close

Вход

Забыли?

вход по аккаунту

?

j.ijheatmasstransfer.2017.10.051

код для вставкиСкачать
International Journal of Heat and Mass Transfer 117 (2018) 787–798
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer
journal homepage: www.elsevier.com/locate/ijhmt
Optimization of thermal performance of multi-nozzle trapezoidal
microchannel heat sinks by using nanofluids of Al2O3 and TiO2
Ngoctan Tran a,⇑, Yaw-Jen Chang b, Chi-Chuan Wang a,⇑
a
b
Department of Mechanical Engineering, National Chiao Tung University, 1001 University Road, Hsinchu 300, Taiwan
Department of Mechanical Engineering, Chung Yuan Christian University, Chung-Li City, Taiwan
a r t i c l e
i n f o
Article history:
Received 28 June 2017
Received in revised form 2 October 2017
Accepted 12 October 2017
Keywords:
Nanofluids
Trapezoidal microchannel heat sink
Substrate materials
High heat flux
Hydraulic diameters
Novel equation
Inlet-coolant temperatures
a b s t r a c t
In this study, a new multi-nozzle trapezoidal microchannel heat sink (MNT-MCHS) was proposed. Five
substrate materials, two nanofluids with nanoparticle volume fractions, 0.1% u 1%, and channel
hydraulic diameters, 157.7 mm Dh 248.2 mm, were numerically examined in detail. In addition, heat
fluxes in the range of 100–1450 W/cm2 subject to inlet coolant temperature from 15 °C to 75 °C were
examined in detail. A locally optimal MNT-MCHS was defined, and a novel equation was proposed for
predicting the maximum temperature on the locally optimal MNT-MCHS depending on the heat flux,
coolant inlet temperature, and the Reynolds number. It was found that at a Reynolds number of 900,
the overall thermal resistance of a MNT-MCHS using copper as a substrate material is improved up to
76% as compared to that using stainless steel 304. The locally optimal MNT-MCHS, using TiO2-water
nanofluid with u ¼ 1%, could dissipate a heat flux up to 1450 W/cm2 at a Re of 900. A minimum thermal
resistance in the present study is improved up to 11.6% and 36.6% in association with those of a multinozzle MCHS and a double-layer MCHS, respectively.
Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction
In parallel with the development of scientific technology, electronic products not only have continued to shrink their sizes, but
also have added more functions and operated at even higher processing speeds. As a consequence, a huge amount of heat is generated in a rather small volume that makes traditional air-cooling
heat sinks in a dilemma. Hence, liquid-cooling heat sinks had been
implemented to resolve the tough thermal management in many
high-power applications. A great breakthrough in the implementation of liquid-cooled heat sinks was created by Tuckerman and
Pease [1] in 1981. They proposed microchannel heat sinks (MCHS)
using water as the working fluid. One of the MCHSs could dissipate
a heat flux up to 790 W/cm2 with an overall thermal resistance of
0.09 °C/W and kept a maximum junction temperature under 94 °C.
Thereafter, many researchers were involved in this field due to its
promisingly heat-dissipation capability.
Investigations in MCHSs can be classified into three main
groups. Most research efforts devoted to the first group by examining the effects of geometric parameters on the heat transfer and
⇑ Corresponding authors.
E-mail
addresses:
ngoctantran73@gmail.com,
ngoctantran@nctu.edu.tw
(N. Tran), justin@cycu.edu.tw (Y.-J. Chang), ccwang@mail.nctu.edu.tw, ccwang@
hotmail.com (C.-C. Wang).
https://doi.org/10.1016/j.ijheatmasstransfer.2017.10.051
0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.
fluid flow characteristics of the MCHSs, including influences of
channel shapes, channel dimensions, manifold shapes, manifold
dimensions, channel layers, channel distributions, substrate
dimensions and the like. The second group investigated the effects
of the thermophysical parameters of the coolants on the heat
transfer and fluid flow characteristics of the MCHSs, and the third
group, with the fewest reports in this field, studied the effects of
the thermophysical properties of the substrate’s materials on the
heat transfer of the MCHSs. In the first group, a great number of
the studies had concentrated on the performance of single-layer
parallel microchannel heat sinks (SL-P-MCHS). However, the
SL-P-MCHSs had not been widely applied due to concerns of
high-pressure drop and non-uniform temperature distribution.
To tailor the non-uniform temperature distribution, Vafai and
Zhu [2] first proposed a double-layered microchannel heat sink
(DL-MCHS) in 1999. The inlets of the upper layer of a DL-MCHS
were located on top of the outlets of the lower layer, thereby
lowering the temperature near the outlet region, and a more uniform temperature prevails on the bottom surface. However, the
DL-MCHS design showed no appreciable improvements in overall
thermal resistance and pressure drop as compared to those of
the SL-MCHSs. To ease pressure drop penalty of the MCHSs, Boteler
et al. [3] were the first to propose a manifold microchannel heat
sink (M-MCHS). The coolant paths of the M-MCHS were shortened
788
N. Tran et al. / International Journal of Heat and Mass Transfer 117 (2018) 787–798
Nomenclature
a
Abt,s
b
Bth
Cp
Dh
Dc
Hs
Lc
Lm
Ln
Lt
MCHS
Q
qw
Re
RT
Tbt,max
length of the top edge of the trapezoidal channel (m)
heat transfer area of the bottom wall of the heat sink
(m2)
length of the bottom edge of the trapezoidal channel
(m)
bottom thickness (m)
specific heat at constant pressure (J/kg K)
channel hydraulic diameter (m)
channel depth (m)
substrate height (m)
channel length (m)
model length (m)
inlet-nozzle length (m)
top cover length (m)
microchannel heat sink
heat transfer rate (W)
heat flux applied on the bottom wall (W/cm2)
Reynolds number
thermal resistance (°C/W)
maximum temperature on the bottom wall (°C)
considerably when compared to those of the SL-MCHSs and DLMCHSs. In this regard, the M-MCHS remarkably reduced the pressure drop and considerably increased the temperature uniformity
as compared to the SL-MCHSs and the DL-MCHSs. Although the
pressure drop and temperature uniformity of the M-MCHS were
conspicuously improved, it still suffers from comparatively high
overall thermal resistance as compared to that of the SL-MCHSs
or DL-MCHSs. For further improvements to balance the pressure
drop penalty, temperature uniformity, and thermal resistance into
a microchannel heat sink, Tran et al. [4] recently proposed a multinozzle microchannel heat sink (MN-MCHS). The key features of the
MN-MCHS are those channel lengths are much shorter as compared to those of the SL-MCHS and DL-MCHS, and channel heat
transfer areas are larger than that of the M-MCHS subject to the
same channel shape and hydraulic diameter. They showed that
the overall thermal resistance, temperature uniformity and the
pressure drop of the MN-MCHS were significantly improved.
