International Journal of Heat and Mass Transfer 177 (2021) 121542

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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier.com/locate/hmt

Heat transfer and pressure drop of refrigerant flow boiling in metal

foam filled tubes with different wettability
Haitao Hu∗, Zhancheng Lai, Yaxin Zhao
Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, Shanghai 200240, China

a r t i c l e i n f o a b s t r a c t

Article history: Surface wettability has a significant effect on the flow boiling heat transfer coefficient in metal foam
Received 23 February 2021 filled tubes. In the present study, the flow boiling characteristics of metal foam filled tubes with different
Revised 12 May 2021
wettability were experimentally investigated, covering the surface wettability of uncoated, hydrophobic
Accepted 28 May 2021
and hydrophilic surfaces. The results showed that, for the hydrophilic metal foam filled tubes, the heat
transfer coefficient and pressure drop are decreased by 2%–18% and 4%–15%, respectively than those for
Keywords: the uncoated ones; for the hydrophobic metal foam filled tubes, both the heat transfer coefficient and
Metal foam pressure drop are larger than those for uncoated ones, and the increments in the heat transfer and pres-
Wettability sure drop are 6%–30% and 8%–35%, respectively. Based on the experimental data, the correlations for heat
Flow boiling
transfer and pressure drop of flow boiling in metal foam filled tubes with different wettability were de-
Heat transfer
veloped with the deviations of ±6.4% and ±9.7%, respectively.
Pressure drop
© 2021 Elsevier Ltd. All rights reserved.

1. Introduction foam enhances the flow boiling heat transfer coefficient by a max-
imum of 185%, while the enhancement effect of metal foam is
Metal foam has large heat transfer area and high thermal con- weakened by the presence of lubricant oil [15]. Visualization re-
ductivity, which can enhance the flow boiling in metal foam filled sults show that slug flow, plug flow and annular flow occur in
tubes [1–3]. Therefore, inserting metal foam in tubes has become sequence with the increasing vapor quality in metal foam filled
one of the most effective heat transfer enhancement techniques tubes, and the transition from slug flow to plug flow happens at
[4–6]. Metal foam filled tubes show 2–4 time higher heat trans- lower vapor qualities with the increasing mass flux and pore den-
fer coefficient than traditional smooth tubes [7], while the pressure sity of metal foam [16]. Compared with a mini-channel evapora-
drop in metal foam filled tubes could also be increased due to the tor (ME) with the same footprint area, the heat transfer coefficient
flow resistance by metal foam [8]. Surface modification is an effec- in metal foam filled channels is enhanced by up to 1.5 time and
tive method to accelerate the boiling process and reduce the flow the dry-out is delayed [17]. Metal foam promotes the shift of flow
resistance in microchannels [9–14], and it may have the potential pattern from intermittent flow to annular flow [18]; the pressure
for enhancing flow boiling in metal foam filled tubes. In order to drop increases with the increasing vapor quality and velocity, and
quantitively effect of surface wettability on flow boiling in metal R1234ze(E) exhibits slightly higher two-phase pressure drop than
foam filled tubes, the heat transfer and pressure drop characteris- R134a and R1234yf, while the heat transfer performance of the
tics in metal foam filled tubes with different wettability should be three refrigerants are similar [19]. Correlations for the heat transfer
experimentally investigated. coefficient and pressure drop of flow boiling in metal foam filled
For the flow boiling in metal foam filled tubes, the existing re- tubes were developed [20,21]. The boiling heat transfer coefficient
search focuses on uncoated metal foam filled tube [15–23], and of nanofluid in metal foam filled tubes is enhanced by 9.4% due to
there is no research on the metal foam filled tubes with differ- the presence of nanoparticles, while the pressure drop is increased
ent wettability. The research results on uncoated metal foam filled by 82.7% [22]. However, the effect of surface wettability on flow
tubes show that, the heat transfer coefficient in the metal foam boiling in metal foam filled tubes was not reflected in the existing
filled tubes is about 2.5–3 time higher than that in smooth chan- research.
nels [23]; for the flow boiling of refrigerant-oil mixture, metal For the effect of surface wettability on heat transfer and pres-
sure drop in metal foam, the existing research focuses on pool boil-
ing [24,25], dehumidification [26,27] and condensation [28]. The
∗
Corresponding author. existing research results on the effect of surface wettability for
E-mail address: huhaitao2001@sjtu.edu.cn (H. Hu). pool boiling in metal foam show that, compared with uncoated

