Vibration-enhanced direct contact heat exchange using gallium as a solid phase change material

International Communications in Heat and Mass Transfer xxx (xxxx) xxx

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Vibration-enhanced direct contact heat exchange using gallium as a solid phase change material S.A.B. Al Omari a, *, A.M. Ghazal b, E. Elnajjar a, Z. Qureshi a a b

Department of Mechanical Engineering, UAE University, Al Ain, United Arab Emirates Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, Canada

A R T I C L E I N F O

A B S T R A C T

Keywords: Solid gallium Heat sink Direct contact vibration-enhanced heat ex­ change Phase change material, thermal energy capture and storage

This study experimentally addresses cooling hot liquid in a heat sink under mechanical vibrational excitations. We investigated vibration-enhanced direct contact heat exchange between hot water and a heat sink composed of a phase change material, solid gallium (Ga). The whole sink assembly was vibrated with a sinusoidal wave in the vertical direction. Latent heat and low melting temperature of Ga restricted the maximum temperature rise and the superheating of molten Ga between the water and the solid Ga body. The total amount of Ga melted during the heat exchange with water was measured, providing the share of latent and, in turn, sensible heat absorbed by Ga during the process. Vibration drastically enhanced the cooling rates of hot water under the tested frequencies (20 and 50 Hz) and amplitudes (0.3, 0.5 and 0.7 mm). The enhancement in water cooling was better pronounced for amplitudes higher than 0.3 mm. Under 50 Hz frequency and 0.7 mm amplitude, 99% of heat lost by water was dumped into the gallium sink and 1% was dissipated into the surrounding environment. Under static nonvibrating conditions the heat sink could only capture about 60% of the heat lost by the water. The rest was dissipated into the environment.

1. Introduction Many heat-generating devices require effective cooling, which is achieved by using liquid coolants such as water. Such cooling liquids need to be re-cooled, and the thermal energy needs to be discharged from them before they can be reused in a closed-loop system to achieve the continuous cooling of the heat-generating source. Consequently, effective methods and techniques that can remove heat from hot liquids to bring these liquids back to low starting temperature and qualify them as effective coolants are of paramount significance. When two immiscible liquids are brought into direct contact, they exchange heat with each other at a faster rate than when being separated by an intervening solid surface (e.g., tube wall or a metallic plate) [1–5]. Moreover, this direct contact heat exchange between the two immiscible liquids is even further enhanced when the hot liquid loses its heat directly to a heat sink material that has relatively high thermal con­ ductivity and low melting temperature, such as Ga (the thermal con­ ductivity and melting temperature of Ga are about 30 W/m.oC and 29 ◦ C, respectively). This allows solid Ga to melt at a low temperature and hence form a mushy high thermal conductivity liquid layer that interfaces the to-be-cooled liquid with the rest of the unmelted solid Ga

body. The direct contact between the mushy region and the hot liquid would facilitate enhanced heat exchange rates (see for example [3,5]). However, irrespective of the favorable role played by the low melting temperature of Ga (used as the heat sink material in our research), experimental findings [6,7] still indicate some superheating effects of liquid Ga in the mushy layer sandwiched between the hot liquid source and the rest of the solid Ga body. This superheating effect leads to increased temperatures at the contact interface beyond 30 ◦ C (the nominal melting temperature of Ga). The extent of this superheating largely depends on water temperature; hence, it depends on the level of heat flux from water, as well as the specific heat capacity of the heat sink material (Ga in this research). Nevertheless, the thermal conductivity of Ga is still incapable of completely suppressing and smoothing out the tendency of the rapid temperature stratification in the mushy Ga region because of the limited specific heat capacity of Ga, especially under a high heat flux. This temperature stratification and liquid Ga super­ heating would lower the temperature difference between water and the mushy Ga region and thus adversely affect the heat exchange rate be­ tween the two and, in turn, the rate of water cooling. One passive cooling approach the present authors adopted in pre­ vious research [6,7] to alleviate the adverse superheating effects of the mushy Ga region interfacing the hot source and the unmelted solid Ga is

* Corresponding author. E-mail address: [email protected] (S.A.B. Al Omari). https://doi.org/10.1016/j.icheatmasstransfer.2020.104990 0735-1933/© 2020 Elsevier Ltd. All rights reserved.

Please cite this article as: S.A.B. Al Omari, https://doi.org/10.1016/j.icheatmasstransfer.2020.104990