Normally, water was utilized as a working fluid in MCHSs for its
superior thermal-physical properties. For further augmentation of
the heat-transfer capability of the coolants, Choi and Eastman [5]
first proposed a nanofluid concept. Eastman et al. [6] reported that
by adding 5% CuO nanoparticles, it could improve thermal conductivity by approximate 60% in comparison with that of pure water.
In recent years, the number of investigations on nanofluids in the
MCHSs increased drastically. For example, Hung et al. [7,8] used
Al2O3-water nanofluids as coolants in a SL-MCHS and a DLMCHS, respectively. They concluded that the thermal resistance
of SL-MCHS and DL-MCHS could be minimized by properly adjusting the nanoparticle volume fraction. Kuppusamy et al. [9] created
various combinations amid nanoparticles (Al2O3, CuO, SiO2, and
ZnO) and base fluids (water, ethylene glycol, and engine oil), and
conducted tests in a triangular grooved microchannel heat sink
(TG-MCHS). They reported that the thermal performance of the
TG-MCHS with Al2O3-water nanofluid having a volume fraction
of 0.04% (nanoparticle diameter of 25 nm) outperformed the
straight MCHS using pure water. A MCHS using CuO-water
nanofluids as working fluids was experimentally investigated by
Rimbault et al. [10]. Their results showed that the thermal performance of the MCHS using CuO-water nanofluids with u 6 1:03%
was slightly increased when compared to that using water. Sakanova et al. [11,12] reported results from a DL-MCHS and a
double-side MCHS (DS-MCHS) using Al2O3-water nanofluid [11],
Ti
DT
Wm
Ws
inlet-coolant temperature (°C)
temperature difference between inlet and outlet coolant
(°C)
model width (m)
substrate width (m)
Greek symbols
l
dynamic viscosity of the coolant (kg/ms)
q
density of the coolant (kg/m3)
u
nanoparticle volume fraction (%)
Subscripts
bf
base fluid
bt,max bottom maximum
f
fluid
i,o
inlet_outlet
nf
nanofluid
p
nanoparticle
with a wavy MCHS using three different nanofluids [12]. They
showed that the thermal performances of the heat sinks using
the Al2O3-water nanofluid with u ¼ 1% and u ¼ 5% were substantially better than those using water. The convective heat transfer
and friction factor of Cu-water nanofluids in a cylindrical
microchannel heat sink were experimentally studied by Azizi
et al. [13,14]. For the same Reynolds number, the corresponding
Nusselt numbers of the heat sink with u being 0.05%, 0.1% and
0.3% were enhanced approximately 17%, 19%, and 23%, compared
to that using pure water, respectively. A ribbed MCHS using
Al2O3-water nanofluids was numerically investigated by Ghale
et al. [15]. They revealed that the Nusselt number and friction factor of nanofluids in the ribbed microchannel were higher than
those of a straight microchannel without rids inside. Nebbati and
Kadja [16] presented a numerical study on a microchannel heat
sink using Al2O3-water nanofluid. They reported that the heat
transfer coefficient of a heat sink using nanofluid was significantly
increased in comparison with pure water. Parametthanuwat et al.
[17] presented an experimental study on thermal properties of silver nanofluids. They revealed that a silver nanofluid with u ¼ 1%
at a temperature of 80 °C yielded the highest heat transfer
enhancement. PCM slurry and nanofluid coolants were numerically
investigated in a DL-MCHS by Rajabifar [18]. The author revealed
that the pumping power of both PCM slurry and nanofluid was significantly raised for their higher viscosity. A M-MCHS using
nanofluids was numerically investigated by Yue et al. [19]. They
concluded that the increase in the nanoparticle diameter led to
the decrease in the Nusselt number, pumping power, and performance index. Recent investigations using nanofluids in microchannel heat sinks were reported by Kim et al. [20], Radwan et al. [21],
Xia et al. [22], Yang et al. [23], and Zhao et al. [24]. The results in
[20] showed that the thermal resistance of the flat-plate heat pipes
with Al2O3-Acetone nanofluids containing sphere-, brick- and
cylinder-shaped nanoparticles were decreased by 33%, 29%, and
16%, respectively, as compared to that using pure acetone. Radwan
et al. [21] concluded that the use of nanofluids in MCHSs was quite
effective. Xia et al. [22] revealed that the thermal conductivity and
dynamic viscosity of Al2O3 and TiO2 nanofluids were both
increased with the increase in u. Yang et al. [23] reported that
the nanoparticle volume fraction and the fins aspect ratio played
a very important role in the enhancement in the heat transfer of
the MCHSs. Zhao et al. [24] reported that the pressure drop could
N. Tran et al. / International Journal of Heat and Mass Transfer 117 (2018) 787–798
be improved by increasing the nanoparticle volume fraction and
decreasing particle size. Very recently, investigations on nanofluids
in MCHSs were reported by Abdollahi et al. [25], Anbumeenakshi
and Thansekhar [26], Duangthongsuk and Wongwises [27], Sarafraz et al. [28], and Tafarroj et al. [29]. In these reports, the thermal
performances of the nanofluids were experimentally examined,
and nanofluids with high thermal conductivities were recommended in MCHSs.
Based on the foregoing reviews, it is found that the multi-nozzle
microchannel heat sinks could significantly improve the overall
thermal resistance, remarkably decrease the pressure drop, and
considerably enhance the temperature uniformity in association
with those of the SL-MCHSs, DL-MCHSs, and M-MCHSs. However,
the MN-MCHSs had been only examined by using water as a working fluid with rectangular and square microchannel shapes [4].
Recently, Tran et al. [30] reported performance for five different
channel shapes. They found that the thermal performances of
trapezoidal channel shapes with 0:33 6 c 6 1 outperformed that
of a square channel shape at the same Reynolds number and
hydraulic diameter. However, in their study, the height of the
trapezoidal channels was fixed at 200 mm, and the trapezoidal
channel is not yet implemented in MN-MCHSs. In addition, the
investigated MN-MCHSs only utilized silicon and copper as substrate’s materials in two individual studies. Therefore, more studies
pertaining to the MN-MCHSs should be carried out for elaboration
of related details.
