International Journal of Heat and Mass Transfer 79 (2014) 241–250

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer

journal homepage: www.elsevier .com/locate / i jhmt

Numerical investigation of ammonia falling film absorptionoutside vertical tube with nanofluids

http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.08.0160017-9310/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author at: Key Laboratory of Energy Thermal Conversion andControl of Ministry of Education, Southeast University, Nanjing 210096, China. Tel.:+86 25 83793214.

E-mail address: windy4ever@163.com (L. Yang).

Liu Yang a,b,⇑, Kai Du a,b, Xiaofeng Niu c, Yuan Zhang b, Yanjun Li b

a Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, Southeast University, Nanjing 210096, Chinab School of Energy and Environment, Southeast University, Nanjing 210096, Chinac College of Urban Construction and Safety Engineering, Nanjing University of Technology, Nanjing 210009, China

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

Article history:Received 24 August 2013Received in revised form 4 August 2014Accepted 6 August 2014Available online 27 August 2014

Keywords:Ammonia waterNumericalFalling-film absorptionNanofluid

In the last years the ammonia-water refrigeration cycle has been gradually improved by using nanofluidtechnology. In this work, a numerical model for the absorption of ammonia on a falling film was devel-oped for different ammonia-water mixtures containing nanoparticles and dispersants. The variation ofboth falling film thickness and physical properties of the mixture were considered to find the best fittingmodel. Results show that when absorption pressure decreases or when initial concentration of mixtureincreases, the relative intensity of effect on absorption rate is weakened by the variation of thermalconductivity but enhanced by the variation of mass transfer coefficients and flow resistance, while thevariation of mixture’s viscosity exhibits very low effect. When the results are compared to similar exper-imental data for the ammonia falling film absorption with nanofluids, it was found that the heat and masstransfer are mainly affected by the film drag reduction and its physical properties. The numerical modelobtained can be used for calculating the absorption rate of ammonia-water-nanofluid mixtures withacceptable accuracy, since 87% of relative errors are lower than 20%.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Ammonia water absorption refrigerators have recaptured scien-tists’ attention due to the phenomenon of global warming andozone depletion. However, the performance of the absorption cycleneeds to be improved because it is lower than the performance ofthe vapor compression refrigeration system. Since the size and per-formance of the absorber can significantly impact on the system’soverall performance, the latest research have focused on theabsorption enhancement unit. Generally, there are three methodsto enhance the efficiency of heat and mass transfer of absorbers:the mechanical treatment, the chemical treatment, and nanotech-nology [1].

A nanofluid is defined as a liquid suspension of particles whosediameter are smaller than 100 nm. As a result of the limitation ofheat transfer in a working fluid, solid particles are dispersedthroughout it to improve its thermal properties as well as its heattransfer coefficient. In recent years, nanofluids have been graduallyused as engineering fluids because of their superior performance

on stability [2,3], thermal conduction [4–6], thermal convection[7–10] and boiling heat transfer [11–16]. Recently, the nanofluidsapplied in ammonia water absorption refrigeration system haveinvolved Cu, CuO [17], CNTs [18], Ag [19], Fe2O3, ZnFe2O4 [20],Al2O3 [21], and even nano emulsifier [22]. The performances ofthose kinds of nanofluids on absorbing ammonia were investigatedfor bubble or falling film absorption, and the results aresatisfactory.

According to the research results of Kang et al. [23], the masstransfer coefficients has greater effect on system’s performancerunning in bubble mode than that in falling film mode. Besidesthis, the heat transfer coefficients have more significant effectson heat exchanger size (absorption rate) in the falling film modethan in the bubble mode. The fluid flow and heat transfer aspectsof nanofluids have been studied by many researchers. However,the researches on absorption process of ammonia by nanofluidsare relatively deficient. A few existing literatures are mainlyfocused on the experimental studies with a predominating portionof bubble absorption type. A latest theoretical study on ammoniabubble absorption of nanofluids has been just found [18]. Never-theless, to the authors’ best knowledge, the theoretical study onammonia falling film absorption of nanofluids has not been found.For this reason, there is a great need of theoretical research on

Nomenclature

u film velocity in the direction of falling, m � s�1

v film velocity in the direction of film thickness, m � s�1

g gravity acceleration, m � s�2

Cp constant-pressure specific heat, kJ � kg�1 � K�1

Dm diffusion coefficient, m2 � sT temperature, �CP absorption pressure, MPaK mass transfer coefficientmab absorption amount in the interface of the control vol-

ume in unit time, kg � s�1

Dhab heat of absorbing unit mass of ammonia gas, kJ � kg�1

M gross absorption in unit time, g � s�1

S mass transfer interface area of falling film, m2

Re Reynolds numberSc Schmidt number

Greek lettersq density, kg �m�3

C flow rate, m3 � s�1

n mass concentration of fluid, %d film thickness, mmk thermal conductivity, W � (m � K)�1

g dynamic viscosity, Pa � s

s effective flow time in absorption, sm kinematic viscosity, m2 � s�1

Super/subscriptsi vapor–liquid interfacein inlet of falling filmw cooling waterr relativen nanofluidf basefluidff falling films solutions in containers and distributora Fig. (a)b Fig. (b)c Fig. (c)

AbbreviationsAS absolute slope of the fitting straight line about absorp-

tion rateRS relative slop, defined by the ratio of absolute slope to

the absorption rate when kr (or gr, Kr, sr) = 1

242 L. Yang et al. / International Journal of Heat and Mass Transfer 79 (2014) 241–250

ammonia-water falling film absorption with nanofluid and herebyobtain the main variables of ammonia-water nanofluid falling filmabsorption. In this work, a numerical model for an ammonia-water-nanoparticles falling film absorption outside vertical tubewas developed. The variation of falling film thickness along thetube and the changes in physical properties of ammonia-watermixture was considered when adding nanoparticles and disper-sants. The influence of physical properties of nanofluids over theefficiency of ammonia-water absorption is studied in detail.Finally, the numerical results were compared with experimentaldata. It is expected that this study brings some basic ideas that helpto understand how mixture’s physical properties affect on the heatand mass transfer coefficients in the absorption process and also toestablish some theoretical foundation for further research on theapplication of nanofluids.