https://doi.org/10.1016/j.ijheatmasstransfer.2021.121542
0017-9310/© 2021 Elsevier Ltd. All rights reserved.
H. Hu, Z. Lai and Y. Zhao International Journal of Heat and Mass Transfer 177 (2021) 121542

wet air in metal foams show that, for hydrophobic metal foam,
Nomenclature the heat transfer coefficient and the pressure drop of wet air are
5%–34% and 1%–95% larger than those in uncoated metal foam, re-
A area, m2 spectively [26]; for hydrophilic metal foam, the heat transfer co-
C coefficient efficient of wet air is increased by 2–21%, and the pressure drop
d diameter, m is decreased by 1–15% [27]. For condensation in metal foams, hy-
EF effect factor drophobic metal foam filled tube achieves better heat transfer per-
G mass flux, kg m−2 s−1 formance and lower pressure drop than the uncoated metal foam
h heat transfer coefficient, W m−2 K−1 filled tube [28]. Till now, the effect of surface wettability on the
L length, m flow boiling in metal foam is still unknown and should be investi-
M molecular mass, g mol−1 gated
P pressure, kPa The purpose of present study is to experimentally investigate
Porosity porosity the flow boiling heat transfer and pressure drop in metal foam
PPI pore density filled tubes with different wettability, and to develop the heat
Pr prandtl number transfer and pressure drop correlations of flow boiling in metal
pr reduced pressure foam filled tubes.
Q heat power, W
q heat flux, W m−2 2. Design of experiment
R radius, m
Re reynolds number 2.1. Experimental apparatus and test section
T temperature, K
v velocity, m s−1 In the present study, the experimental apparatus for investigat-
x vapor quality ing the flow boiling characteristics in metal foam filled tubes with
different wettability was built, and it consists of a refrigerant loop,
Greek symbols
a cooling water loop and a data acquisition system, as shown in
λ thermal conductivity, W m−1 K−1
Fig. 1.
ν kinematic viscosity, m2 s−1
In the refrigerant loop, the mass flow rate in the test section
ε void fraction
is adjusted by the opening degree of the needle valve of the by-
σ surface tension, N m−1
pass circuit and the expansion valve of the main loop, and it can
μ dynamic viscosity, Pa s−1
be measured by the mass flow meter (Emerson CMF010 M Corio-
Ф two-phase multiplier
lis mass flowmeter, ± 0.1% FS). The vapor quality of the refrigerant
Xtt martinelli parameter
entering the test section can be adjusted by the cooling capacity of
Subscripts the subcooler and the heating power of the preheater. The refrig-
a advancing erant in the test section is vaporized, and the heat flux is adjusted
acc accelerate by the electric heating tape wrapped around the metal foam filled
af specific surface area tube. R134a is used as the working fluid in the experiment. The
crit critical temperature is measured by the T-type thermocouple with accu-
cb convective boiling racy of ± 0.1 K. The pressure is measured by the pressure senor
dry dry with accuracy of ±1 kPa. The pressure drop in the metal foam
tp two-phase filled tube is measured by the differential pressure senor with ac-
g gas curacy of ± 0.1 kPa. The measured data are recorded by the data
h heat transfer acquisition system, which consists of an Agilent data logger and
in inlet experimental sensors.
l liquid The test samples in this study are the copper foam filled tubes
mf metal foam with different wettability and various pore densities and porosities.
nb nucleate boiling The schematic diagram of the metal foam filled tube is shown in
out outlet Fig. 2. The copper foam and copper tube are welded together by
p pore the amorphous solder in vacuum furnace to reduce thermal resis-
࢞P pressure drop tance. The inner diameter of the copper tube is 7.9 mm, and the
r receding thickness of the tube wall is 1 mm.
ref refrigerant The metal foams with various structures inserted in tubes are
sat saturate shown in Fig. 3, covering the PPI (Pore number per inch) of 10–
SM surface modification 40 and the porosity of 0.90–0.95. The PPI is measured by counting
total total the cell number per unit length, and the porosity is obtained by
uncoated uncoated measuring the solid volume and the total volume [29,30].
w wall
2.2. Fabrication of hydrophilic and hydrophobic coating

metal foam, the pool boiling heat transfer coefficient in hydropho- In the present study, the effects of surface wettability on flow
bic metal foam is increased by a maximum of 36% at heat flux boiling heat transfer and pressure drop characteristics are inves-
smaller than 1.3 × 106 W m−2 , and the incipient boiling super- tigated. The wettability of metal foam surface includes uncoated,
heated degree is decreased by 0.4–1.4 K [24]; the super-hydrophilic hydrophilic, hydrophobic surfaces.
copper foam surface achieves better pool boiling heat transfer per- The hydrophilic and hydrophobic coatings on the metal sur-
formance in a high-heat flux region (q>20 W cm−2 ), while the face are fabricated by Alkali assisted oxidation method [31] and
super-hydrophobic surface shows a better performance when q<20 the molecular self-assembly method [32], respectively. For the hy-
W cm−2 [25]. The existing research results on dehumidification of drophilic surface modification process, the test sample is washed