For fulfilling and bridging the gap of the aforementioned lacking
datum in the MN-MCHS field, and a strong desire for finding out a
heat sink that can dissipate a higher heat transfer rate in a smaller
size with a more uniform temperature and a lower pressure drop is
the objective of this study. Effects of the substrate materials,
nanofluids, and channel hydraulic diameters on the thermosfluids characteristics of a multi-nozzle trapezoidal microchannel
MNT-MCHS in association with some optimal layouts will be
reported in this study.
789
2.2. Geometric design of a new multi-nozzle trapezoidal microchannel
heat sink
Fig. 1(a) presents a structure of a multi-nozzle microchannel
heat sink with trapezoidal channel shapes (MNT-MCHS). Gray
parts on the top of the Fig. 1(a) are the top cover of the heat sink.
A yellow part is a substrate. Blue and red parts are inlet and outlet
channel nozzles, respectively. Fig. 1(b) presents a unit cell of the
MNT-MCHS, which includes parts of the MNT-MCHS such as the
substrate, channel, channel inlet, channel outlet and top cover.
In this study, the unit cell was used as a computational model
for analysis. The detailed dimensions of the substrate, computational model, and channels are shown in Fig. 1(c) and (d). All
dimensions, which were presented by specific numbers in the
Fig. 1(c) and (d), are constant in this study, while the dimensions,
presented by symbolic texts, will be altered in Section 3.2. The
function of the top cover is not only to cover the channel, but also
to separate the inlet and outlet nozzle of the channel. Therefore,
the top cover length must always exist, and its length, Lt, can be
calculated by
Lt ¼ Lc 2Ln :
ð1Þ
The substrate height, Hs, is fixed, but the channel depth, Dc, is
variable in the investigative process leading to the values of the
bottom thickness, Bth , to be changed depending on the channel
depth, and can be calculated by:
Bth ¼ Hs Dc :
ð2Þ
With this structure of the MNT-MCHS, the channels can be
arrayed on the substrate following both row and column directions. The number of channels can be calculated for a row, Nr, a column, Nc, or a total number of the channels on the heat sink, Nt,
respectively, as follows:
Nr ¼ W s =W m ;
ð3Þ
Nc ¼ Ls =Lm ;
ð4Þ
2. Methodology
Nt ¼ Nr Nc :
ð5Þ
2.1. Work description
where Ws, Ls, Wm, and Lm are the substrate width, substrate length,
model width, and model length, respectively.
In the present study, the effects of substrate materials, channel
hydraulic diameters, nanofluids, heat fluxes, and inlet-coolant temperatures on thermodynamic properties of multi-nozzle trapezoidal microchannel heat sinks were individually investigated in
four sections. In Section 3.1, five substrate’s materials, including
copper, aluminum, silicon, iron, and stainless steel 304, were
examined in detail based on the following given parameters: a
constant heat flux, qw = 250 W/cm2, Reynolds numbers from 100
to 900, a top-channel edge, a = 100 mm, a bottom-channel edge,
b = 300 mm, a channel depth, Dc = 200 mm, a constant inletcoolant temperature, Ti = 24 °C, and three coolants, including two
nanofluids Al2O3-water and TiO2-water and pure water. It is noted
that the nanoparticle volume fraction was fixed at u = 0.5% in Sections 3.1 and 3.2. In Section 3.2, the channel hydraulic diameters,
from 157.7 mm to 248.2 mm, were examined in detail by using
the above-given parameters and altering the channel depth (Dc),
from 150 mm to 350 mm. Based on the results obtained in Sections
3.1 and 3.2, a substrate material and a channel hydraulic diameter,
which yielded the best thermal performance in these sections,
would be selected as a locally optimal model for analysis in
subsequent sections. In Section 3.3, the nanofluids with various
nanoparticle volume fractions, u, of 0.1%, 0.5% and 1.0%, were
examined in detail. Finally, heat fluxes in the range from 100 W/cm2
to 1450 W/cm2 and inlet-coolant temperature ranging from 15 °C
to 75 °C were investigated in detail in Section 3.4.
2.3. Mathematic model
For simplifying in analyzing processes, assumptions of the computational model were analogous to some previous studies
[4,19,30,31]:
(1) thermophysical properties of the fluids and the solid were
assumed to be temperature independent;
(2) the flow was assumed to be three-dimensional, single phase,
steady state, incompressible and laminar;
(3) the gravitational force was neglected, and there was no
internal heat generation within the model;
(4) the walls of the channel had a no-slip condition for velocity
and temperature.
According to the above assumptions and some literatures
[4,7,8,12,30,32–35], the governing equation for computing thermodynamic processes in this study could be written as follows:
Continuity equation
@u @ v @w
þ
¼ 0;
þ
@x @y @z
ð6Þ
where u, v and w are the velocity components of the coolant in x-,
y-, and z-directions, respectively.
790
N. Tran et al. / International Journal of Heat and Mass Transfer 117 (2018) 787–798
Fig. 1. A multi-nozzle trapezoidal microchannel heat sink.
Momentum equations
!
@u
@u
@u
@p
@2u @2u @2u
¼ þl
q u þv þw
þ
þ
;
@x
@y
@z
@x
@x2 @y2 @z2
q u
@v
@v
@v
þv
þw
@x
@y
@z
¼
!
@p
@2v @2v @2v
;
þl
þ
þ
@y
@x2 @y2 @z2
ð7aÞ
ð7bÞ
!
@w
@w
@w
@p
@2w @2w @2w
þw
¼ þl
q u þv
þ 2 þ 2 ;
@x
@y
@z
@z
@x2
@y
@z
ð7cÞ
where l, q and p are the dynamic viscosity, density, and pressure
drop of the coolants, respectively. The boundary conditions of the
inlet flow are u ¼ 0; v ¼ 0 and w ¼ w0 . The boundary condition of
the outlet flow is p = p0, where p0 is the pressure of the ambient
environment (atmosphere pressure).
791
N. Tran et al. / International Journal of Heat and Mass Transfer 117 (2018) 787–798
Energy equation for the coolants
u
kf
@T
@T
@T
þv
þw
¼
@x
@y
@z qf cp;f
2.5. Thermophysical properties of nanofluids
!