Fig. 1. Sketch of ammonia-water nanofluid falling film absorption.

2. Model descriptions

The physical model and mathematical model introduced hereinare similar to our previous studies on numerical model of fallingfilm absorption with ammonia-water affected by a magnetic field[24]. The difference in this work is that the magnetic field isreplaced by a nanofluid, considering the changes in the mixture’sflow and its physical properties when nanoparticles and disper-sants are added. The detailed description about the physical modeland mathematical model are presented at the end of this section.

2.1. Physical model

In conventional water-cooled absorption cooling devices, thesolution flow takes place on the external surface of horizontaltubes in conventional falling film configuration of the absorber.However, wettability of the falling film affects the heat and masstransfer performance greatly. In order to observe, check and adjustthe wettability of the falling film all through the experiment, theshell of the main body of the absorber is made up of transparentacrylic glass. Therefore, to observe the conditions of solution filmdistribution in real-time through the transparent shell of the

absorber all through the experiment, the configuration selectedfor the absorber is that of falling film on the external surface of avertical tube in our previous experimental study [20]. And in thispaper, the combined and follow-up theoretical study also adoptsthis selection.

The process of ammonia falling film absorption outside verticaltube with nanofluids is shown in Fig. 1. The absorber unit consistsof the top shell and the falling film tube. The ammonia water (ornanofluid) solution enters the absorber from the top and then itforms a film in the distributor, and finally it falls along the exteriorsurface of the heat-transfer tube. Ammonia gas enters to the absor-ber from the bottom and is evenly distributed in the absorber. Thusabsorption heat is generated as a result of the absorption of ammo-nia vapor by the solution. Cooling water enters from the bottom of

L. Yang et al. / International Journal of Heat and Mass Transfer 79 (2014) 241–250 243

the heat-transfer tube, and flows upwards in countercurrent flowto the falling film. It also removes the heat generated in absorptionprocess to ensure an optimal working condition at this stage [24].

2.2. Mathematical model

The mathematical model was developed on the followingassumptions:

(1) The ammonia water (or nanofluids) cannot be compressed.(2) The nanoparticles are dispersed evenly in the liquid, and the

influence of bubbles is neglected.(3) There are no molecular diffusion and heat conduction in the

direction of falling neither in radial plane of the tube.(4) The pressure of ammonia vapor remains constant and the

heat conduction in this phase is neglected.(5) All phases in the system are in thermodynamic equilibrium,

the heat generated at the absorption stage is completelytransferred throughout the vapor–liquid interface and thereis no viscous shearing stress at this interface.

(6) The variation in the cooling water’s temperature is linearalong the heat-transfer tube. The temperature differencebetween cooling water and the outside wall of tube is setas an arbitrary value.

The coordinate system is set as shown in Fig. 1. The X axis isalong the falling direction, and the Y axis is along the thicknessdirection of the falling film. The instantaneous velocity compo-nents in X and Y axis through the control volume are u and v,respectively. In a time interval of dt, the quantities generated inthe control volume can be considered as zero. The continuity equa-tion, momentum equation, energy equation and quality equation isdescribed respectively as follows [24]:

@ðquÞ@x

þ @ðqvÞ@y

¼ 0 ð1Þ

qu@u@xþ qv @u

@y¼ @

@yl @u@y

� �þ qg ð2Þ

qCpu@T@xþ qCpv

@T@y¼ @

@yk@T@y

� �ð3Þ

Table 1The operating conditions employed as a standard of reference.

Item Tin (�C) Cin (m3/s) nin (%) Tw (�C) Cw (m3/s) P (MPa)

Value 20 0.00001 0 15 0.00007 0.1

qu@n@xþ qv @n

@y¼ @

@yqDm

@n@y

� �ð4Þ

The boundary conditions are expressed as follows:At the inlet of the falling film solution:

x ¼ 0; u ¼ u0 ¼ uin; v ¼ 0; T ¼ Tin; n ¼ nin ð5Þ

At the outside wall of the heat transfer tube:

y ¼ 0; u ¼ v ¼ 0; T ¼ Tw;@n@y

� �y¼0¼ 0 ð6Þ

At the vapor–liquid interface:

y ¼ d;@u@y

� �y¼d

¼ 0; Pv ¼ FðTi; niÞ ¼ const; k@T@y

����y¼d

¼ mabDhabjy¼d; mab ¼qDm

1� n� @n@y

����y¼d

ð7Þ

To obtain the mathematical solution of these equations, thefollowing variables were considered: the properties of ammonia-water nanofluids at different ammonia concentration, the phenom-enon of convection along the thickness direction of film and the

variation in thickness of falling-film in the absorption process.The details of this mathematical solution can be obtained fromreference [24,25].

3. Simulation results and discussion

The main parameters of the falling film and the tube the follow-ing: the outer and inner diameter of the tube is 25 and 22 mm,respectively. The length is 1000 mm. The mixing area is evenlydivided into 2000 � 2000 mesh (in the direction of falling � in thedirection of film thickness). A standard operating condition isemployed to investigate the influence of operating conditionsand the physical properties of nanofluids on the heat and masstransfer of ammonia falling film absorption process. Parametersof the standard operating condition are listed in Table 1.

The standard operating condition is defined according to theprevious experimental operating conditions [20]. The experimentaloperating condition is set to ensure the absorption process contin-uously proceed in all section of the falling film along the tube.Otherwise, if the solution is saturated and the absorption processstops before the end of the tube, the enhancement of nanofluidson the absorption performance cannot be verified from the satu-rated solutions. When the absorption process continuously pro-ceed in all section of the tube, the operating condition is set toobtain a more obvious difference results between the ammoniawater and ammonia water nanofluid.

