrodynamics performance. The width and height of this rib are 0.14 mm and 4 mm, respectively. The effects of volume fraction of nanofluid on the Nusselt number and friction factor of the MCHS with aspect ratio of 2.875 are shown in Figs. 14 and 15. By increasing the nanofluid concentration, heat transfer performance of the MCHS enhances, while the friction factor is not significant change. The results clearly show that the heat transfer
O
290 291
3. Conclusion
309
Computational fluid dynamics analysis was developed to predict the Nusselt number and friction factor of Al2O3/water nanofluids in a straight and ribbed microchannel heat sink, MCHS. In the present work, all of the simulations were performed under steady conditions using the software Ansys Fluent 14, which is based on the finite volume approach.
310
R O
301 302
C
288 289
Figs. 16, 17, and 18 show the effects of numbers of ribs on the thermal performance and friction factor. Three microchannels equipped with 3, 5, and 9 ribs were investigated. Increasing number of the ribs has two opposing effects. According to Figs. 16 and 17, by increasing number of the ribs, thermal performance of the MCHS increases, while the hydraulics performance decreases. As shown in Fig. 18, an MCHS equipped with five ribs has the optimum thermal and hydraulics performance.
N
286 287
300
U
284 285
C
281 282 283
2.4. Effects of rib number on hydrodynamics and thermal performance
P
274 275
D
272 273
performance of the channel decreases. By comparison of Fig. 9 with Fig. 12, it can be found that the effects of the rib width on the thermal performance of MCHS are more remarkable than the effects of the rib height. With a 28% increase in the rib width, the heat transfer performance increases 31%, while a 66% increase in the rib height cause to 15% enhancement in thermal performance. Because according to Fig. 1, the height of the channel is about four times greater than the channel width; therefore, change in the rib width is more effective on reduction of the flow area. For evaluation of the best dimension for a rib, an aspect ratio was defined as follow:
293
T
270 271
performance of the nanofluid is higher than the base fluid, distilled water. The Nusselt number of 2% Al2O3/water is about 16.1% and 34.7% higher than 1% nanofluid and pure water respectively. The nanoparticles provide higher heat transfer rate due to the larger thermal conductivity of nanofluids and large energy exchange resulting from the chaotic movement of nanoparticles. This behavior is more significant as Reynolds number and volume fraction increases.
E
Fig. 12. Variation of η with Re for different values of “l.”
Fig. 13. Variation of η with Re for different values of “α .”
Fig. 15. Friction factor for Al2O3/water nanofluid at different concentrations versus Re number.
Please cite this article as: Z.Y. Ghale, et al., Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models, Int. Commun. Heat Mass Transf. (2015), http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.012
294 295 296 297 298 299
303 304 305 306 307 308
311 312 313 314 315
Fig. 18. Variation of η in the ribbed MCHS with different ribs number.
333 334 335 336 337 338 339 340 341
Fig. 17. Variation of f/f0 in the ribbed MCHS with different ribs number.
R O
P
[26]
342 Q2 343
References
344
D
331 332
4. Uncited reference
345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395
[1] H.A. Mohammed, P. Gunnasegaran, N.H. Shuaib, Influence of various base nanofluids and substrate materials on heat transfer in trapezoidal microchannel heat sinks, Int. Commun. Heat Mass Transfer 38 (2) (2011) 194–201. [2] D.B. Tuckerman, R.F.W. Pease, High-performance heat sinking for VLSI, IEEE Electron Device Lett. 2 (5) (1981) 126–129. [3] S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, ASME Publ. Fed. 231 (1995) 99–106. [4] J. Lee, I. Mudawar, Assessment of the effectiveness of nanofluids for single-phase and two-phase heat transfer in micro-channels, Int. J. Heat Mass Transf. 50 (3) (2007) 452–463. [5] L. Asmaei, M. Haghshenasfard, M. Nasr Esfahany, Thermal performance analysis of nanofluids in a thermosyphon heat pipe using CFD modeling, Heat Mass Transf. 49 (5) (2013) 667–678. [6] M. Izadi, A. Behzadmehr, D. Jalali-Vahida, Numerical study of developing laminar forced convection of a nanofluid in an annulus, Int. J. Therm. Sci. 48 (11) (2009) 2119–2129. [7] M.A. Ahmed, M.Z. Yusoff, N.H. Shuaib, Effects of geometrical parameters on the flow and heat transfer characteristics in trapezoidal-corrugated channel using nanofluid, Int. Commun. Heat Mass Transfer 42 (2013) 69–74. [8] 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) 1368–1375. [9] S. Göktepe, K. Atalık, H. Ertürk, Comparison of single and two-phase models for nanofluid convection at the entrance of a uniformly heated tube, Int. J. Therm. Sci. 8 (2014) 83–92. [10] R. Chein, J. Chuang, Experimental microchannel heat sink performance studies using nanofluids, Int. J. Therm. Sci. 46 (1) (2007) 57–66. [11] C.J. Ho, L.C. Wei, Z.W. Li, An experimental investigation of forced convective cooling performance of a microchannel heat sink with Al2O3/water nanofluid, Appl. Therm. Eng. 30 (2) (2010) 96–103. [12] K. Anoop, R. Sadr, J. Yu, S. Kang, S. Jeon, D. Banerjee, Experimental study of forced convective heat transfer of nanofluids in a microchannel, Int. Commun. Heat Mass Transfer 39 (9) (2012) 1325–1330. [13] S. Zeinali Heris, T.H. Nassan, S.H. Noie, H. Sardarabadi, M. Sardarabadi, Laminar convective heat transfer of Al2O3/water nanofluid through square cross-sectional duct, Int. J. Heat Fluid Flow 44 (2013) 375–382. [14] M. Haghshenafard, M.R. Talaei, S. Nasr, Numerical and experimental investigation of heat transfer of ZnO/water nanofluid in the concentric tube and plate heat exchangers, Therm. Sci. 15 (1) (2011) 183–194. [15] M. Akhtari, M. Haghshenasfard, M.R. Talaie, Numerical and experimental investigation of heat transfer of α-Al2O3/water nanofluid in double pipe and shell and tube heat exchangers, Numer. Heat Transfer Part A Appl. 63 (12) (2013) 941–958. [16] A. Behzadmehr, M. Saffar-Avval, N. Galanis, Prediction of turbulent forced convection of a nanofluid in a tube with uniform heat flux using a two phase approach, Int. J. Heat Fluid Flow 28 (2) (2007) 211–219. [17] M. Haghshenas Fard, M.N. Esfahany, M.R. Talaie, Numerical study of convective heat transfer of nanofluids in a circular tube two-phase model versus single-phase model, Int. Commun. Heat Mass Transfer 37 (1) (2010) 91–97. [18] E. Manay, B. Sahin, M. Yilmaz, K. Gelis, Thermal performance analysis of nanofluids in microchannel heat sinks, World Academy of Science, Eng. Technol. 67 (2012).