@2T @2T @2T
þ
þ
;
@x2 @y2 @z2
ð8aÞ
where T, cp;f , qf , and kf are temperature, specific heat at a constant
pressure, density, and thermal conductivity of the fluid (coolants),
respectively. The boundary condition for the inlet is T = Ti, where
Ti is the inlet temperature of the coolant.
Energy equation for the solid
ks
@2T @2T @2T
þ
þ
@x2 @y2 @z2
!
¼ 0;
ð8bÞ
where ks is the thermal conductivity of the solid. Boundary conditions for the solid are given as follows: the bottom wall of the substrate is a constant heat flux and the four side walls of the
computational mode are symmetric while the other walls are
adiabatic. For no-slip condition, uwall = vwall = wwall = 0. For a steady
state condition and an incompressible flow, @@tq ¼ 0; @V
¼ 0; @T
¼0
@t
@t
and@p
¼ 0.
@t
C p;nf ¼
In the present study, three-dimensional, fluid-solid, conjugate
modules of the CFD-ACE+ [36] software package were employed
to analyze the computational models. A high accurate meshing
method, which was proposed in [30], was employed for the meshing process, and one of the meshed computational models is
presented in Fig. 2(a). According to the assumptions of the computational model as presented in Section 2.3, all outer walls except
the bottom wall of the computational model are symmetrical or
thermally insulated, and there is no heat generation within the
model. Therefore, Eq. (9) is utilized to verify all the simulated
results with maximum percentage errors being less than 1.5%.
ð9Þ
where qw is the heat flux applied on the bottom wall of the computational model, M is the mass flow rate of the coolant passed
through the channel, C p is the specific heat of the coolant, T o is
the outlet-coolant temperature, and T i is the inlet-coolant temperature. Lm and W m are the length and width of the computational
model, respectively. In addition, experimental results of a cylindrical microchannel heat sink, which was reported by Azizi et al. [14],
were utilized to verify the present simulated results. The C-MCHS
included 86 channels with a channel width of 0.526 mm, a channel
depth of 0.6 mm, a channel length of 50 mm, and a rib width
of 0.5 mm. The channels were equilaterally circularly arrayed outside of a cylinder with an outside diameter of 30 mm, as presented
in Fig. 2(b). A constant heat flux was applied along the centered axis
of the C-MCHS by using a single cartridge heater with an outside
diameter of 10 mm and a length of 50 mm. A unit cell as presented
in Fig. 2(c), including parts of the cylindrical heat sink such as the
channel, substrate, rib, inlet and outlet, was utilized as a verifying
model. All boundary conditions for the verifying model were
applied by the experimental conditions reported in [14]. Fig. 2(d)
shows relevant dimensions of the unit cell and Fig. 2(e) presents a
comparison between simulated results and experimental results
by Azizi et al. [14]. As depicted in the figure, good agreements
between the simulation and measurements were achieved with a
maximum deviation being less than 3%. Fig. 2(f) presents a temperature profile of the verifying model at a Reynolds number of 400.
The temperature distribution of the temperature profile was similar
to that reported in [14].
ð1 uÞqbf C p;bf þ uqp C p;p
qnf
¼
ð1 uÞqbf C p;bf þ uqp C p;p
;
ð1 uÞqbf þ uqp
ð10Þ
where C p , u, and q are the specific heat at a constant pressure,
nanoparticle volume fraction, and density, respectively. The subscripts, nf, bf, and p, stand for nanofluids, base fluid, and nanoparticle, respectively. It is noted that the subscripts for nanofluids
mentioned here are used for all sections in this study. The density
of the nanofluids was calculated by the following equation [9,19]:
qnf ¼ qp u þ qbf ð1 uÞ;
ð11Þ
where u is the nanoparticle volume fraction. The thermal conductivity of nanofluids with spherical particles, which was proposed
by Yu and Choi [37] as follows [2,9,14]:
knf ¼
2.4. Computational model validation
qw ¼ MC p ðT o T i Þ=ðLm W m Þ;
For calculations of the performance of nanofluids in microchannels, the thermophysical properties of nanofluids are needed and
can be obtained from some published literatures. The specific heat
of the nanofluids was calculated by using Eq. (10) [8,14,18]:
kp þ 2kbf þ 2uðkp kbf Þ
kbf ;
kp þ 2kbf þ uðkp kbf Þ
ð12Þ
where k is the thermal conductivity, u is the nanoparticle volume
fraction. The dynamic viscosity of nanofluids was calculated as follows [14,38,39]:
lnf ¼ lbf ð1 þ 2:5u þ 6:2u2 þ . . .Þ;
ð13Þ
where lnf and lbf are the dynamic viscosity of nanofluids and the
base fluid, respectively. u is the nanoparticle volume fraction. Specifications of nanoparticles, which were used in this study, are listed
in Table 1 [22]. Thermophysical properties of nanofluids based on
water, which were examined in this study, are listed in Table 2.
3. Results and discussion
3.1. Substrate material examination
To examine the effects of substrate materials on the MNTMCHS, five substrate materials, including copper, aluminum, silicon, iron, and stainless steel 304, were examined in detail. The unit
cell in Section 2.2 (Fig. 1(b)) was utilized as a computational model.
The given parameters mentioned in Section 2.1 were applied in
analytical processes. A channel depth of 200 mm, an inlet-nozzle
length of 400 mm, and a top cover length of 800 mm were considered. Three coolants, including Al2O3-water and TiO2-water with
a nanoparticle volume fraction of 0.5%, and pure water, were used
in the examinations. The thermophysical properties of the substrate and top cover’s materials are listed in Table 3 with Reynolds
number ranging from 100 to 900:
Re ¼
w q Dh
l
;
ð14Þ
where l, w, and q are the dynamic viscosity, inlet velocity, and density of the coolant, respectively. Dh is the channel hydraulic diameter, and calculated by the following equation:
Dh ¼
4A
¼
P
2ða þ bÞDc
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ;
2
ða þ bÞ þ ðb aÞ þ 4D2c
ð15Þ
where a, b and Dc are the channel-top edge, channel-bottom edge,
and channel depth, respectively. The overall thermal resistance,
RT , was calculated by the following equation [1,4]:
792
N. Tran et al. / International Journal of Heat and Mass Transfer 117 (2018) 787–798
Fig. 2. A comparison between Num. and Exp. results, which presented by Azizi et al. [14].