To study the effect of the physical properties of nanofluids onthe performance of absorption, it was defined a set of the followingrelative variables: relative thermal conductivity, relative viscosity,relative mass transfer coefficient and relative flow resistance ofnanofluids. Their corresponding equations are:

kr ¼ kn=kf ð8Þ

gr ¼ gn=gf ð9Þ

Kr ¼ Kn=Kf ð10Þ

sr ¼ sn=sf ð11Þ

3.1. Influence of nanofluid’s thermal conductivity

Fig. 2 shows the influences of thermal conductivity on theabsorption rate in different working conditions. It can be seen that,whatever it is, in reference condition (a), or in 0.2 MPa absorptionpressure (b), or in 15% initial concentration of falling film (c), theinfluence of thermal conductivity has very low impact on theabsorption since it increases less than 1% when the thermal con-ductivity of nanofluids increases by 40%. This small effect may becaused due to the fact that the film is very thin and its thermalresistance is much smaller than the entire thermal resistance.The variation of the thermal conductivity of falling film has littleeffect on the performance of overall heat transfer coefficient andthe absorption performance. The above mentioned considerationsare applied just for the case of thin falling film absorption outsidea vertical tube, but not for other kind of absorption processes, suchas bubble absorption, horizontal tubular absorption, etc.

0.9 1.0 1.1 1.2 1.3 1.4

0.4492

0.4496

0.4500

0.4504

0.4508

0.733

0.734

0.735

Abs

orpt

ion

rate

(g·

s-1 )

absorption rate Linear fit of absorption rate

λ

Hea

t of

abso

rptio

n (k

J·s-1

)

heat of absorption

0.9 1.0 1.1 1.2 1.3 1.40.925

0.926

0.927

0.928

0.929

1.481

1.482

1.483

1.484

1.485

1.486

1.487

Abs

orpt

ion

rate

(g·

s-1 )

λ

absorption rate Linear Fit of absorption rate

Hea

t of

abso

rptio

n (k

J· s-1

)

heat of absorption

0.9 1.0 1.1 1.2 1.3 1.4

0.2458

0.2460

0.2462

0.2464

0.2466

0.4045

0.4050

0.4055

0.4060

Abs

orpt

ion

rate

(g·

s-1 )

λ

bsorption rate Linear fit of absorption rate

Hea

t of

abso

rpti

on (

kJ·s-1 )

heat of absorption

0 1

10

ASc=0.00589

ASa=0.00111

ASb=0.00212

RS

AS

0.007

ASa ASb ASc

RSa=0.00471RSb=0.00636

RSc=0.00451

0.007

RSa RSb RSc

(a) (b)

(c) (d)

Fig. 2. Influences of thermal conductivity on the absorption rate in different working conditions. (a): In reference condition; (b): in 0.2 MPa absorption pressure; (c): in 15%initial concentration of falling film; (d): comparisons of AS and RS.

244 L. Yang et al. / International Journal of Heat and Mass Transfer 79 (2014) 241–250

To further compare the influence of thermal conductivity on theabsorption performance at different operating conditions, absoluteslope (AS) was defined as the slope of the fitting straight lines onabsorption rate. According to this, ASa, ASb and ASc in Fig. 2(d) rep-resents the absolute slope of the fitting straight lines of absorptionrate in Fig. 2(a–c), respectively. It can be concluded that the abso-lute slope reflects the absolute rate of change of absorption withrespect to the relative thermal conductivity. However, as a resultof different operating conditions showed in Fig. 2(a–c), differentbase numbers on absorption rate can be obtained. Therefore thedirect absolute slope comparison can not reflect the relative inten-sity of the effect of thermal conductivity on the absorption perfor-mance. Consequently, it was necessary to define the relative slope(RS) as the ratio of absolute slope to the absorption rate when kr (orgr, Kr, sr) = 1 for each different operating condition. Hence inFig. 2(d), RSa represents the ratio of ASa to the absorption rate whenkr = 1 and similar reasoning is applied for the definition of RSb andRSc. This definition is also applied to other physical properties (vis-cosity, mass transfer coefficient, flow resistance) throughout thispaper. It can be concluded that RS reflects the percentage of changeof absorption with respect to the relative thermal conductivity.

Fig. 2(a–c) shows the trend of AS. A comparison of these twoslopes (AS and RS) is shown in Fig. 2(d), where it can be seen thatthe operating condition with the highest absorption rate has alsothe highest AS. This is because it has highest cardinal numberson absorption rate value. Therefore, the AS parameter can revealthe rate of change of absorption with respect to the relativethermal conductivity in each working condition, but again, it can-not be used for comparing the influence of thermal conductivity atdifferent operating conditions. However, it can be seen from thepicture of Fig. 2(d) that the RSb has the largest values. This revealsthat the enhancement of thermal conductivity improves theabsorption rate at higher absorption pressure conditions. And the

initial mixture’s concentration has little effect, because there isno significant difference between RSa and RSc.

3.2. Influence of nanofluid’s viscosity

Fig. 3(a–c) shows the influence of nanofluids’ viscosity on theabsorption rate at the reference condition, 0.2 MPa absorptionpressure and 15% initial mixture’s concentration, respectively. Itcan be seen that the viscosity has negative impact on the absorp-tion performance and its influence intensity is much greater thanthat is shown by thermal conductivity under all working condi-tions. The absorption rate decreases more than 20% when the vis-cosity increases by 30%. This confirms that the viscosity is animportant parameter. Fig. 3(d) shows the comparison of AS andRS of Fig. 3(a–c). It can be seen that the operating condition withthe highest absorption rate has the highest AS as a result of ithas the highest base number on absorption rate. However, it canbe seen from the picture of Fig. 3(d) that the working conditionshardly affects the influence of viscosity of nanofluids on absorptionrate because the RS of all working conditions are almost equal.

