Experimental investigation of the effect of magnetic field on vapour absorption with LiBr–H2O nanofluid

Journal Pre-proof Experimental Investigation of the Effect of Magnetic Field on Vapour Absorption with LiBr-H2O Nanofluid

Shenyi Wu, Camilo Rincon Ortiz PII:

S0360-5442(19)32335-7

DOI:

https://doi.org/10.1016/j.energy.2019.116640

Reference:

EGY 116640

To appear in:

Energy

Received Date:

13 February 2019

Accepted Date:

26 November 2019

Please cite this article as: Shenyi Wu, Camilo Rincon Ortiz, Experimental Investigation of the Effect of Magnetic Field on Vapour Absorption with LiBr-H2O Nanofluid, Energy (2019), https://doi.org/10. 1016/j.energy.2019.116640

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.

Journal Pre-proof Experimental Investigation of the Effect of Magnetic Field on Vapour Absorption with LiBr-H2O Nanofluid Shenyi Wu* and Camilo Rincon Ortiz+ Fluids and Thermal Engineering Research Group Faculty of Engineering University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom

Abstract This work presents a new approach for further research in enhancing vapour absorption rate and understanding the enhancement mechanism in the process. The experimental study explored enhancing vapour absorption from using an external magnetic field to induce slip movement of nanoparticles in a nanofluid. The experiment were carried out in an adiabatic falling film absorber with a mixture of LiBrH2O solution and Iron(III) nanopowder, <50nm at the mass fraction 0.17% in the fluid. The experimental results show that the vapour absorption rates increased by 17.6% and 4.9% with the nanofluid circulating at 3L min-1 and 3.5L min-1, respectively, compared with that with the base fluid. A further increase was observed when the movement of the nanoparticles in the fluid was influenced by an external magnetic field. The vapour absorption rates obtained with the magnetic field in place were 1.58 times and 1.32 times higher than that without it for the nanofluid circulating at 3.5L min-1 and 3.0L min-1, respectively. A further analysis on the experimental data suggested that the enhancement of vapour absorption rate was associated with the frequency of the nanoparticles movement. A high frequency movement of the nanoparticles helped the vapour absorption process in our experimental tests. Keywords: Nanofluid, heat and mass transfer, vapour absorption refrigeration, magnetic field 1. Introduction This work presents a new approach for further research in enhancing vapour absorption rate and understanding the enhancement mechanism in the process. An effective vapour absorption relies on efficient heat and mass transfer in the process. Due to low mass diffusivity in liquids, an efficient vapour absorption process requires a large ratio of surface area to volume to reduce the resistance to heat/mass transfer in the liquid phase. Creating very thin film on a vertical plate or very fine liquid droplets are a conventional approach to increase heat/mass transfer in the process. Use of surfactant agent to increase instability at the vapour-liquid interface is another way to boost the mass transfer in vapour absorption systems. These technologies have been extensively investigated and widely employed in modern vapour absorption refrigeration/heat pump systems to improve mass transfer. However, the potential for further improvement with these technologies appears to be limited. Kim et al reported their works on bubble absorber with binary nanofluid [1, 2]. With the addition of nanoparticles: Cu, CuO or Al2O3, to an NH3-H2O solution, they found that the NH3-H2O binary nanofluids demonstrated excellent absorption ability. The effective absorption ratio, which is defined as the ratio of the absorption rate by the nanofluid to the base fluid (without addition of nanoparticles), was increased in all cases with the maximum effective absorption ratio of 3.21 when the nanofluid contained 18.7% ammonia and 0.10% of Cu nanoparticles [1]. More encouragingly, their work also found that as the absorption potential of the solution decreases, the absorbers with nanofluids performed better than those without nanofluid. Kang et al [3] observed that carbon nanotubes at concentrations of 0.01 and 0.1% have a higher rate of mass transfer increase compared with Fe nanoparticles, concluding that CNT is the most optimal nanoparticles to be used in absorption systems. They measured the absorption rate in a H2O/LiBr solution for a falling film absorber. The maximum mass transfer for CNT * Corresponding author: Tel. +44 115 8467875; email address [email protected] + Present email address: [email protected]