Table 1
Specifications of nanoparticles.
Nanoparticles
Diameter (nm)
Density (kg/m3)
Specific heat (J/kg K)
Purity (%)
Al2O3
TiO2
5
5
3680
4230
79.77
69.09
99
99
793
N. Tran et al. / International Journal of Heat and Mass Transfer 117 (2018) 787–798
Table 2
Thermophysical properties of nanofluids based on deionized water.
Nanofluids
u (%)
k (W/mK)
Cp (J/kgK)
q (kg/m3)
m (kg/ms)
Al2O3
0.1
0.5
1.0
0.621
0.633
0.642
4163
4116
4056
1000
1010
1024
0.000990
0.000995
0.001010
TiO2
0.1
0.5
1.0
0.631
0.638
0.651
4163
4104
4034
1000
1013
1030
0.000993
0.001016
0.001019
DI water
0
0.611
4178
996
0.000859
Table 3
Thermophysical properties of substrates and top cover’s materials.
Materials
k (W/mK)
Cp (J/kgK)
q (kg/m3)
Copper
Aluminum
Silicon
Iron
Stainless steel 304
PMMA
386
220
148
71.8
15.5
0.19
380
896
702
452
510
1960
8954
2707
2329
7897
7955
1420
RT ¼
T max T min T bt;max T i
¼
;
Q
Q
substrate with lower thermal conductivity depicts a larger temperature difference between the bottom wall of the substrate and the
bottom wall of the channel. A maximum temperature of the model
using stainless steel as a substrate material was much higher than
that using copper as seen in Fig. 3(d). In this regard, the effective
thermal resistance of stainless steel significantly exceeds other
materials as shown in Fig. 3(a). A further comparison of Fig. 3(c)
and (d), the temperatures on the bottom of the MNT-MCHSs were
very uniform for each single substrate material. This is one of the
improvements of the MNT-MCHS in comparison with those of
SL-MCHS, and DL-MCHS.
ð16Þ
3.2. Influence of channel hydraulic diameter
where T max is a maximum temperature of the heat sink, T min is a
minimum temperature of the heat sink, and Q is the heat transfer
rate of the heat sink.
Fig. 3(a) presents an overall thermal resistance, RT, of the MNTMCHS, using TiO2-water with u ¼ 0:5% as a working fluid, subject
to the influence of substrate materials and Reynolds number (Re).
As expected, RT declined consecutively with the rise of Reynolds
number and the trend is in line with previous efforts [30]. When
the Re is increased from 100 to 900, the RT of the MNT-MCHS using
copper as a substrate material and TiO2-water nanofluid decreased
from 0.289 °C/W to 0.089 °C/W. It was found that with the same
coolant and Reynolds number, the overall thermal resistance of a
MNT-MCHS using a substrate material with higher thermal conductivity was smaller than those with smaller thermal conductivities. At a Reynolds number of 900 and a heat flux of 250 W/cm2,
the overall thermal resistance of a MNT-MCHS using copper as a
substrate material is improved up to 15.3%, 21.6%, 41.1%, and
76% as compared to those using aluminum, silicon, iron, and stainless steel 304, respectively. It is noted that the thermal conductivity of copper is higher than those of aluminum, silicon, iron, and
stainless steel being 1.75 times, 2.6 times, 5.3 times, and 24.9
times, respectively.
Fig. 3(b) presents the overall thermal resistance versus
Reynolds number for MNT-MCHSs subject to various nanofluids.
For the present nanofluids, it was found that the overall thermal
resistance of a MNT-MCHS using a coolant with higher thermal
conductivity was smaller than those with smaller thermal conductivities [21].
Fig. 3(c) presents temperature profiles of the computational
model using copper as a substrate material with three different
coolants at a Reynolds number of 450. In this case, all boundary
conditions and the substrate material are the same except the difference of the coolants. The profiles show that the bottom temperature of the model using TiO2-water as a coolant was smaller than
those using Al2O3-water and pure water. This reflects the distribution of the overall thermal resistance associated with the different
coolants in Fig. 3(b).
Fig. 3(d) presents surface temperature distributions using
TiO2-water as a working fluid with five different substrate’s materials at a Reynolds number of 450. With the same wall thickness, a
To examine the effects of channel hydraulic diameter on the
performance of the MNT-MCHS, the channel depth was altered
from 150 mm to 350 mm that corresponds with the hydraulic diameter from 157.7 mm to 248.2 mm. To maintain a constant mean
velocity of the coolant along the channel from the inlet to the outlet, the nozzle length must be satisfied with the following
equation.
Ln ¼ Dc aþb
¼ 2Dc ;
2a
ð17Þ
where Dc is the channel depth, a is the top edge of the channel, and
b is the bottom edge of the channel. In this case, the inlet-nozzle
length was altered from 300 mm to 700 mm. Copper and TiO2water nanofluid were selected as the substrate material and the
working fluid for the simulation.
Fig. 4(a) presents the overall thermal resistance versus the Reynolds number subject to the influence of channel depths. It was
found that the RT of a model with deeper channel depth was smaller than those with shallower channel depths. At a Reynolds number of 900, the overall thermal resistances of the MNT-MCHS, with
channel depths of 150 mm, 200 mm, 250 mm, 300 mm, and 350 mm,
were 0.114 °C/W, 0.089 °C/W, 0.088 °C/W, 0.083 °C/W, and 0.076
°C/W, respectively. Fig. 4(b) shows that the pressure drop also rose
with the increase in Reynolds number [14,40] and the decrease in
channel depth (shallower channels) [4,41]. Fig. 4(c) presents temperature profiles of the computational model with five different
channel depths at a Reynolds number of 450. Since the effective
surface area rises with the steeper channel, a smaller thermal resistance is therefore expected, and the incurred maximum temperature of a deeper channel depth was smaller than those with
shallower channel depth as presented in Fig. 4(c). Fig. 4(d) presents
the velocity profiles of the computational model with different
channel depths at a Reynolds number of 450. At the same Reynolds
number, the coolant velocity in a channel with a deeper channel
depth or a greater hydraulic diameter was smaller than those with
shallower channel depths or smaller hydraulic diameters
(Eq. (14)). The significant rise in the pressure drop, in Fig. 4(b), is
associated with the considerable rise of the coolant velocity as presented in Fig. 4(d).