3.3. Influence of nanofluid’s mass transfer coefficient

Fig. 4(a–c) shows the effect of mass transfer coefficient ofnanofluids on the absorption rate at the reference condition of:0.2 MPa absorption pressure and 15% initial mixture’s concentra-tion of falling film, respectively. It can be seen that under all oper-ating conditions, the mass transfer coefficient has a positive impacton the absorption performance and its influence intensity is a littleweaker than that is shown by viscosity, but considerably higherthan that exhibited by thermal conductivity. Fig. 4(d) shows thecomparison of AS and RS of Fig. 4(a–c). It can be seen that AS variesin the same way as thermal conductivity and viscosity. However,

0.8 0.9 1.0 1.1 1.2 1.30.35

0.40

0.45

0.50

0.55

0.60

0.6

0.7

0.8

0.9 absorption rate

Abs

orpt

ion

rate

(g ·

s-1 )

ηr

heat of absorption

Hea

t of

abso

rpti

on (

J·s-1

)

0.8 0.9 1.0 1.1 1.2 1.30.7

0.8

0.9

1.0

1.1

1.2

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

ηr

absorption rate

Abs

orpt

ion

rate

(g·

s-1 ) heat of absorption

Hea

t of

abso

rpti

on (

J·s-1

)

0.8 0.9 1.0 1.1 1.2 1.3

0.20

0.25

0.30

0.30

0.35

0.40

0.45

0.50

ηr

absorption rate

Abs

orpt

ion

rate

(g·

s-1 ) heat of absorption

Hea

t of

abso

rpti

on (

J·s-1

)

0 1

1

-1 -1

0

ASb=-0.7174

ASc=-0.1912

ASa=-0.3526

RS

AS

ASa ASb ASc

RSa=-0.7837RSb=-0.7741RSc=-0.7766

RSa RSc RSb

(a) (b)

(c) (d)

Fig. 3. Influences of viscosity of nanofluids on the absorption rate in different working conditions. (a): In reference condition; (b): in 0.2 MPa absorption pressure; (c): in 15%initial concentration of falling film; (d): comparisons of AS and RS.

L. Yang et al. / International Journal of Heat and Mass Transfer 79 (2014) 241–250 245

the variation of RS showed in the picture of Fig. 4(d) is very differ-ent form the two previous nonofluids’ physical parameters (ther-mal conductivity and viscosity). RSc has the highest value, whichreveals that incrementing the mass transfer coefficient has greaterimpact on the absorption performance, under the operating condi-tion of higher initial concentration of nanofluids. It also revealsthat the influence of absorption pressure on the absorption rateis not significant, because RSa is just a little bigger than RSb. There-fore, in plain words, the mass transfer coefficient has greater effectunder the working condition of weaker absorption performance. Apossible reason for this circumstance can be explained as follows:when the absorption performance is weaker, the mass transfercoefficient is the main factor of resistance to the absorption pro-cess. The enhancement of mass transfer coefficient can play animportant role when absorption is weak. However, when theabsorption performance is higher, the mass transfer coefficienttakes a secondary role in resisting absorption. Consequently, theenhancement of mass transfer coefficient has less importance atthat moment.

3.4. Influence of nanofluid’s flow resistance

Fig. 5(a–c) shows the influence of nanofluid’s flow resistance onthe absorption rate at the reference condition: 0.2 MPa absorptionpressure and 15% initial mixture’s concentration. The relative flowresistance is defined by the ratio of effective flow time of the nano-fluid compared to the basefluid’s flow time. It can be seen that therelative flow resistance has a very negative impact on the absorp-tion performance and its influence intensity is the greatest on allmixture’s physical parameters. Also the absorption rate decreasesabout 50% when the relative flow resistance increases by 30%.The greatest impact of flow resistance on the absorption perfor-mance is mainly due to the high flow resistance, which causes

the decrease in flow’s velocity and its volumetric rate. Hence theReynolds number decreases, which eventually causes the diminu-tion of heat and mass transfer performance.

The comparison between the slopes AS and RS, shown inFig. 5(a–c), is resumed in Fig. 5(d). It can be seen that AS is almostproportional to the base number of absorption rate of eachoperating condition. The same behavior is observed for thermalconductivity, viscosity and mass transfer coefficient. In the insertpicture of Fig. 5(d), it is clear that the operating condition has sim-ilar influence over the RS to that of thermal conductivity but differ-ent to that of mass transfer coefficient. It can also be seen InFig. 5(d) that RSb has the highest value, which reveals that therelative flow resistance has greater impact on absorption perfor-mance at higher pressure. The absolute value of RS is very highand the flow’s resistance has more impact on absorption thanmixture’s other physical properties. Therefore, the absorption per-formance can be more greatly improved in higher absorption pres-sure. Especially for some kind of nanofluids which cause a dragreduction effect when are combined with a surfactant [26].

4. Comparison between simulation results and experimentaldata

The numerical results were compared with some experimentaldata for ammonia falling film absorption outside vertical tube withnanofluids to verify the accuracy of the mathematical model. Theexperimental apparatus, procedure, parameters, physical nanofl-uids’ properties and calculation methods have been demonstratedin our previous research [24].