Journal Pre-proof nanoparticles was 2.48 at 0.01 wt% while the maximum enhancement for Fe was 1.90 for 0.1 wt%. Kim et al experimentally studied the effect of combination of SiO2 nanoparticles with the surfactant on the falling film heat and mass transfer. They found that the performance enhancement with only the nanoparticles becomes higher than that with both the nano-particles and the surfactant. This is because the convective motion of nano-particles such as Brownian movement gives a big impact on the absorption performance in SiO2 binary nanofluids and then the surfactant makes the convective motion of nanoparticles weak. [4]. Their finding supports the argument that the significance of the slip motion of nanoparticles in the base fluid to the enhancement of heat and mass transfer in the vapour absorption process. Recently, Zhang et al reported their experimental study on enhancement of falling film absorption with various nanoparticles in aqueous lithium bromide solution. They found that the enhancement is associated with the size and mass fraction of the nanoparticles: the small nanoparticle size and high mass fraction of nanoparticles enhance the absorption ratio [5]. They also found experimentally that with Fe3O4 nanoparticles, the mass transfer enhancement ratio was achieved as high as 2.28 [6]. Wang et al also found that the mass transfer coefficient of absorber increased by 1.28 and 1.41 times for 0.05% and 0.1% added nanoparticles, respectively [7]. A recent review by Amaris et al provided more information about the research development of nanoparticles in working fluid for absorption cooling/heating technologies [8]. Using magnetic field to enhance the thermal conductivity of nanofluid has been investigated. One of these is the conduction through linear agglomerates of nanoparticles in the working fluid. Philip et al [9] observed a 300% enhancement from the nanofluids with 2–10nm surfactant-coated Fe3O4 magnetic nanoparticles. Angayarkanni & Philip [810] reported an increase in the thermal conductivity in a certain magnetic field range for ferro-oxidizer nanoparticles. A thermal conductivity increment of 300% was observed with the 6.3vol% particle loading. This intensification in thermal conductivity is accredited to the effective conduction of heat through the chainlike structure formed under a magnetic field when the dipolar interaction energy becomes greater than the thermal energy. Suresh and Bhalerao [11] used the ferromagnetic nanofluid influenced by a magnetic field of 50Hz to intensify mass transfer in the interfacial region. They found numerically a 40% enhancement in the mass transfer with the oscillating magnetic field on but non-effect with the magnetic field off. However, Komati and Suresh [12] found no further enhancement using a periodic oscillating magnetic field in their experiment using nano ferrofluid/ MDEA for a CO2 absorption in a wetted wall column. They attributed the difference to the nature of the particles that the 15nm particles lost the single-domain making it difficult to follow the external magnetic field. Komati and Suresh [13] also experimentally investigated the effect of magnetic iron oxide nanoparticles on the gases absorbed where a mixture of carbon dioxide and oxygen is absorbed by liquid nanofluid in a capillary tube and a wetted wall column. They found a considerable increase in mass transfer coefficient at the presence of both the magnetic field and the nanoparticles and the enhancement depends on the size and volume of the particles. They also observed a relation between the increases in Sherwood Number. Wu et al reported their study on Nanoferrofluid addition enhances ammonia/water bubble absorption in an external magnetic field. They found that with an external magnetic field to influence the nanoparticles Fe3O4, the effective absorption rate reached a maximum value of 1.0812 under the adiabatic condition [14]. The past researches show that nanofluids can enhance vapour absorption process; however, the researches were dominantly focused on the enhancement in relation to the types and concentration of nanoparticles in different base fluids. A few of publication reported in the past that the enhancement could be achieved under influence of magnetic field, in which the external magnetic fields were used for intensifying the mass transfer in the interfacial region or increasing the thermal conductivity of the liquid. In this work, by contrast, the external magnetic field was used for purposely-inducing slip movement of nanoparticles in the film flow in order to bring in two effects, i.e., enhancing micro convection in the liquid phase and triggering the Marangoni effect in the liquid-vapour interfacial region due to the slip movement. In addition, an analysis of the experimental data was carried out to reveal the relationship between the vapour absorption rate and the frequency of the slip movement of the 2

Journal Pre-proof nanoparticles in the base fluid. The frequency of the slip movement represents the nanoparticles’ slip velocity against bulk fluid velocity and indicates the frequent quantity variation of the nanoparticles at the liquid-vapour interfacial region within a specific period, which are associated with the intensity of the micro convection and Marangoni effect due to the purposely-induced slip movement of nanoparticles. The finding from the analysis may help understanding the mechanism of the nanoparticles’ role in the vapour absorption process. 2. Experimental setup The experimental investigation was carried out on a rig shown in Figures 1 and 2. The rig consists of a generator-condenser assembly at the top and an evaporator-absorber assembly under the desorbercondenser assembly. Two electrical heaters were used to supply heat to the generator (2.4kW) and evaporator (800W). Both heaters were immersed in the fluids at the bottom of the vessels. The temperatures of the solution in the desorber and refrigerant in the evaporator were controlled by two temperature controllers (Watlow EZ-ZONE PID controller). In the absorber, the solution was sprayed through a nozzle in a hollow cone shape before it reached the wall. The solution then flowed in a film flow down along the wall. The cooling to the absorber and the condenser was by the tap water through a heat exchanger outside the absorber vessel; therefore, it was an adiabatic vapour absorption process. The condensing and absorption temperatures were controlled from manually adjusting the tap water flow rate.