794
N. Tran et al. / International Journal of Heat and Mass Transfer 117 (2018) 787–798
Fig. 3. RT vs. Re with different coolants and substrate’s materials.
3.3. Different nanofluids with different nanoparticle volume fractions
examination
Fig. 5(a) presents the overall thermal resistance of the MNTMCHS with different nanofluids, nanoparticle volume fractions,
and Reynolds numbers. It was found that the overall thermal resistance of the MNT-MCHS using a nanofluid with a greater thermal
conductivity and a greater nanoparticle volume fraction was smaller than those with smaller thermal conductivities and smaller
nanoparticle volume fractions [23,24]. On the other hand, the
negligible difference in the overall thermal resistances between
Al2O3-water and TiO2-water nanofluids is encountered. However,
a minimum overall thermal resistance of the MNT-MCHS using
TiO2-water nanofluid at a nanoparticle volume fraction of 1% was
improved up to 6.7% relative to that using pure water
[9,11,12,16]. In fact, at a Reynolds number of 900, the minimum
overall thermal resistances of the MNT-MCHS, using TiO2-water
nanofluid at a nanoparticle volume fraction of 1% and using water,
were 0.0761 °C/W and 0.0818 °C/W, respectively. Fig. 5(b) presents
temperature profiles of the MNT-MCHS with different nanofluids
and different nanoparticle volume fractions at a Reynolds number
of 450. The profiles show that the maximum temperature on the
bottom wall of the MNT-MCHS using a nanofluid with a higher
thermal conductivity and a higher nanoparticle volume fraction
was smaller than those using nanofluids with smaller thermal conductivities and smaller nanoparticle volume fractions or pure
N. Tran et al. / International Journal of Heat and Mass Transfer 117 (2018) 787–798
795
Fig. 4. RT and pressure drop vs. Re with different channel depths (different hydraulic diameters).
water, corresponding to the RT distribution presented in Fig. 5(a)
[22,24].
Fig. 5(c) presents velocity profiles of the MNT-MCHS using different nanofluids with different nanoparticle volume fractions at a
Reynolds number of 450. The velocity distributions show that the
velocities of the MNT-MCHS using nanofluids with different
nanoparticle volume fractions were insignificantly different. The
velocity of the MNT-MCHS using water was slightly smaller than
those using nanofluids. The velocity distributions indicated that
the pressure drops among the MNT-MCHSs using nanofluids were
insignificantly different [25,27], but were slightly higher than that
using water. For all cases in Sections 3.1–3.3, it was found that a
minimum overall thermal resistance of 0.0761 °C/W or the best
thermal performance was achieved by a MNT-MCHS with a
channel depth of 350 mm using TiO2-water nanofluid with a
nanoparticle volume fraction of 1% as a working fluid and copper
as a substrate’s material. Therefore, this model was selected as a
locally optimal model and was utilized for analysis in the rest of
this study.
3.4. Heat flux and inlet-coolant temperature examination
To examine the effects of the heat flux and the inlet-coolant
temperature on the thermodynamic characteristics of the MNTMCHS, the locally optimal model was employed for the analysis.
Heat fluxes, from 100 W/cm2 to 1450 W/cm2, were examined in
detail using the boundary conditions mentioned in Section 3.3
with an inlet-coolant temperature of 24 °C. Inlet-coolant temperatures, from 15 °C to 75 °C, were also examined in detail with a fixed
heat flux of 250 W/cm2.
796
N. Tran et al. / International Journal of Heat and Mass Transfer 117 (2018) 787–798
Fig. 5. RT vs. Re with different coolants and different nanoparticle volume fractions.
Fig. 6(a) presents overall thermal resistances and the maximum
temperatures of the locally optimal MNT-MCHS versus heat fluxes.
The results show that the overall thermal resistances were independent of the heat flux [4]; however, the maximum temperature
linearly increased with the increase in the heat flux. With the
increase in the heat flux on the same heat transfer area, the heat
transfer rate would be increased that leads to the increase in the
temperature difference between the bottom wall of the heat sink
and the bottom wall of the channels. In addition, with the increase
in heat transfer rate at the same mass flow rate, the temperature
difference between coolant inlet and outlet would also be
increased. It was found that the locally optimal MNT-MCHS, using
the TiO2-water nanofluid with a nanoparticle volume fraction of
1%, could dissipate a heat flux up to 1450 W/cm2, and kept the
temperature rise above the inlet-coolant under 97.3 °C at a
Reynolds number of 900. At the same Reynolds number of 900
with copper as the substrate material, the minimum overall thermal resistance of the MNT-MCHS in the present study is improved
up to 11.6% and 36.6% as compared to those of a MN-MCHS with a
square channel shape which was reported by Tran et al. [30], and
an optimal DL-MCHS was also reported by Hung et al. [42],
respectively.
Fig. 6(b) presents maximum temperatures on the bottom wall
of the heat sink and the temperature differences between inlet
and outlet versus inlet coolant temperatures. The results show that
the maximum temperature of the bottom wall of the heat sink
increased with the increase in the inlet coolant temperature. It
was found that the overall thermal resistance and the temperature
difference between coolant inlet and outlet were independent on
the inlet-coolant temperature. In this case, the heat flux, the
N. Tran et al. / International Journal of Heat and Mass Transfer 117 (2018) 787–798
797
Fig. 6. Tmax, RT, and DT vs. heat flux and Ti.
bottom wall area of the substrate, the thermophysical properties of
the coolant, and the overall thermal resistance were constant;
therefore, when the inlet coolant temperature increased, the heat
sink changed to another thermal equilibrium, and the maximum
temperature would be increased exactly equal to the increase in
the inlet temperature (Eq. (16)).
Based on the results obtained in this study, a novel equation for
predicting the maximum temperature on the bottom wall of the
optimal MNT-MCHS depending on the inlet coolant temperature,
heat flux, and Reynolds number was proposed as follows:
The maximum temperatures of the optimal MNT-MCHS with
different heat fluxes at a Re = 900 depending on the inlet-coolant
temperature, which were obtained by the proposed equation, are
presented in Fig. 6(c). Maximum temperatures of the optimal
MNT-MCHS with different Reynolds numbers at a heat flux of
250 W/cm2, which were also obtained by the proposed equation,
are presented in Fig. 6(d).