Fig. 6 shows the schematic diagram of the experimental devicefor NH3/H2O nanofluid falling film absorption process [20]. Theabsorption takes place simultaneously at the interface of solutionsin the containers and the distributor. For this reason, the

0.8 0.9 1.0 1.1 1.2 1.3

0.40

0.44

0.48

0.52

0.60

0.65

0.70

0.75

0.80

0.85 absorption rate

Abs

orpt

ion

rate

(g·

s-1 )

Kr

heat of absorption

Hea

t of

abso

rptio

n (k

J·s-1

)

0.8 0.9 1.0 1.1 1.2 1.3

0.85

0.90

0.95

1.00

1.05

1.10

1.3

1.4

1.5

1.6

1.7

Kr

absorption rate

Abs

orpt

ion

rate

(g·

s-1 ) heat of absorption

Hea

t of

abso

rpti

on (

J ·s-1

)

0.8 0.9 1.0 1.1 1.2 1.3

0.22

0.24

0.26

0.28

0.36

0.40

0.44

Kr

absorption rate

Abs

orpt

ion

rate

(g·

s-1 ) heat of absorption

Hea

t of

abso

rptio

n (k

J·s-1

)

0 1

10

ASb=0.40034

ASa=0.20265

ASc=0.12525

RS

AS

1 ASa ASb ASc

RSa=0.45046

RSc=0.50884

RSb=0.43202

1 RSa RSb RSc

(a) (b)

(c) (d)

Fig. 4. Influence of mass transfer coefficient of nanofluids on the absorption rate in different working conditions. (a): In reference condition; (b): in 0.2 MPa absorptionpressure; (c): in 15% initial concentration of falling film; (d): comparisons of AS and RS.

246 L. Yang et al. / International Journal of Heat and Mass Transfer 79 (2014) 241–250

experimental data should be trimmed to show only information ofthe falling film absorption process. After this, numerical and exper-imental results can trustily be compared.

The following equations were used to perform the trimming ofexperimental data:

M ¼ Mff þMs ð12Þ

Mff ¼ Kff Sff ð13Þ

MS ¼ KSSS ð14Þ

Due to the slow variation of liquid level in containers and in thedistributor (can be considered approximately as static masstransfer). The falling film’s mass transfer coefficient at very lowReynolds Number (Res = 49), whose corresponding flow rate is alsovery slow (can also be considered approximately as static masstransfer), were used to conveniently replace the mass transfercoefficient at the interface of the solutions in containers and dis-tributor. As a result, the ratio of mass transfer coefficient of fallingfilm and solution in container and distributor were obtained byfollowing two equations [27]:

Kff

Dv2

g

� �1=3

¼ 9:777� 10�4 Re0:6804ff Sc1=2

ff For 1600 < Re < 10500

ð15Þ

Ks

Dv2

g

� �1=3

¼ 1:099� 10�2 Re0:3955s Sc1=2

s For 49 < Re < 300

ð16Þ

The gross absorption can be calculated by the final trimmingequation, which has the following form:

Mff ¼9:777�10�4 Re0:6804

ff Sc1=2ff �Sff

9:777�10�4 Re0:6804ff Sc1=2

ff �Sff þ1:099�10�2 Re0:3955s Sc1=2

s �Ss

M

ð17Þ

In our previous experimental studies, to obtain the suitablenanofluids applied in ammonia absorption refrigeration system,20 types of nanoparticles mixed pairwise orthogonally with 10types of surfactants were added in ammonia-water, respectivelyto observe the dispersion stability of suspension and hereby obtainthe functioning surfactant for each type of nanoparticles [28]. Thenthree kinds of nanoparticles (Al2O3, ZnFe2O4, Fe2O3) with SDBS asdispersant were selected and employed in the comparative exper-iments of ammonia absorption based on an overall consideration ofstability, viscosity and other physical properties [20]. The prepara-tion, selection and ingredient of nanofluids, as well as the compar-ative experimental results can be referenced in our previousexperimental studies about preparation and ammonia absorptionperformance of nanofluids [20,29–31].

Fig. 7 shows the absorption rate at different initial ammoniaconcentrations in order to make possible the comparison betweenthe model data, raw experimental data, and trimmed experimentaldata. When is considered the absorption in containers and distrib-utor, the raw experimental data seem to be below the model data,and seem to be above without considering the absorption. How-ever, when the model calculates the absorption rate, consideringthe initial concentration of water, the data results are concordantwith raw and trimmed experimental data. As a result of the mod-el’s assumptions and the errors in the experiments, measurementsand calculations, the disparity between the model and the experi-ments is unavoidable. However, the model is deemed to be usedfor approximately design the absorber vessel since the relativeerrors are within 20%.

0.8 0.9 1.0 1.1 1.2 1.3

0.3

0.4

0.5

0.6

0.7

0.8

0.4

0.6

0.8

1.0 absorption rate

Abs

orpt

ion

rate

(g·

s-1 )

τr

heat of absorption

Hea

t of

abso

rptio

n (k

J·s-1 )

0.8 0.9 1.0 1.1 1.2 1.3

0.6

0.8

1.0

1.2

1.4

1.6

0.8

1.2

1.6

2.0

τr

Abs

orpt

ion

rate

(g·

s-1 )

absorption rate

Hea

t of

abso

rptio

n (k

J·s-1 )

heat of absorption

0.8 0.9 1.0 1.1 1.2 1.3

0.15

0.20

0.25

0.30

0.35

0.40

0.2

0.3

0.4

0.5

0.6

τr

Abs

orpt

ion

rate

(g·

s-1 ) absorption rate

Hea

t of

abso

rptio

n (k

J ·s-1 )

heat of absorption 0 1

-1

1

-1

0

ASb= -1.6532

ASc= -0.3533

ASa= -0.7501

RSA

S ASa ASb ASc

RSa= -1.6673

RSb= -1.784

RSc= -1.4351

RSa RSc RSb

(a) (b)

(c) (d)

Fig. 5. Influence of flow resistance of nanofluids on the absorption rate in different working conditions. (a): In reference condition; (b): in 0.2 MPa absorption pressure; (c): in15% initial concentration of falling film; (d): comparisons of AS and RS.

1

2

3

4

5

6

78

9

10

1112

15

13

14

1 NH3 vessel 2 decompression valve 3 constant pressure controller; 4,11 container of solution 5 inlet of cooling water 6, 10 constant flow controller; 7 falling film tube8 visible absorbor body 9 solution distributor 12tubes for balancing pressure; 13 outlet of cooling water 14 HP data acquisition instrument 15 computer

Fig. 6. Schematic diagram of the experimental system for NH3/H2O nanofluidfalling film absorption.