Figure 1 Schematic diagram of the rig

3

Journal Pre-proof

Figure 2 Photo of the rig with main component indicators 3. Experimental test 3.1 The test procedures The absorption and desorption processes in the experimental tests were separated. The absorption test started with releasing a fixed amount of the solution already concentrated from the desorber via the path V6 – H – V3 into the absorber shown in Figure 1 and the water level in the evaporator was initially at a pre-set point in the previous desorption. During the test, the solution was circulated continuously between the absorption vessel and the heat exchanger. The water level in the evaporator dropped gradually with the progress of the vapour absorption. The test continued until the water level dropped to a pre-set point. The average absorption rate can be calculated from the level difference and duration time as follows:

𝑚=

(𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑤𝑎𝑡𝑒𝑟 𝑙𝑒𝑣𝑒𝑙 ― 𝑒𝑛𝑑 𝑤𝑎𝑡𝑒𝑟 𝑙𝑒𝑣𝑒𝑙 ) × 𝑀 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑡𝑖𝑚𝑒 (sec)

(1)

where M is a mass conversion rate for every centimetre water level change in the evaporator vessel. Its value is 0.02kg/mm for this particular setup. In this investigation, the vapour absorption rate was tested with the circulation flow rates at 3L min-1 and 3.5L min-1. The solution temperature was maintained at 25℃ before the solution flowed into the absorber. The quantity of the solution released to the absorber vessel for each vapour absorption test was fixed at 5.92kg with the solution concentration at 54.7%. This was counted by releasing the solution to the absorber vessel to the point marked with “Solution charge level” and the condensate to the evaporator to the point marked with “Water level 1” in Figure 3. The water level change between the “Water level 1” and “Water level 2” was reserved for stabilising the evaporating and absorption temperatures to the set conditions. The level change in this period was not counted for the average absorption rate. The vapour absorption reduced the solution concentration to 53.9% at the end of this period while the quantity of the solution increased to 6.01kg. The average absorption rate was counted 4

Journal Pre-proof for the water level change from the points marked with “Water level 2” to the “Water level 3”. In this period, a fixed amount of 0.3kg water were absorbed by the solution. The solution concentration ended at 51.3% in the test. After the absorption test, the solution in the absorber was sent back to the desorber by the solution circulation pump (ABS.) via V5 in Figure 1 for regeneration. During the regeneration, the condensate in the condenser continuously flowed down to the evaporator via V8 until the water level reached the point marked with “Water level 1”. At this point, all water absorbed in the previous absorption test was extracted out of the solution. The solution concentration in the desorber was therefore back to the original concentration and the solution was ready for the next absorption test.

Figure 3 Schematic diagram to illustrate the absorption test

3.2 Nanofluid preparation The nanofluid was a mixture of aqueous lithium bromide solution with Aldrich Iron(III) oxide nanopowder, <50nm. It consisted of 25 grams of the nanoparticles and 15kg aqueous lithium bromide solution with concentration of 53%, which gave 0.17% mass fraction of the nanoparticles in the mixture. The nanoparticles were dispersed in the solution with ultrasonic generator for half an hour before it was charged into the rig. It was noted the deposition of nanoparticles in the vessel after several hours; however, the nanoparticles were uniformly suspended in the solution after the circulation. 3.3 The external Magnetic field configurations The external magnetic field was constructed by spirally winding a continue piece of magnetic strip onto the outside of the absorber vessel with the gap “a” and the width of the section covered by magnetic strip “b” as shown in Figure 4(a). Three configurations were constructed for investigation: a) no gap (a = 0cm, b = 15.4cm), small gap (a = 2cm, b = 38.4cm) and large gap (a = 3.5cm, b = 41cm). Figure 4(b) is a photo of the vessel wound with magnetic strip. A handheld Gauss meter GM 08 was used to measure the magnetic flux density. The measured magnetic flux density was 52.2 mT (milliTesla) without the glass vessel in place. The magnetic flux density decreased to 44 mT when measured inside the glass vessel, i.e., a 14mm thickness of glass wall is in between the probe and the magnetic strip as shown in Figure 4(c).