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H. Hu, Z. Lai and Y. Zhao International Journal of Heat and Mass Transfer 177 (2021) 121542

Fig. 1. Schematic diagram of experimental apparatus.

Fig. 2. Schematic diagram of the experimental sample.

temperature for 15 min, and then heated in a vacuum oven at

100 °C for 1 h.
The contact angles of the test samples with different wettabil-
ity are measured by the optical contact angle measurement device
(KINO Industry Co., Ltd., USA). During the measurement process,
a small droplet is formed on the surface and then the needle is
brought close to the surface. The advancing contact angle is mea-
sured by increasing volume of the droplet whereas the receding
angle is obtained by the decreasing the volume of the droplet [33].
For the hydrophilic sample, the advancing and receding contact an-
gles are 15.4° and 7.3°, respectively; for the hydrophobic sample,
the advancing and receding contact angles are 163.9 o and 149.1 o ,
respectively [34].
The influence of different vapor quality, mass flux and heat
flux on the flow boiling heat transfer characteristics in metal foam
filled tubes should be analyzed. The experimental conditions cover
the vapor quality of 0.1–0.9, the mass flux of 90–180 kg m−2 s−1
Fig. 3. Photo of metal foam samples with different structures. and the heat flux of 12.4–18.6 kW m−2 .

2.3. Data reduction and uncertainty analysis

by hydrochloric acid, alcohol and acetone, and is immersed in an
aqueous solution of 2.5 mol L−1 sodium hydroxide (NaOH) and In the present study, the flow boiling heat transfer coefficient
0.1 mol L−1 ammonium persulphate ((NH4)2 S2 O8 ) for 30 min; the and pressure drop of refrigerant in metal foam filled tubes are ob-
hydrophilic CuO/Cu(OH)2 micro/nanostructures are formed on the tained based on the measured parameters. The calculation of flow
test sample surface. During the hydrophobic surface modification boiling heat transfer coefficient is shown in Eqs. (1)–(3):
process, the test sample with CuO/Cu(OH)2 micro/nanostructures q
is immersed in a 1% wt 1-dodecanethiol/alcohol solution at room h= (1)
Tin − Tref

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H. Hu, Z. Lai and Y. Zhao International Journal of Heat and Mass Transfer 177 (2021) 121542

Fig. 4. Repeatability results for experimental apparatus.

the accuracy of calibrated thermocouples is ± 0.1 °C. The uncer-

Rout
Q · ln Rin tainty of heat transfer coefficient can be calculated by the mea-
Tin = Tout − (2)
2π · K · L surement errors of heat flux, wall temperature and refrigerant tem-
perature, as shown in Eq. (9). The maximum uncertainty of heat
Q transfer coefficient is ± 12.1%. The pressure drop is measured by
q= (3)
2π Rin · L the pressure difference sensor with accuracy of ± 0.1 kPa, and the
maximum uncertainty of two-phase pressure drop is ± 3.8%. The
where, h is the heat transfer coefficient, kW m−2 K−1 ; Tin and Tout experimental instruments and uncertainties are listed in Table 1.
are the inside and outside tube wall temperature, K; Tref is the sat- 
uration temperature of refrigerant, K; Q is the heating power, kW;  2  2  2
q is the heat flux, kW m−2 ; K is the thermal conductivity of cop-
1
δ q + (T q2
δ Tw2 + q2
δ Tsat
2
δh Tw −Tsat w −Tsat )
2
(Tw −Tsat )2
per, kW m−1 K−1 ; L is the length of the metal foam filled tube, = q
h Tw −Tsat
m.
The calculation equation for the two-phase pressure drop is 2 2 2
δq δ Tw δ Tsat
shown as below: = + + (9)
q Tw − Tsat Tw − Tsat
Ptp = Ptotal − Pacc (4)
2.4. Repeatability test for experimental apparatus
   