0 5 10 150.2

0.3

0.4

0.5

0.6

0.7

0.8

Model data Raw experimental data Regulated experimental data by Eq(17)

Abs

orpt

ion

rate

(g·

s-1 )

Initial ammonia concentration of water

Fig. 7. The comparisons between the model data, raw experimental data, andregulated experimental data about absorption rate in different initial ammoniaconcentration of water.

L. Yang et al. / International Journal of Heat and Mass Transfer 79 (2014) 241–250 247

Figs. 8–10 show the comparison between the model data andtrimmed experimental data for the absorption rate at different ini-tial ammonia concentration when the Al2O3, ZnFe2O4 and Fe2O3

nanofluids are employed. It can be seen that, for each kind ofnanofluid, there are great errors between the model and the raw

experimental data and the majority of them exceed 20%. However,the errors between the model and the trimmed experimental dataobtained by Eq. (17) are much smaller, and most of them arewithin 20%. Hence, it can be concluded that experimental datatrimming is important for obtaining the real absorption rate ofammonia falling film absorption outside vertical tube. The modelaccuracy of absorption rate for each kind of fluid is illustrated inFig. 11, which shows the relative errors for each kind of nanofluidat different initial ammonia concentration. When is considered the

0 5 10 150.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Abs

orpt

ion

rate

(g·

s-1 )

Model data Raw experimental data Regulated experimental data by Eq(17)

Initial ammonia concentration of Al2O

3nanofluids

Fig. 8. The comparisons between the model data, raw experimental data, andregulated experimental data about absorption rate in different initial ammoniaconcentration of Al2O3 nanofluids.

0 5 10 15

0.4

0.6

0.8

1.0

Abs

orpt

ion

rate

(g·

s-1 )

Model data Raw experimental data Regulated experimental data by Eq(17)

Initial ammonia concentration of ZnFe2O

4nanofluids

Fig. 9. The comparisons between the model data, raw experimental data, andregulated experimental data about absorption rate in different initial ammoniaconcentration of ZnFe2O4 nanofluids.

0 5 10 15

0.4

0.6

0.8

1.0

1.2

Abs

orpt

ion

rate

(g·

s-1 )

Model data Raw experimental data Regulated experimental data by Eq(17)

Initial ammonia concentration of Fe2O

3 nanofluids

Fig. 10. The comparisons between the model data, raw experimental data, andregulated experimental data about absorption rate in different initial ammoniaconcentration of Fe2O3 nanofluids.

-0.4

-0.2

0.0

0.2

0.4Regulated experimental data by Eq(17)

0% initial ammonia content 5% initial ammonia content 10% initial ammonia content 15% initial ammonia content

Raw experimental data 0% initial ammonia content 5% initial ammonia content 10% initial ammonia content 15% initial ammonia content

Fe2O

3ZnFe2O

4Al

2O

3Water

Fluid types

Rel

ativ

e er

rors

of

abso

rptio

n ra

te

Fig. 11. The relative errors for each kind of nanofludis in different initial ammoniaconcentration.

248 L. Yang et al. / International Journal of Heat and Mass Transfer 79 (2014) 241–250

absorption at the interface of solution in containers and distribu-tor, 87.5% of the relative errors are within 20% and the maximumis 21.5%. However, if the absorption at the interface of solution incontainers and distributor are not taken into account, the relativeerrors between model and raw experimental data are much greaterbecause 62.5% of the relative errors exceed 20% and the maximumreaches 36.9%.

In our previous experimental study, to observe the conditions ofsolution film distribution in real-time through the transparentshell of the absorber all through the experiment, the transparentshell is made up by acrylic glass. To ensure the strength and secu-rity of the experimental unit, the experimental was not carried outfor higher ammonia concentration of fluids which matched withhigher absorption pressure. It can be found by experiment ormodel that the ammonia absorption rate decreases with theincrease of the ammonia concentration in initial fluid. Therefore,to obviously comparing the ammonia absorption performancebetween nanofluids and pure ammonia water, the experimentswere carried out with lower ammonia concentration fluid. In thispaper, the results of higher ammonia concentration fluid can also

be calculated. However, as a result of the value of model calcula-tion cannot yet be verified by our experimental results, the resultsof higher ammonia concentration fluids are not listed in this paper.

The improvement of absorption rate by nanofluids is mainly asa result of drag reduction and the physical properties of nanofluids.In previous studies of some researchers [5,6,20,26,31,32], theincrease of thermal conductivity, the decrease of viscosity and dragreduction are found in some kinds of nanofluids. These variationsin the nanofluid’s properties may be caused by the rod-shapedmicelles formed by surfactants [33–37] and the smoothing effecton the solid surface caused by the nanoparticles [26]. The experi-mental results showed that when the ammonia mass fraction ofinitial nanofluid increases, the absorption potential capacitydecreases, but the enhancing effect induced by the nanofluid isgreater than the effect without nanoparticles [20].

Broadly speaking, the model presented herein includes somephysical factors that impact on the absorption performance ofammonia falling film absorption outside vertical tube when

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

Fe2O

3ZnFe

2O

4Al

2O

3Water

Fluid types

Model data Heat absorbed by falling film (experimental)

-1) Heat absorbed by cooling water (experimental)

-0.4

-0.2

0.0

0.2

0.4

-21.22%

Fe2O

3ZnFe2O

4Al

2O

3Water

Fluid types

Rel

ativ

e er

rors

of

heat

of

abso

rptio

n

(a) (b)

Fig. 12. The comparisons of the absorption heat (a) and relative errors (b) between the model and experimental data in 0% initial ammonia concentration nanofluids.