5

Journal Pre-proof

Figure 4 the magnetic strip configuration on the absorber vessel wall 4. Experimental results and discussions Table 1 is a summary of the tests carried out with different combinations of the solutions, the circulating flow rates and the configurations of magnetic strip on the absorption vessel. Table 1 the tests completed in the investigation

No Magnetic strip Magnetic strip with no gap Magnetic strip with 2cm gap Magnetic strip with 3.5cm gap

LiBr-H2O (25℃) 3.0 L min-1 3.5 L min-1 √ √ N/A N/A N/A N/A N/A

N/A

LiBr-H2O+Fe2O3 (25℃) 3.0 L min-1 3.5 L min-1 √ √ √ √ √ √ √

√

4.1 Vapour absorption rate with the base absorption fluid (LiBr-H2O) Figure 5 shows the vapour absorption rates for the base absorption fluid circulating at 3.0L min-1 and 3.5L min-1. The vapour absorption rate at 3.5L min-1 was higher than that at 3L min-1 because the higher circulation flow rate created a larger contacting surface area for absorption. It also shows that the vapour absorption rates decreased continuously with time, which was due to the decrease of the solution concentration. The average absorption rates for the period were 1.21 × 10 ―4 𝑘𝑔 ∙ 𝑠 ―1 for 3.5L min-1 and 1.04 × 10 ―4 𝑘𝑔 ∙ 𝑠 ―1 for 3.0L min-1.

Figure 5 the vapour absorption rates with the base fluid LiBr-H2O 4.2 Vapour absorption rate with the nanofluid (LiBr-H2O+Fe2O3) Figure 6 shows the absorption rates from the experimental tests without applying the magnetic field to the nanoparticles for the nanofluid circulating at 3L min-1 and 3.5L min-1. It can be found again that the vapour absorption rates for the 3.5L min-1 were always higher than that for 3.0L min-1. The trend lines based on the two sets of experimental data show that the gap between the trend lines does not change 6

Journal Pre-proof significantly with time, which reflects the influence of the solution coverage areas and flow characteristics caused by the different circulation flow rates.

Figure 6 vapour absorption rates with nanofluid for the circulating flow rates 3L min-1 and 3.5L min-1 4.3 Vapour absorption rate with nanoparticles influenced by the external magnetic field The test results for the vapour absorption under influence of the external magnetic field are shown in Figure 7. The tests were carried out with the gaps 0cm, 2cm and 3.5cm between the magnetic strips; see Figure 4(a). For both 3L min-1 and 3.5L min-1 circulation flow rates, the test with 2cm gap (a = 2cm) gave the highest average absorption rate followed by the 3.5cm gap (a = 3.5cm). The lowest absorption rate was found for the configuration with no gap (a = 0cm). A comparison of the average absorption rates for the three cases: a) Libr-H2O, b) LiBr-H2O+Fe2O3 and c) LiBr-H2O+Fe2O3+magnetic field (with 2cm gap) can be found in Figure 8. For the solution circulating at 3L min-1, the average absorption rates with the magnetic field is 1.32 times higher than that without it. For the 3.5L min-1 circulation flow rate, the average absorption rate becomes 1.58 times higher than that without it. The average absorption rate for the case of nanofluid + magnetic field was 1.65 times higher than that for the base fluid when the fluid circulated at 3.5L min-1.

Figure 7 the vapour absorption rates with magnetic strip with 3L min-1 solution circulating flow rate (left) and 3.5L min-1 solution circulating flow rate (right)

7

Journal Pre-proof 0.25

Absorption rate (g s-1)

0.2 0.15 0.1 0.05 0 LiBr-H20

LiBr-H20 + Fe2O3 3 L per min.

LiBr-H20 + Fe2O3 + magnetic field

3.5 L per min.

Figure 8 Comparison of the vapour absorption rates from the experimental tests with/without additions of nanoparticles (2cm gap in the case with magnetic field) 4.4 The effectiveness of applying magnetic field to vapour absorption process Figure 9 shows the absorption rates from the experimental tests with and without magnetic field applied for the solution circulating at 3.5L min-1 and the 2cm gap (a = 2cm) configuration of magnetic field. It can be found in Figure 9 that the gap between the two linear trend lines is large at the early stage and become smaller at the late stage. This trend indicates that the effect of the nanoparticle movement was more significant on the vapour absorption process when a large concentration gradient exists in the liquid phase. At the early stage, the overall concentration was high in the liquid phase. The absorption on the solution surface, therefore, resulted in a large concentration gradient across the film flow. The movement of the nanoparticles reduced the concentration gradient, i.e., helped to move the high concentration solution to the surface. The micro flows caused by the nanoparticles accelerated the heat/mass transport, which enhanced the overall vapour absorption process. Since the overall concentration of the solution is low at the late stage; therefore, the concentration gradient in the liquid phase became small, consequently, the effect of nanoparticle movement on the overall vapour absorption process became less. The influence of the external magnetic field on the vapour absorption rate was stronger in 3.5L min-1 circulation flow rate than 3.0L min-1. The ratios of the vapour absorption rate with the magnetic field applied to that without it were 1.58 for 3.5L min-1 and 1.32 for 3.0L min-1. The high ratio obtained with 3.5L min-1 suggests that the magnetically assisted process was effective on the thick film flow.