x ( 1 − x )2 x (1 − x )2
Pacc = G2 + − G2 + (5) In order to verify the reliability of the experimental apparatus,
ε ρ g ( 1 − ε ) ρ1 out
ε ρ g ( 1 − ε ) ρ1 in a repeatability test was conducted for the uncoated 10 PPI metal
foam filled tube by repeating the measurement three time for each
  x 1−x  1.18 1 − x gσ ρ −ρ 0.25 −1
x ( )[ ( l v )] specific experimental condition. Fig. 4 shows the repeatability re-
ε= (1+0.12(1 − x )) + +
ρv ρv ρl Gρl0.5 sults for the experimental apparatus. The repeatability deviations
of the heat transfer coefficient and pressure drop are within 5.8%
(6) and 3.1%, respectively. Therefore, the measurements with the ex-
where ε is the void fraction [35]; ࢞Ptp is the two-phase pressure perimental apparatus are reliable.
drop, and ࢞Pacc is the acceleration pressure drop, kPa m−1 ; ρ is
the density, kg m−2 ; and G is the mass flux, kg m−2 s−1 . 3. Results and discussion
In order to quantitatively analyze the effect of wettability, the
surface modification heat transfer effect factor (EFh,SM ) and pres- 3.1. Heat transfer characteristics in metal foam filled tubes with
sure drop effect factor (EFp,SM ) are defined as the ratio of heat various wettability
transfer coefficient and pressure drop between the surface modi-
fied metal foam filled tubes and the uncoated ones, respectively, The flow boiling heat transfer coefficient in the metal foam
as shown in Eqs. (7) and (8): filled tubes with different wettability are shown in Fig. 5. With the
increasing mass flux (G) and heat flux (q), the boiling heat transfer
hsurfacemodified
E Fh,SM = (7) coefficient in the uncoated metal foam filled tube increases. The
huncoated possible reason is that, as the mass flux increases, the gas and liq-
uid velocities of refrigerant are increased and the convective heat
 psurfacemodified
E Fp,SM = (8) transfer is enhanced [21]; as the heat flux increases, the activation
 puncoated
of nucleation sites is promoted [38] and more bubbles generate in-
The experimental uncertainties are estimated with the analysis side the metal foam and on the wall, enhancing the boiling heat
method of error propagation [36]. The error of wall temperature transfer.
measurement can be reduced by taking the average of 9 thermo- Fig. 5(a) illustrates that, the heat transfer coefficient in the hy-
couples arranged on three planes of the experimental section, and drophilic metal foam filled tube is 2−18% smaller than that in the

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H. Hu, Z. Lai and Y. Zhao International Journal of Heat and Mass Transfer 177 (2021) 121542

Fig. 5. Flow boiling heat transfer coefficient in hydrophilic and hydrophobic metal foam filled tubes.

Table 1
Uncertainties of the measured and calculated parameters.

Parameter Source of uncertainty Instrument Range Uncertainty

Mass flux Instrumentation calibration Coriolis mass flowmeter (Emerson CMF010M) 0–108 kg h−1 ± 0.1% FS
Pressure Instrumentation calibration Pressure senor (Druck 5702PTX) 0–1 MPa ± 0.1% FS
Pressure drop Instrumentation calibration Differential pressure senor (Zhengde 106DP) 100 kPa ± 0.1% FS
Heating power Instrumentation calibration Power meter (YOTO) 0–1 kW ± 0.1% FS
Temperature Instrumentation calibration T-type thermocouple (OMEGA PX655–0.5DI) 0–100 °C ± 0.1 °Cs
Heat transfer coefficient Uncertainties and error propagation Calculated / ± 12.1%
Two-phase pressure drop Uncertainties and error propagation Calculated / ± 3.8%

uncoated metal foam filled tube. The reason for this phenomenon hydrophobic coating enhancing the flow boiling heat transfer is
is that, for the hydrophilic surface, the bubble detachment fre- consistent with the conclusion for pool boiling on hydrophobic
quency and the number of nucleation sites are decreased, resulting metal foam surface [24,38] due to the increasing nucleate sites and
in the deteriorated boiling heat transfer. This mechanism for de- the decreasing incipient boiling superheated degree.
creasing heat transfer coefficient is consistent with that in the mi-
crochannel [37]. Hydrophilic coating can improve the critical heat 3.2. Pressure drop characteristics in metal foam filled tubes with
flux on metal foam surface [38]. However, the heat flux under ex- various wettability
perimental conditions is much smaller than the critical heat flux,
and the hydrophilic modification deteriorates the flow boiling heat The flow boiling pressure drop of in the metal foam filled tube
transfer. with various wettability are shown in Fig. 6. Compared with the
Fig. 5(b) illustrates that, the flow boiling heat transfer coef- uncoated metal foam filled tube, the two-phase pressure drop of
ficient in the hydrophobic metal foam filled tube increases by the hydrophilic and hydrophobic metal foam filled tubes is in-
6−30% compared with that in the uncoated metal foam filled tube. creased by 4%−15% and 6%−30%, respectively, and the increment
Through the hydrophobic modification, the surface energy of metal effect of the hydrophobic modification on the pressure drop is
fiber surface is decreased, and the nucleation sites are increased, larger than that of the hydrophilic one. The possible reason is that,
resulting in the enhanced flow boiling. The phenomenon for the the hydrophilic surface has stronger adhesion force to the liquid