L. Yang et al. / International Journal of Heat and Mass Transfer 79 (2014) 241–250 249

nanofluids are employed. There are other factors, such as stability[28–30,38], surface tension, specific heat, etc. that were not consid-ered in this model. The mass transfer coefficient was also not con-sidered in calculating the gross absorption. Consequently, thismodel can still be improved by considering those parameters. Itis expected that this model can establish the foundation for furthernumerical research on ammonia falling film absorption outsidevertical tube with nanofluids.

Fig. 12 shows the comparisons of the absorption heat (a) andthe relative errors (b) between the model and experimental dataat 0% initial ammonia concentration nanofluids. It can be seen thatthe heat of absorption is used for heating the nanofluids and thecooling water. The experimental data of absorption heat are nottrimmed like the data of absorption rate. The reason for this is thatthe phenomenon of absorption at the interface of solution in con-tainers and distributor, besides the heat released to the metal tubeand the environment, are factors that can cancel each other out. Itcan be found from Fig. 12(b) that the model has a high accuracywhen calculating the absorption heat of the pure water–Al2O3 mix-ture, since the maximum error is within 5%. But it shows a relativelow accuracy when calculating the absorption heat of pure water–ZnFe2O3 and water–Fe2O3 nanofluids mixtures, because the maxi-mum error is about 20%. Altogether, the model is considered tobe able to predict the absorption heat of ammonia falling filmabsorption outside vertical tube with nanofluids and it is expectedthat this model can be further improved by modifying it or enhanc-ing the accuracy of experiments and measurements.

The theoretical model of this paper is mainly focused on the influ-ence of physical properties and flow state of nanofluids on theammonia falling film absorption performances. It is not specific toa certain kind of nanoparticles. And the physical properties and flowstate of nanofluids need to be obtained by experimental or mathe-matical method when the model is applied to a specific kind of nano-fluid. However, the nanofluids for ammonia falling film absorptionshould be stable and highly mobile, otherwise the sedimentationand adsorption of nanoparticles on the tube will affect the ammoniaabsorption performance which is not considered in the model.

5. Conclusions

(1) A numerical model of ammonia falling film absorption out-side vertical tube with nanofluid was established by consid-ering the variation of falling film thickness along falling, andthe changes in physical properties of ammonia water whenadding nanoparticles and dispersants.

(2) The numerical results show that when absorption pressuredecreases or when initial concentration of mixture increases,the relative intensity of effect on absorption rate is weak-ened by the variation of thermal conductivity but enhancedby the variation of mass transfer coefficients and flow resis-tance, while the variation of mixture’s viscosity exhibits verylow effect.

(3) The numerical results are compared to similar experimentaldata for the ammonia falling film absorption with nanofl-uids. The comparison results show that the heat and masstransfer are mainly affected by the film drag reduction andits physical properties. The numerical model obtained canbe used for calculating the absorption rate of ammonia-water-nanofluid mixtures with acceptable accuracy, since87% of relative errors are lower than 20%.

Conflict of interest

None declared.

Acknowledgments

The work of this paper is financially supported by the ScienceFoundation of China (51176029), the 12th Five Year NationalScience and Technology support Key Project of China (Nos.2011BAJ03B05 and 2011BAE14B06) and the Scientific ResearchFoundation of Graduate School of Southeast University(YBPY1205). The supports are gratefully acknowledged.

References

[1] Y.T. Kang, J. Kim, J.-K. Kim, C.K. Choi, Comparisons of mechanical, chemical andnano technologies for absorption applications, in: Proceedings of InternationalSeminar on Thermally Powered Sorption Technology (Japan), 2003, pp. 69–77.

[2] G.D. Xia, H.M. Jiang, R. Liu, Y.L. Zhai, Effects of surfactant on the stability andthermal conductivity of Al2O3/de-ionized water nanofluids, Int. J. Therm. Sci.84 (2014) 118–124.

[3] A. Ghadimi, I.H. Metselaar, The influence of surfactant and ultrasonicprocessing on improvement of stability, thermal conductivity and viscosityof titania nanofluid, Exp. Therm. Fluid Sci. 51 (2013) 1–9.

[4] B.Q. Xiao, Y. Yang, L.X. Chen, Developing a novel form of thermal conductivityof nanofluids with Brownian motion effect by means of fractal geometry,Powder Technol. 239 (2013) 409–414.

[5] L. Yang, K. Du, X.S. Zhang, Influence factors on thermal conductivity ofammonia-water nanofluids, J. Cent. South Univ. 19 (2012) 1622–1628.

[6] L. Yang, K. Du, A thermal conductivity model for low concentrated nanofluidscontaining surfactants under various dispersion types, Int. J. Refrig. 35 (2012)1978–1988.

250 L. Yang et al. / International Journal of Heat and Mass Transfer 79 (2014) 241–250

[7] A.A.R. Darzi, M. Farhadi, K. Sedighi, Heat transfer and flow characteristics ofAl2O3–water nanofluid in a double tube heat exchanger, Int. Commun. HeatMass Transfer 47 (2013) 105–112.

[8] B.Q. Xiao, B.M. Yu, Z.C. Wang, L.X. Chen, A fractal model for heat transfer ofnanofluids by convection in a pool, Phys. Lett. A 373 (2009) 4178–4181.

[9] A. Ghadimi, R. Saidur, H.S.C. Metselaar, A review of nanofluid stabilityproperties and characterization in stationary conditions, Int. J. Heat MassTransfer 54 (2011) 4051–4068.

[10] A.A.R. Darzi, M. Farhadi, K. Sedighi, S. Aallahyari, M.A. Delavar, Turbulent heattransfer of Al2O3–water nanofluid inside helically corrugated tubes: numericalstudy, Int. Commun. Heat Mass Transfer 41 (2013) 68–75.

[11] B.Q. Xiao, B.M. Yu, A fractal model for critical heat flux in pool boiling, Int. J.Therm. Sci. 46 (2007) 426–433.

[12] G.L. Ding, H. Peng, W.T. Jiang, Y.F. Gao, The migration characteristics ofnanoparticles in the pool boiling process of nanorefrigerant andnanorefrigerant–oil mixture, Int. J. Refrig. 32 (2009) 114–123.