E
T
329 330
C
327 328
E
325 326
R
323 324
R
322
N C O
320 321
Single-phase and two-phase models were used for prediction of temperature profile and fluid flow distribution and calculation of friction factor and Nusselt number. The CFD predictions based on singlephase and mixture models were compared to the experimental data, and it was concluded that the two-phase model is more precise than the single-phase model. The average relative error between the experimental data and CFD results based on the single-phase model and the two-phase mixture model for 1% nanofluid is 32.6% and 11.39%, respectively. The heat transfer coefficient of nanofluids increases with increasing the volume fraction of nanofluids and Reynolds number. Increasing the nanofluid volume fraction from 1% to 2% results in 16.1% increase in the Nusselt number. For the investigation of the effects of the ribs on the thermal performance of an MCHS, a ribbed microchannel was considered, and the effects of the height, width, and number of the ribs on the hydraulics and thermal performance of an MCHS were studied. According to the CFD predictions, it was found that in the ribbed microchannel, both friction coefficients and Nusselt numbers are higher than those in a channel without rib. By increasing the channel width, the heat transfer performance increases, while by increasing the rib height, the thermal performance of the channel decreases. The variation of thermal enhancement factor for the ribbed channel with different aspect ratios was investigated, and the results showed that under the low Reynolds numbers, the dimensions of the rib have not important effects on the thermal enhancement. However, under the higher Reynolds numbers, the ribbed channel with aspect ratio of 2.875 showed the best performance.
U
318 319
O
Fig. 16. Variation of Nu/Nu0 in the ribbed MCHS with different ribs number.
316 317
7
F
Z.Y. Ghale et al. / International Communications in Heat and Mass Transfer xxx (2015) xxx–xxx
Please cite this article as: Z.Y. Ghale, et al., Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models, Int. Commun. Heat Mass Transf. (2015), http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.012
8
[23] P.K. Namburu, D.K. Das, K.M. Tanguturi, R.S. Vajjha, Numerical study of turbulent flow and heat transfer characteristics of nanofluids considering variable properties, Int. J. Therm. Sci. 48 (2009) 290–302. [24] W. Qu, I. Mudawar, Measurement and correlation of critical heat flux in two-phase micro-channel heat sinks, Int. J. Heat Mass Transf. 47 (10–11) (2004) 2045–2059. [25] L. Chai, G. Xia, M. Zhou, J. Li, J. Qi, Optimum thermal design of interrupted microchannel heat sink with rectangular ribs in the transverse microchambers, Appl. Therm. Eng. 51 (1-2) (2013) 880–889. [26] M. Manninen, V. Taivassalo, S. Kallio, On the mixture model for multiphase flow, VTT Publications 288Technical Research Centre of Finland, 1996.
N
C
O
R
R
E
C
T
E
D
P
R O
O
F
[19] M. Kalteh, A. Abbassi, M. Saffar-Avval, J. Harting, Eulerian–Eulerian two-phase numerical simulation of nanofluid laminar forced convection in a microchannel, Int. J. Heat Fluid Flow 32 (1) (2011) 107–116. [20] O. Manca, S. Nardini, D. Ricci, A numerical study of nanofluid forced convection in ribbed channels, Appl. Therm. Eng. 37 (2012) 280–292. [21] S.E.B. Maiga, C.T. Nguyen, N. Galanis, G. Roy, Heat transfer behavior of nanofluids in a uniformly heated tube, Superlattice. Microst. 35 (2004) 543–557. [22] A. Akbarnia, A. Behzadmehr, Numerical study of laminar mixed convection of a nanofluid in horizontal curved tube, Appl. Therm. Sci. 27 (2007) 1327–1337.
U
396 397 398 399 400 401 402 403 404 405
Z.Y. Ghale et al. / International Communications in Heat and Mass Transfer xxx (2015) xxx–xxx
Please cite this article as: Z.Y. Ghale, et al., Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models, Int. Commun. Heat Mass Transf. (2015), http://dx.doi.org/10.1016/j.icheatmasstransfer.2015.08.012
406 407 408 409 410 411 412 413