T bt;max ¼ T i þ P qw R Abt;s ;
In this study, a new MNT-MCHS was proposed. A plate of 9 9 0.5 mm was considered as a fixed substrate. Effects of substrate
materials, channel hydraulic diameters, nanofluids, heat fluxes, and
inlet-coolant temperatures were reported in detail. Based on the
present analyzed results, conclusions can be summarized as follows:
ð18Þ
where T bt;max is the maximum temperature on the bottom wall of
the heat sink, T i is the inlet-coolant temperature, qw is the heat flux
applied on the bottom wall of the heat sink, R is a thermal resistance, Abt;s is the heat transfer area of the bottom wall of the heat
sink, and II is a novel dimensionless number depending on Reynolds
number. For the optimal MNT-MCHS using TiO2-water nanofluid
with u ¼ 1% as a working fluid, the dimensionless number, II,
was proposed as follows:
II ¼ 8:909 Re0:818 þ 0:042
where Re is Reynolds number.
ð19Þ
4. Conclusions
1. The thermal performance of a MNT-MCHS using a substrate
material with higher thermal conductivity was better than
those with smaller thermal conductivities.
2. An overall thermal resistance of a MNT-MCHS with a deeper
channel depth was smaller than those with shallower channel
depths.
798
N. Tran et al. / International Journal of Heat and Mass Transfer 117 (2018) 787–798
3. The overall thermal resistance of the MNT-MCHS, using TiO2water nanofluid with a nanoparticle volume fraction of 1%,
could improve up to 6.7% as compared to that using pure water.
4. A minimum overall thermal resistance in the present study
could be improved up to 11.6% and 36.6% as compared to those
of a MN-MCHS reported by Tran et al. [30], and an optimal DLMCHS reported by Hung et al. [42], respectively.
5. A nanofluid with higher thermal conductivity and higher
nanoparticle volume fraction would be achieved a higher
thermal performance compared to those with smaller thermal
conductivities and smaller nanoparticle volume fractions.
6. The overall thermal resistance of a MNT-MCHS was independent of heat fluxes or inlet-coolant temperatures, and the temperature difference between the coolant inlet and outlet were
also independent of the inlet-coolant temperature.
Conflicts of interest
The authors declare that there is no conflict of interest.
Acknowledgement
This work was supported by Ministry of Science Technology of
Taiwan, under a project number: MOST 106-2811-E-009-013. The
supports are deeply appreciated.
References
[1] D.B. Tuckerman, R.F.W. Pease, High-performance heat sinking for VLSI, IEEE
Electron Dev. Lett. EDL-2 (1981) 126–129.
[2] K. Vafai, L. Zhu, Analysis of two-layered micro-channel heat sink concept in
electronic cooling, Int. J. Heat Mass Transf. 42 (1999) 2287–2297.
[3] L. Boteler, N. Jankowski, P. McCluskey, B. Morgan, Numerical investigation and
sensitivity analysis of manifold microchannel coolers, Int. J. Heat Mass Transf.
55 (2012) 7698–7708.
[4] N. Tran, Y.-J. Chang, J.-T. Teng, T. Dang, R. Greif, Enhancement thermodynamic
performance of microchannel heat sink by using a novel multi-nozzle
structure, Int. J. Heat Mass Transf. 101 (2016) 656–666.
[5] S.U.S. Choi, A.J.A. Eastman, Enhance thermal conductivity of fluids with
nanoparticles, in: ASME International Mechanical Engineering Congress &
Exposition, ASME International Mechanical Engineering Congress &
Exposition, 1995, pp. 12–17.
[6] J.A. Eastman, S.U.S. Choi, I.J.T.S. Li, A.S. Lee, Enhanced thermal conductivity
through the development of nanofluids, Nanophase Nanocompos. Mater. II
MRS (1997) 3–11.
[7] T.-C. Hung, W.-M. Yan, Enhancement of thermal performance in doublelayered microchannel heat sink with nanofluids, Int. J. Heat Mass Transf. 55
(2012) 3225–3238.
[8] T.-C. Hung, W.-M. Yan, X.-D. Wang, C.-Y. Chang, Heat transfer enhancement in
microchannel heat sinks using nanofluids, Int. J. Heat Mass Transf. 55 (2012)
2559–2570.
[9] N.R. Kuppusamy, H.A. Mohammed, C.W. Lim, Thermal and hydraulic
characteristics of nanofluid in a triangular grooved microchannel heat sink
(TGMCHS), Appl. Math. Comput. 246 (2014) 168–183.
[10] B. Rimbault, C.T. Nguyen, N. Galanis, Experimental investigation of CuO–water
nanofluid flow and heat transfer inside a microchannel heat sink, Int. J. Therm.
Sci. 84 (2014) 275–292.
[11] A. Sakanova, S. Yin, J. Zhao, J.M. Wu, K.C. Leong, Optimization and comparison
of double-layer and double-side micro-channel heat sinks with nanofluid for
power electronics cooling, Appl. Therm. Eng. 65 (2014) 124–134.
[12] A. Sakanova, C.C. Keian, J. Zhao, Performance improvements of microchannel
heat sink using wavy channel and nanofluids, Int. J. Heat Mass Transf. 89
(2015) 59–74.
[13] Z. Azizi, A. Alamdari, M.R. Malayeri, Thermal performance and friction factor of
a cylindrical microchannel heat sink cooled by Cu-water nanofluid, Appl.
Therm. Eng. 99 (2016) 970–978.
[14] Z. Azizi, A. Alamdari, M.R. Malayeri, Convective heat transfer of Cu–water
nanofluid in a cylindrical microchannel heat sink, Energy Convers. Manage.
101 (2015) 515–524.
[15] Z.Y. Ghale, M. Haghshenasfard, M.N. Esfahany, Investigation of nanofluids heat
transfer in a ribbed microchannel heat sink using single-phase and multiphase
CFD models, Int. Commun. Heat Mass Transf. 68 (2015) 122–129.
[16] R. Nebbati, M. Kadja, Study of forced convection of a nanofluid used as a heat
carrier in a microchannel heat sink, Energy Procedia 74 (2015) 633–642.
[17] T. Parametthanuwat, N. Bhuwakietkumjohn, S. Rittidech, Y. Ding,
Experimental investigation on thermal properties of silver nanofluids, Int. J.
Heat Fluid Flow 56 (2015) 80–90.