[13] H. Peng, G.L. Ding, H.T. Hu, W.T. Jiang, Effect of nanoparticle size on nucleatepool boiling heat transfer of refrigerant/oil mixture with nanoparticles, Int. J.Heat Mass Transfer 54 (2011) 1839–1850.

[14] B.Q. Xiao, B.M. Yu, A fractal analysis of subcooled flow boiling heat transfer, Int.J. Multiphase Flow 33 (2007) 1126–1139.

[15] H.T. Hu, H. Peng, G.L. Ding, Nucleate pool boiling heat transfer characteristicsof refrigerant/nanolubricant mixture with surfactant, Int. J. Refrig. 36 (2013)1045–1055.

[16] H. Peng, G.L. Ding, H.T. Hu, Effect of surfactant additives on nucleate poolboiling heat transfer of refrigerant-based nanofluid, Exp. Therm. Fluid Sci. 35(2011) 960–970.

[17] J.-K. Kim, J.Y. Jung, Y.T. Kang, The effect of nano-particles on the bubbleabsorption performance in a binary nanofluid, Int. J. Refrig. 29 (2006) 22–29.

[18] F.M. Su, Y.B. Deng, H.B. Ma, Numerical analysis of ammonia bubble absorptionin a binary nanofluid, Chem. Eng. Commun. (in press), http://dx.doi.org/10.1080/00986445.2013.850578.

[19] C.W. Pang, W.D. Wu, W. Sheng, H. Zhang, Y.T. Kang, Mass transferenhancement by binary nanofluids (NH3/H2O + Ag nanoparticles) for bubbleabsorption process, Int. J. Refrig. 35 (2012) 2240–2247.

[20] L. Yang, K. Du, X.F. Niu, B. Cheng, Y.F. Jiang, Experimental study onenhancement of ammonia-water falling film absorption by adding nano-particles, Int. J. Refrig. 34 (2011) 640–647.

[21] A. Sözen, E. Özbas�, T. Menlik, M.T. Çakır, M. Gürü, K. Boran, Improving thethermal performance of diffusion absorption refrigeration system withalumina nanofluids: an experimental study, Int. J. Refrig. 44 (2014) 73–80.

[22] J.K. Kim, J.K. Lee, Y.T. Kang, The effect of oil-droplet on bubble absorptionperformance in binary nanoemulsions, Int. J. Refrig. 30 (2011) 1734–1740.

[23] Y.T. Kang, A. Akisawa, T. Kashiwagi, Analytical investigation of two differentabsorption modes: falling film and bubble types, Int. J. Refrig. 23 (2000) 430–443.

[24] X.F. Niu, K. Du, S.X. Du, Numerical analysis of falling film absorption withammonia-water in magnetic field, Appl. Therm. Eng. 27 (2007) 2059–2065.

[25] X.F. Niu, The research of the effect on ammonia-water absorption process ofammonia-water absorption refrigeration by external magnetic field (Doctoratedissertations), School of Energy and Environment, Southeast University, 2008,pp. 27–44 (in Chinese).

[26] L. Liao, The flow and heat transfer characteristics of drag-reducingnanoparticle suspension (Doctorate dissertations), School of MechanicalEngineering, Shanghai Jiao Tong University, 2009, pp. 50–55 (in Chinese).

[27] I. Eremisinoff, P. Bucgilas, Handbook of Heat and Mass Transfer, V. 2. MassTransfer and Reactor Design, Gulf Publishing Company, Texas, United States,1986, pp. 238–244.

[28] L. Yang, K. Du, S.Y. Bao, Y.L. Wu, Investigations of selection of nanofluid appliedto the ammonia absorption refrigeration system, Int. J. Refrig. 35 (2012) 2248–2260.

[29] L. Yang, K. Du, X.S. Zhang, B. Cheng, Preparation and stability of Al2O3

nanoparticle suspension of ammonia-water solution, Appl. Therm. Eng. 31(2011) 3643–3647.

[30] L. Yang, K. Du, X.F. Niu, Y.J. Li, Y. Zhang, An experimental and theoretical studyof the influence of surfactant on the preparation and stability of ammonia-water nanofluids, Int. J. Refrig. 34 (2011) 1741–1748.

[31] L. Yang, K. Du, Y.H. Ding, B. Cheng, Y.J. Li, Viscosity-prediction models ofammonia water nanofluids based on various dispersion types, PowderTechnol. 215–216 (2012) 210–218.

[32] Z.L. Li, J.M. Li, B.X. Wang, H.T. Hu, Influence of SDBS on viscosity of copperoxide nano-suspensions, J. Eng. Thermophys. (China) 24 (2003) 849–851.

[33] K. Schmitt, P.O. Brunn, F. Durst, Scaling-up correlations for drag reducingsurfactants, Rheol. Acta 26 (1988) 249–252.

[34] H. Rehage, H. Hoffman, Rheological properties of viscoelastic surfactantsystems, J. Phys. Chem. 92 (1988) 4712–4719.

[35] Y. Kawaguchi, H. Daisaka, A. Yabe, Turbulent characteristics in transitionregion of dilute surfactant drag reducing flows, in: Proc. 11th Int. Sym,Turbulent Shear Flows, Grenoble, vol. 9, 1997, pp. 49–54.

[36] J.L. Zakin, J. Myska, Z. Chara, New limiting drag reduction and velocity profileasymptotes for nonpolymeric additives systems, AIChE J. 42 (1996) 3544–3546.

[37] M. Fichman, G. Hetsroni, Electrokinetic aspects of turbulent drag reduction insurfactant solutions, Phys. Fluids 16 (2004) 4346–4352.

[38] L. Yang, K. Du, An optimizing method for preparing natural refrigerant:ammonia-water nanofluids, Integr. Ferroelectr. 147 (2013) 24–33.