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H. Hu, Z. Lai and Y. Zhao International Journal of Heat and Mass Transfer 177 (2021) 121542

Fig. 6. Two-phase pressure drop in hydrophilic and hydrophobic metal foam filled tubes.

refrigerant while the hydrophobic surface increases the nucleation 4. Development of new correlation for flow boiling in metal
site number on metal fiber surface and hence more boiling bub- foam filled tubes
bles; the influence of hydrophobic modification is more significant
than that of hydrophilic modification, resulting in greater two- 4.1. Comparison between experimental data and existing correlations
phase pressure drop [11].
Until now, there is no heat transfer and pressure drop corre-
lations for the metal foam filled tubes with different wettability.
For the flow boiling heat transfer characteristics in metal foam
3.3. Surface wettability effect factors for heat transfer and pressure
filled tube, the correlations for heat transfer [21] and pressure drop
drop of flow boiling in metal foam filled tubes
[8] in uncoated metal foam filled tube were developed, but the
predictability of these correlations for the metal foam filled tubes
Fig. 7 shows the variation of surface wettability effect factors
with different wettability should be validated based on the ob-
for heat transfer and pressure drop of flow boiling in metal foam
tained data in the present study.
filled tubes with different wettability. The EFh,SM for hydrophobic
The deviations between predictions by the existing correlations
and hydrophilic metal foam filled tubes ranges within 1.06–1.30
and the experimental data are shown in Fig. 8. For flow boiling in
and 0.82–0.98, respectively, and the EFp,SM for hydrophobic and hy-
metal foam filled tubes with different wettability, the prediction
drophilic metal foam filled tubes ranges within 1.08–1.35 and 1.04–
deviation of heat transfer coefficient is within 40%, and the predic-
1.15, respectively. The hydrophobic modification always enhances
tion deviation of pressure drop is up to 70%. The possible reason
the heat transfer characteristics, and the maximal enhancement
for the large deviation is that the existing correlation does not re-
is 30%; while the hydrophilic modification always deteriorates the
flect the influence of different wettability.
heat transfer characteristics, and the maximal decrement is 18%.
Both the hydrophobic and hydrophilic modifications increase the
pressure drop, and the increment of the hydrophobic modification 4.2. New heat transfer correlation for flow boiling in metal foam
is larger than that of hydrophilic modification. Therefore, the flow filled tubes with different wettability
boiling performance of hydrophobic metal foam filled tubes is bet-
ter than that of hydrophilic metal foam filled tubes under experi- In the present study, the new heat transfer correlation for flow
mental conditions. boiling in metal foam with different wettability was developed

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H. Hu, Z. Lai and Y. Zhao International Journal of Heat and Mass Transfer 177 (2021) 121542

Fig. 7. Surface wettability effect factor for heat transfer and pressure drop in metal foam filled tubes.

based on the heat transfer correlation [21] of flow boiling in un- of vapor and liquid, respectively; hnb is the nucleate boiling heat
coated metal foam filled tubes. Zhu et al. correlation [21] was pro- transfer coefficient [21]; Pr is the reduced pressure and equals to
posed based on the experimental data of R410A and R134a in un- the ratio of refrigerant pressure to the critical pressure [21]; θ dry
coated metal foam filled tubes with inner diameter of 7.9–26 mm, is the dry angle [21].
and it could reflect the influence of metal foam structure and heat The key for developing the correlation is to obtain the ex-
flux, but the influence of surface wettability on heat transfer was pression of the surface wettability effect factor for heat trans-
not reflected. Therefore, the new correlation was developed based fer (EFh,SM ). The experimental results indicate that EFh,SM depends
on the modification of Zhu et al. correlation [21] by introducing upon the surface wettability, pore density and mass flux. Therefore,
the multiplier of surface wettability effect factor for heat transfer the correlation for EFh,SM is expressed as below:
(EFh,SM ), as shown in Eqs. (10)–(14). a·P P Ib ·(θA −θA,0 )·( GG )
c