Figure 9 Comparison of the vapour absorption rates between the processes with/without being influenced by the external magnetic field

8

Journal Pre-proof The thermal images in Figure 10 show the high temperature on the absorber vessel wall with the magnetic field applied. The higher temperature at 3.5L min-1 than at 3L/min is consistent with the fact that the vapour absorption rate was higher at 3.5L min-1.

Figure 10 The thermal images of the absorber vessel with different flow rate and magnetic field 4.4 The frequency of the nanoparticle movement and the vapour absorption rate The sectional profile of the magnetic strip used for creating the magnetic fields was 10mm by 4mm in width and thickness, respectively. The magnetic intensity profile of such a magneto is schematically shown in Figure 11(a). With the magnetic strip being helically wound on to the absorber vessel, it asserts a variable magnetic field in the absorber vessel. The magnetic force attracts the nanoparticles moving towards the wall of the absorber vessel. The force of diffusiophoresis due to concentration gradient in the base fluid tends to move the nanoparticles oppositely. Figure 11(b) shows a possible path of a nanoparticle travelling in the fluid flow under the combination of these forces, which can be characterised as the frequency of movement. If one strip is counted as one slipping movement towards the wall, the frequency of the movement is the ratio of the velocity of the flow to the distance of two neighbouring magnetic strips. In this case, the frequency is determined by the gap distance “a” and the velocity of the film flow. 4.4.1 The velocity of the film flow For a laminar flow, the governing equation and the boundary conditions for this flow can be expressed as follows: 𝑑2𝑤 2

𝑑𝑟

𝑤 = 0 for 𝑟 = 𝑅;

𝑑𝑤 𝑑𝑟

1𝑑𝑤

𝑔

(2)

+ 𝑟 𝑑𝑟 + 𝜈 = 0

= 0 for 𝑟 = 𝑅 ― 𝛿. Here R and δ are the internal radius glass vessel and thickness

of the film flow on the wall. Integration of Equation (2), we obtain velocity distribution across the film from above equation and boundary conditions: 𝑤=

𝑔(𝑅 ― 𝛿)2 𝑟 𝑙𝑛𝑅 2𝜈 𝛿

―

𝑔(𝑟2 ― 𝑅2) 4𝜈

(3)

Substituting the relative cross curvature ratio 𝜀𝑅 = 𝑅 into Equation (3) and rearrange the equation, we have:

9

Journal Pre-proof 𝑤=

[0.5(1 ― ) + (1 ― 𝜀 ) 𝑙𝑛 ]

𝑔𝑅2 2𝜈

𝑟2

𝑅

𝑅

2

2

𝑟 𝑅

(4)

The average velocity of the film flow can be obtained from Equation (4) from: 𝑅

𝑤=

∫𝑅 ― 𝛿𝑤𝑟𝑑𝑟 𝑅 ∫𝑅 ― 𝛿𝑟𝑑𝑟

𝑔𝑅2

= 4𝜈(1 ― 0.5𝜀𝑅)𝜀𝑅(0.25 ― (1 ― 𝜀𝑅)2 ― (1 ― 𝜀𝑅)4(𝑙𝑛(1 ― 𝜀𝑅) ― 0.75))

(5)

4𝐺

Since Reynolds number and mass flow rate for the film flow are defined as 𝑅𝑒 = 2𝜋𝑅𝜌𝜈 and 𝐺 = 𝑤𝜌𝑆𝑓, respectively. The cross-sectional area of the film flow is determined from 𝑆𝑓 = 𝜋(𝑅2 ― 𝑟2) = 𝜋𝑅2𝜀𝑅 (1 ― 𝜀𝑅). We have the following relationship between Reynolds number and cross curvature ratio from Equation (5):

𝑅𝑒 =

𝑔𝑅3(0.25 ― (1 ― 𝜀𝑅)2 ― (1 ― 𝜀𝑅)4(𝑙𝑛(1 ― 𝜀𝑅) ― 0.75)) 𝜈2

(6)

From Equations (5) and (6), we can calculate the thickness, Reynolds number and average velocity of the film flow. The above analysis does not consider particle size and clustering because the velocity of nanoparticles slipping in the base fluid flow under the gravity is negligible. Buongiorno [15] pointed out that for nanoparticles with size less than 100nm, the slipping velocity in the base fluid under gravity is less than 1.6 × 10 ―8𝑚 ∙ 𝑠 ―1. The slipping velocity of the nanoparticles caused by the gravity is much less than the average flow velocity in this case. Therefore, it is considered that the nanoparticles move with the base fluid even with certain degree of clustering. The internal radius, R, of absorber vessel is 0.1075m. Since the solution concentration varied during the absorption test from 53.9% to 51.3%, an average concentration 52.6% is used here for the evaluation. The solution temperature used for the evaluation is 25℃. The density and viscosity of the aqueous lithium bromide solution for the evaluation were taken from R. J. Lee et al [16]. Table 2 shows the calculation results for the flow rates 3.0L/min and 3.5L/min of Libr-H2O + nanoparticles solution from Equations (5) and (6). Table 2 The flow parameters in the absorber vessel (solution concentration 52.6%, temperature 25℃ ) Flow rate, L min-1 3.0 3.5