[18] B. Rajabifar, Enhancement of the performance of a double layered
microchannel heatsink using PCM slurry and nanofluid coolants, Int. J. Heat
Mass Transf. 88 (2015) 627–635.
[19] Y. Yue, S.K. Mohammadian, Y. Zhang, Analysis of performances of a manifold
microchannel heat sink with nanofluids, Int. J. Therm. Sci. 89 (2015) 305–313.
[20] H.J. Kim, S.-H. Lee, S.B. Kim, S.P. Jang, The effect of nanoparticle shape on the
thermal resistance of a flat-plate heat pipe using acetone-based Al2O3
nanofluids, Int. J. Heat Mass Transf. 92 (2016) 572–577.
[21] A. Radwan, M. Ahmed, S. Ookawara, Performance enhancement of
concentrated photovoltaic systems using a microchannel heat sink with
nanofluids, Energy Convers. Manage. 119 (2016) 289–303.
[22] G.D. Xia, R. Liu, J. Wang, M. Du, The characteristics of convective heat transfer
in microchannel heat sinks using Al2O3 and TiO2 nanofluids, Int. Commun.
Heat Mass Transf. 76 (2016) 256–264.
[23] Y.-T. Yang, H.-W. Tang, W.-P. Ding, Optimization design of micro-channel heat
sink using nanofluid by numerical simulation coupled with genetic algorithm,
Int. Commun. Heat Mass Transf. 72 (2016) 29–38.
[24] N. Zhao, J. Yang, H. Li, Z. Zhang, S. Li, Numerical investigations of laminar heat
transfer and flow performance of Al2O3–water nanofluids in a flat tube, Int. J.
Heat Mass Transf. 92 (2016) 268–282.
[25] A. Abdollahi, H.A. Mohammed, S.M. Vanaki, A. Osia, M.R. Golbahar Haghighi,
Fluid flow and heat transfer of nanofluids in microchannel heat sink with Vtype inlet/outlet arrangement, Alexandria Eng. J. 56 (2017) 161–170.
[26] C. Anbumeenakshi, M.R. Thansekhar, On the effectiveness of a nanofluid
cooled microchannel heat sink under non-uniform heating condition, Appl.
Therm. Eng. 113 (2017) 1437–1443.
[27] W. Duangthongsuk, S. Wongwises, An experimental investigation on the heat
transfer and pressure drop characteristics of nanofluid flowing in
microchannel heat sink with multiple zigzag flow channel structures, Exp.
Therm. Fluid Sci. 87 (2017) 30–39.
[28] M.M. Sarafraz, V. Nikkhah, M. Nakhjavani, A. Arya, Fouling formation and
thermal performance of aqueous carbon nanotube nanofluid in a heat sink
with rectangular parallel microchannel, Appl. Therm. Eng. 123 (2017) 29–39.
[29] M.M. Tafarroj, O. Mahian, A. Kasaeian, K. Sakamatapan, A.S. Dalkilic, S.
Wongwises, Artificial neural network modeling of nanofluid flow in a
microchannel heat sink using experimental data, Int. Commun. Heat Mass
Transf. 86 (2017) 25–31.
[30] N. Tran, Y.-J. Chang, J.-T. Teng, R. Greif, A study on five different channel shapes
using a novel scheme for meshing and a structure of a multi-nozzle
microchannel heat sink, Int. J. Heat Mass Transf. 105 (2017) 429–442.
[31] N. Tran, Y.-J. Chang, J.-T. Teng, R. Greif, Enhancement heat transfer rate per unit
volume of microchannel heat exchanger by using a novel multi-nozzle
structure on cool side, Int. J. Heat Mass Transf. 109 (2017) 1031–1043.
[32] C. Leng, X.-D. Wang, T.-H. Wang, An improved design of double-layered
microchannel heat sink with truncated top channels, Appl. Therm. Eng. 79
(2015) 54–62.
[33] H.E. Ahmed, M.I. Ahmed, Optimum thermal design of triangular, trapezoidal
and rectangular grooved microchannel heat sinks, Int. Commun. Heat Mass
Transf.r 66 (2015) 47–57.
[34] B. Rajabi Far, S.K. Mohammadian, S.K. Khanna, Y. Zhang, Effects of pin tipclearance on the performance of an enhanced microchannel heat sink with
oblique fins and phase change material slurry, Int. J. Heat Mass Transf. 83
(2015) 136–145.
[35] N. Tran, Y.-J. Chang, J.-T. Teng, R. Greif, Enhancement heat transfer rate per unit
volume of microchannel heat exchanger by using a novel multi-nozzle
structure on cool side, Int. J. Heat Mass Transf. (2017) HMT_2016_3262.
[36] E.-Group, Advanced CFD-ACE + V2008.2 Modules Manual, ESI -Group
document, vol. 01, 2008, pp. 35–64.
[37] W. Yu, S. Choi, ‘‘The role of interfacial layers in the enhanced thermal
conductivity of nanofluids,” a renovated Maxwell model, J. Nanopart. Res. 5
(2003) 167–171.
[38] K. Khanafer, K. Vafai, A critical synthesis of thermophysical characteristics of
nanofluids, Int. J. Heat Mass Transf. 54 (2011) 4410–4428.
[39] C.T. Nguyen, F. Desgranges, N. Galanis, G. Roy, T. Maré, S. Boucher, et al.,
Viscosity data for Al2O3–water nanofluid—hysteresis: is heat transfer
enhancement using nanofluids reliable?, Int J. Therm. Sci. 47 (2008) 103–111.
[40] N. Tran, C. Zhang, T. Dang, J.-T. Teng, Numerical and Experimental Studies on
Pressure Drop and Performance Index of an Aluminum Microchannel Heat
Sink, 2012, pp. 252–257.
[41] N. Tran, Y.-J. Chang, J.-T. Teng, T. Dang, Numerical and experimental
investigations on heat transfer of aluminum microchannel heat sinks with
different channel depths, Int. J. Mech. Eng. Robot. Res. (2015).
[42] T.-C. Hung, W.-M. Yan, X.-D. Wang, Y.-X. Huang, Optimal design of geometric
parameters of double-layered microchannel heat sinks, Int. J. Heat Mass
Transf. 55 (2012) 3262–3272.
Документ
Категория
Без категории
Просмотров
1
Размер файла
3 789 Кб
Теги
051, ijheatmasstransfer, 2017
1/--страниц
Пожаловаться на содержимое документа