E Fh,SM = e 0 (15)
hMF,SM = E Fh,SM · E Fh,MF · hNon−MF (10)
The coefficients a-c in Eq. (15) were fitted based on the exper-
  
3 1/3
imental data obtained in the present study and those in the liter-
θdry hv + 2π −θdry hnb 3 +hcb ature [2,21], covering the refrigerants of R134a and R410A, the PPI
hNon−MF = (11) of 10–40, the porosity of 90−95%, the mass flux of 90–180 kg m−2
2π
s−1 , and the vapor quality of 0.1–0.9. Based on the nonlinear fit-
0.4 λV ting method, the values of a-c were obtained as 0.0787, 0.1096 and
hv = 0.023Re0v.8 Pr (12) 0.7646, respectively.
v D
Fig. 9 shows the comparison of the proposed correlation with
−0.55
hnb = 55 p0r .12 (− log pr ) M−0.5 q0.67 (13) the obtained data in the present study and those in the literature
[2,3,15,21]. The deviations between the predicted heat transfer co-
efficients and experimental data are within ± 20%, and the average
0.4 λl
hcb = 0.0133Re0l .69 Pr (14) deviation is ± 6.4%.
l δ In the proposed heat transfer correlation, the influence of sur-
where, EFh,MF is the metal foam effect factor for flow boiling heat face wettability, refrigerant properties and structure parameters are
transfer [21]; hv and hcb are the convection heat transfer coefficient reflected. For the uncoated metal foam filled tube, the value of

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H. Hu, Z. Lai and Y. Zhao International Journal of Heat and Mass Transfer 177 (2021) 121542

Fig. 8. Prediction ability of existing correlations for metal foam filled tubes with different wettability.

Fig. 9. Predicted values of new heat transfer correlation versus experimental data
obtained in the present study and in the literature [2,3,15,21]. Fig. 10. Predicted values of new pressure drop correlation versus experimental data
obtained in the present study and in the literature [2,8,39].

EFh,SM is equal to 1.0, and the proposed correlation will be the 2 C 1

l,MF,sm = E Fp,SM · 1+ + (17)
same as that in the literature [21]. The correlation can be used to Xtt Xtt2
predict the flow boiling heat transfer characteristics of refrigerants
in metal foam filled tubes with different structure parameters and a · a2sf (1−ε )2 μl v b · asf (1−ε )ρl v2
Pl,MF = + (18)
different surface wettability. ε3 ε3
c
a·P P Ib ·(θA −θA,0 ) ·( qq )
2
E Fp,SM = e 0 (19)
4.3. New pressure drop correlation for flow boiling in metal foam where, ࢞Pl, MF is the pressure drop of liquid-phase refrigerant in
filled tubes with different wettability metal foam [39], kPa m−1 ; Ф2 is the liquid phase multiplier [39];
Xtt is the Martinelli parameter [39].
In the present study, a new pressure drop correlation for flow The key for developing pressure drop correlation for the metal
boiling pressure drop in metal foam filled tubes with different wet- foam filled tubes with different wettability is to obtain the expres-
tability was developed based on the two-phase multiplier model sion of EFp, SM . The coefficients a-c in Eq. (19) were fitted based
[39]. In the existing correlation, the influence of tube diameter, on the experimental data obtained in the present study and those
metal foam structure and refrigerant on two-phase pressure drop in the literature [2,8,39], covering the refrigerants of R134a and
was reflected, while the influence of surface wettability was not R410A. Based on the nonlinear fitting method, the values of a-c
included. Therefore, the new correlation reflecting the influence of were obtained as 0.0028, 0.985 and 0.9893, respectively.
wettability was developed based on the existing correlation [39] by Fig. 10 show the comparison of the proposed correlation with
introducing the surface wettability effect factor for pressure drop the experimental data obtained in the present study and in the
(EFp,SM ), as shown in Eqs. (16)–(19). literature [2,8,39]. The prediction results can agree with 98% of ex-
perimental data within the relative deviation of ± 25%, and the
PMF,SM = 2
l,MF,sm · Pl,MF (16) average deviation is 9.7%.

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H. Hu, Z. Lai and Y. Zhao International Journal of Heat and Mass Transfer 177 (2021) 121542

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