Film thickness, mm 0.382 0.402

Reynolds number 121 141

Average velocity, m s-1 0.194 0.215

4.4.2 Absorption rate and the frequency of nanoparticles movement The experimental results suggest there was a correlation between the vapour absorption rate and the frequency of the nanoparticles’ movement in the film flow. Vessel Wall

Spray Flow to Wall

Flow Surface 10mm a

Nanoparticle’s Route in Liquid

Intensity of Magnetic field

(b)

(a)

10

Journal Pre-proof Figure 11 (a) Magnetic field of the magneto (cross-sectional view of the magnetic strip), (b) Nanoparticle’s moving route relative to the liquid flow Of all three cases, the 2cm gap distance gave the highest absorption rate. The vapour absorption rate decreases as the gap distance increases to 3.5cm. The lowest vapour absorption rate took place in the case of zero gap distance. This phenomenon could be linked to the frequency of nanoparticles movement caused by the magnetic field. Table 3 lists the frequencies of the nanoparticles’ movement for three configurations. They were calculated from the equation below: 𝑓=

𝑤 𝑙

where, 𝑤 is the average velocity of the flow and l is the centre to centre distance between the magnetic strips. The distance l is equal to the gap distance a plus the width of the magnetic strip, i.e., 𝑙 = 𝑎 + 1 (𝑐𝑚) in this case. Table 3 The frequencies of nanoparticle movement in different gap distance and flow rate Gap distance “a” between the magnetos, cm 0 2.0 3.5

Nano particle movement frequency, Hz Flow rate 3.0 L min-1 Flow rate 3.5 L min-1 0 0 6.5 7.2 4.3 4.8

A zero frequency was given to the zero-gap configuration in Table 3 based on the understanding that there is no variation of the magnetic field over the length covered by the magnetic strip, consequently, no slipping movement. Therefore, it had the lowest absorption rate. With the gap distance increasing from 2.0cm to 3.5cm, the frequency decreased by 43.2% and 42.9% for 3.0L min-1 and 3.5L min-1, respectively. The less frequent movement of the nanoparticles inevitably reduced the heat and mass transfer in the flow layer and so did the vapour absorption rate. This suggests that a high frequency movement of nanoparticles benefited the vapour absorption process. However, further study is needed to understand the relationship between the vapour absorption rate and the frequency of the nanoparticles movement. Given that the frequency of the nanoparticles’ movement is a function of the flow velocity, we can see that the strength and the distribution of the magnetic field have to be determined with reference to the flow velocity. This means that the film flow velocity, the strength and distribution of the magnetic field have to be optimised to maximise heat and mass transfer in the liquid film flow. 5. Error and uncertainty analysis 5.1 Error for the average absorption rate The water level and time readings could introduce the error to the experimental results as they were used to calculate the vapour absorption rates. In the experiment, the level was read from a ruler fixed on to the absorber with millimetre resolution and the duration time was read from a stopwatch. The conversion rate of the mass against the level is 20 grams per centimetre level change in the evaporator vessel, which was calibrated experimentally. In the tests, the smallest level change in the evaporator was 9.0cm for the fluid LiBr-H2O+Fe2O3 circulating at 3.0L min-1 and the largest change was 15.0cm for the fluid LiBr-H2O+Fe2O3 at 3.5L min-1 during 25 minutes of absorption. If the level reading is taken ±0.5mm for a millimetre resolution ruler, for 9.0cm level change, the error from the level reading is ± 0.5 90 =± 0.56%.

11

Journal Pre-proof Assuming ± 5 seconds for taking the water level readings, this counts ± 0.33% for a duration of 25 minutes. The compounded error to the average absorption rate caused by time and level readings is ± 0.562 + 0.332% =± 0.65% for the case of 3.0L min-1 and ± 0.47% for the case of 3.5L min-1. The evaporating and absorption temperature also influence the vapour absorption rate. In this experiment, K type thermocouples were used for measuring the temperature in the evaporator and the absorber. The accuracy of these standard K type thermocouples is recommended ± 0.75%. Squirrel Data Logger (2020/2040 series) was used for temperature and pressure sampling. The instrument has an accuracy of ± (0.05% 𝑟𝑒𝑎𝑑𝑖𝑛𝑔𝑠 + 0.025% 𝑟𝑎𝑛𝑔𝑒). Thus, the maximum compound error caused by the evaporating and absorption temperature measurement is estimated within ± 1.5%. The pressure readings were used only for confirmation of the operation conditions. Therefore, the overall accuracy for the average absorption rate is estimated within ± 2%. 5.2 Uncertainty for the experimental results Watlow EZ-ZONE PID controller was used for the evaporating temperature control. The evaporating temperature was controlled within 5℃ ± 1.5℃. It was observed that the high fluctuation happened randomly within the first 5 minutes and the cycle of the fluctuation was approximately 1 minute in the test. The solution temperature before flowing into the absorber was maintained by manually adjusting the flow rate of cooling water to the heat exchanger. The variation of the solution temperature was maintained within 25℃ ± 1℃ in all tests. Since the saturation vapour pressure, which is a measure of driving force for the vapour absorption, is a function of temperature, the variation of the temperatures inevitably affects the vapour absorption rate. The uncertainty of the experimental results can be analysed from the information provided in Table 4 and Table 5. Table 4 Saturation vapour pressure for the solution concertation 52.6% in the absorber Temperature, ℃ Vapour pressure, mbar Difference, mbar Deviation, %

24 5.848 -0.39 -6.3

25 6.238 0 0

26 6.652 +0.414 +6.6

Table 5 Saturation vapour pressure for water in the evaporator Temperature, ℃ Vapour pressure, mbar Difference, mbar Deviation, %

3.5 7.847 -0.878 -10

5 8.725 0 0

6.5 9.687 +0.962 +9.9

The difference of saturation vapour pressure between the evaporator and the absorber is a driving force for the vapour absorption process. In all possible combinations, the combination of the highest solution temperature with the lowest evaporating temperature gives the highest deviation. Under this worst-case scenario, the temperature fluctuation brings in a compound uncertainty could be as high as 11.98%. However, for the average absorption rate, the uncertainty was significantly smaller than the worst-case scenario. This is because the large fluctuation of the evaporation temperature was short and because the cycle of fluctuation was much shorter than the duration time for a single experimental test. The large part of the plus-minus effects due to the fluctuation could be cancelled each other over the test period. For a duration of 5 minutes the worst-case scenario, its weight is 0.2 on an average vapour absorption rate over 25 minutes. The uncertainty in this case, therefore, is 11.98% × 0.2 = 2.40%. The uncertainty brought in from the comparison of two individual tests is 2 × 2.40% = 3.39%. 5.3 Accuracy of the results 12

Journal Pre-proof Based on the analysis above, it can be concluded that the accuracy of the experimental results should be within ± 22 + 3.392% =± 3.94%. If additional 2% are allowed for anything that may not have been counted but could affect the vapour absorption, such as the air leaking into the system through the fittings, occasional interruption to the cooling water due to unstable the main water supply and variation of the room temperature, the accuracy of the experimental results is estimated within ± 6%. The air leakage of the system itself is tiny at a rate of 6 mbar/day which is not a significant factor because the duration of the absorption test is less than 30 minutes. The uncertainty considered here also is the different amount of remaining air in the system after evacuation each time. Again, this shouldn’t be a significant one as the system was evacuated for an enough time before test. Therefore, the additional 2% are more than enough to cover these uncounted factors and it is a conservative estimation. 6. Conclusions This investigation experimentally investigated the enhancement of the vapour absorption rate by using external magnetic field to induce the slipping movement of the ferric oxide nanoparticles in the aqueous lithium bromide solution. The experimental results show a significant increase in the vapour absorption rate by using this method. The average absorption rates achieved with the magnetic field influence from this experimental study were 1.58 times and 1.32 times higher than that without it for the solution circulating at 3.5L min-1 and 3.0L min-1, respectively. The results show that the nanofluid can enhance the vapour absorption process, particularly, in the case where the heat and mass transfer in the liquid phase dominates the whole process. This is evident that the enhancement in the absorption rate was more significant with the high circulation flow rate, i.e., in the thick film. While the vapour absorption rate can be further increased by applying external magnetic field to induce the slipping movement of the nanoparticles in the fluid, the enhancement was influenced by the configuration of the external magnetic field. In this work, the frequency of the nanoparticles’ movement in the film flow was introduced as a parameter to describe the effect of the magnetic field on the vapour absorption rate. Our analysis shows that the vapour absorption rate increases with the frequency of the slipping movement of the nanoparticles in the film flow. Since the slipping movement of the nanoparticles in the fluid is influenced by not only the magnetic field but also the flow’s characteristics, the frequency of the slipping movement should be optimised according to the flow characteristics, the intensity and distribution of the external magnetic field, which requires for further study. Acknowledgement The authors would like to thank our former undergraduate students Yujia Ji and Junjie Li for their contribution of testing the base fluid’s vapour absorption rates in their dissertation project. References [1] Kim, J., Jung, J. Y., Kang, Y. T., The effect of nano-particles on the bubble absorption performance in a binary nanofluid, International Journal of Refrigeration, 29 (2006) 22-29 [2] Kim, J. K., Jung, J. Y. & Kang, Y. T., Absorption performance enhancement by nano-particles and chemical surfactants in binary nanofluids. International Journal of Refrigeration, 30 (2007) 50-57. [3] Kang, H. J. Kim y K. I. Lee, Heat and mass transfer enhancement of binary nanofluids for H2O/LiBr falling film absorption process, International Journal of Refrigeration, 31 (2008) 850-856. [4] H. Kim, J. Jeong, Y.T. Kang, Heat and mass transfer enhancement for falling film absorption process by SiO2 binary nanofluids, Int J Refrig, 35 (2012), 645-651 [5] Zhang, L., Fu, Z., Liu, Y., Jin, L., Zhang, Q. and Hu, W., Experimental study on enhancement of falling film absorption process by adding various nanoparticles, International Communications in Heat and Mass Transfer, 92 (2018) 100-106.

13

Journal Pre-proof [6] Zhang, L., Liu, Y., Wang, Y., Jin, L., Zhang, Q. and Hu, W., Experimental Study on the Enhancement of Mass Transfer Utilizing Fe3O4 Nanofluids, Journal of Heat Transfer 140(1), (2017) 012404. [7] Wang, G., Zhang, Q., Zeng, M., Xu, R., Xie, G. and Chu, W., Investigation on masstransfer characteristics of the falling film absorption of LiBr aqueous solution added with nanoparticles, International Journal of Refrigeration 89 (2018)149–158. [8] Amaris, C., Vallès, M. and Bourouis, M., Vapour absorption enhancement using passive techniques for absorption cooling/heating technologies: A review, 231 (2018) 826-853. [9] Philip, J., Shima PD., Raj, B. Enhancement of thermal conductivity in magnetite based nanofluid due to chainlike structures, Applied Physics Letter, 91, 203108 (2007); doi: http://dx.doi.org/10.1063/1.2812699. [10] Angayarkanni, S. A. & Philip, J. Review on thermal properties of nanofluids: Recent developments. Colloid and Interface Science, 225 (2015) 146–176. [11] Suresh, A. Bhalerao,. Rate intensification of mass transfer process using ferrofluids, Indian Physical applied, 40 (2001) 172-184. [12] Komati, S. & Suresh, A. Anomalous Enhancement of Interphase Transport Rates by Nanoparticles: Effect of Magnetic Iron Oxide on Gas-Liquid Mass Transfer. Department of Chemical Engineering, Indian Institute of Technology, 49 (2010) 390–405. [13] Komati, S. & Suresh, A. CO2 absorption into amine solutions: a novel strategy for intensification based on the addition of ferrofluids. Journal of Chemical Technology and Biotechnology, 83 (2008) 1094–1100. [14] Wu, W., Liu, G., Chen, S. and Zhang, H., Nanoferrofluid addition enhances ammonia/water bubble absorption in an external magnetic field, Energy and Buildings, 57 (2013) 268-277. [15] Buongiorno, J. Journal of Heat Transfer, Transaction of the ASME, 128, (2006) 240-250. [16] Lee, R.J. DiGuilio, R.M., Jeter, S.M. and Teja, A.S. Properties of lithium bromide-water solutions at high temperatures and concentrations-II: Density and Viscosity. Symposium paper presented at the ASHRAE Winter meeting, February 10-14, 1990, Atlanta, Georgia, 709-714. Nomenclatures a Winding gap edge-to-edge between two magnetic strips, cm f Frequency, s-1 g Gravitational acceleration velocity, m s-2 G Mass flow rate, kg s-1 l Centre to centre distance between two magnetic strips, m r Radial coordinate, m R Internal radius, m Re Reynolds number Sf Cross-sectional area of film flow, m2 w Velocity of film flow, m s-1 𝑤 Average velocity of film flow, m s-1 Greek ν Kinematic viscosity, m2 s-1 δ Thickness of film flow, m εR Relative cross curvature ratio, δ/R ρ Density, kg m-3

14

Journal Pre-proof

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Journal Pre-proof Highlights    

Magnetically induce nanoparticles’ slipping movement in aqueous LiBr solution. The slipping movement significantly increases the vapour absorption rate. The effect of this method is more significant for thick film flow. The enhancement is related to the frequency of the slipping movement.