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vibration on the overall heat transfer enhancement of conventional heat exchangers. The pulsated flow was proved to double the convective heat transfer coefficient and reduce the fouling resistance to one-third of its value. In addition, Liu et al. [19] examined the effect of transverse vi­ bration on the heat transfer characteristics of the flow. Recently, Li et al. [20] investigated the enhancement of heat transfer of fin-tube of vehicle radiator by vibrational effects where they considered effects of fre­ quency in the range from 1 to 20 Hz and amplitude from 1 to 6 mm. They concluded that vibration at the upper limit of the tested frequency and amplitude range leads to very clear enhancement in heat transfer rates, but lead to increase in pressure drop. Sarafraz et al. [21] studied the effect of vibration on the heat transfer performance of micro channel heat exchanger equipped with a (10 Hz/ 50 Hz) resonator. They studied the flow and heat transfer of liquid metal eutectics with composition 90%Ga-10%In and 85%Ga-15%In. They also studied the case of pure liquid gallium flow and heat transfer in the heat exchanger. They concluded that the maximum heat transfer enhance­ ment was 10% belonging to pure gallium and at 50 Hz, followed by pure gallium at 10 Hz. They observed much less effect of vibration on the heat transfer performance when the liquid metal eutectics are used. Research was also expanded to examine nanofluids instead of con­ ventional coolants. Hosseinian et al. [22] described the influence of vibration in a double-pipe heat exchanger with circulating multi-layer carbon nanotube (MWCNT) nanofluids. The researchers also proved that vibration reduces the agglomeration of the nanoparticles and thus enhances the heat transfer. Naphon and Wiriyasart [23] suggested the integration of various heat transfer techniques, including nanofluids, micro-fin tube, magnetic field, and pulsating flow, to increase their thermal efficiency. Sarafraz et al. [24] also studied the effect of vibration on mitigating fouling due to nanoparticles and enhancing heat transfer in plate heat exchangers working with CuO/water nanofluid. It was found that low frequency vibration helped mitigating particles fouling hence reduce thermal resistance and decrease friction and pressure drop. Moreover, the vibrational effects could be applied to various kinds of PCMs to facilitate the phase change process. Boiling heat transfer is considered to be one of the phenomena that are classified under liq­ uid–vapor phase change processes, which can be enhanced by vibration. Zheng et al. [25] investigated the effect of ultrasound vibration on the boiling heat transfer enhancement for different structural tubes. Further, Zheng et al. [26] analyzed the influence of vibration on boiling flow using liquid hydrogen. Boziuk et al. [27] studied the effect of acoustic actuation on the boiling heat transfer enhancement. The contribution of vibration to the heat transfer for solid–liquid PCMs is mostly limited to designs that allow a hot source (e.g., heated plates) to transfer heat to a heat sink enclosure containing PCM under vibration. Quan et al. [28] experimentally studied the effect of vibration on the phase change process of n-octadecane in rectangular enclosures. Quan [29] later analyzed ice instead of n-octadecane. Choi and Hong [30] experimentally studied the effect of ultrasound vibration on the melting process of n-octadecane in a rectangular vessel. Oka [31] studied the effect of vertical-oscillated vibration signals on the melting enhancement of PCMs. Oh et al. [32] modified the experimental setup described in [30] to understand the effect of the ultrasound vibration on the melting process of the PCM. The usage of ultrasound vibration accelerated the melting process by up to 2.5 times. This was attributed to the acoustic streaming and cavitation resulting in the thermal oscillating flow that enhanced the heat transfer coefficients by introducing flow instabilities that can destroy the diffusion-dominant melting mode from the heated plate. Yang and Oh [33] conducted a numerical analysis to analyze the acoustic pressure effect. The authors used two ultrasound vibrators and concluded that the high pressure imposed by the ultra­ sonic wave is responsible for development of intensive flows, resulting in flow instabilities and relative motions. The researchers later used four vibrators instead of two and mentioned that the numerical analysis was conducted only because of the difficulty of using a hydrophone to

Nomenclature c DAQ Ga m P%

specific heat capacity [kJ/kg. K] Data acquisition Gallium mass [kg] confidence (probability) level used in the uncertainty analysis PCM Phase Change Material Q Heat transferred [kJ] Q˙ water Rate at which heat is lost form the hot water, [W] Q′′ Heat flux [W/m2] R Thermal resistance across the water‑gallium interfacial region, [K/W] S The standard error of the mean used in the uncertainty analysis ΔTinterface Temperature difference across the water‑gallium interfacial region, [K] ΔT Temperature difference used in heat transfer calculations [kJ] T’ true estimated value of measured temperature T average value of temperature measurement tv,P is the “t-estimator” used in uncertainty analysis UQ Heat transfer uncertainty Heat flux uncertainty Uq

to embed within the solid Ga body discrete chunks of an additional phase change material (PCM) material that has even lower melting temperatures than the melting point of Ga (i.e., less than 30 ◦ C). These PCM chunks would practically act as a heat sink for Ga. With that, the temperature of both solid Ga and consequently the mushy Ga region would be lowered, leading to the suppression of the extent of mushy Ga superheating and, hence, maintaining a sufficiently high driving tem­ perature difference between the hot water and Ga. Different other approaches have been implemented in the literature to overcome limitations in passing the heat from one location to another within PCM heat sinks and energy storage systems that leads to im­ provements in the heat charging and discharging rates (see for example [8–11] and the references cited therein). In this present work, we test another approach to overcoming the temperature stratification and the superheating effects in the mushy Ga layer between the hot source (water) and solid Ga beneath it. Here we apply external mechanical vibrational excitations to the two immiscible liquids while they exchange heat in a direct contact manner. This approach is aimed at enhancing the mixing of Ga at different sites within the mushy region to allow for the rapid passing of the heat received from water by the upper part of the mushy layer downward toward solid Ga that is undergoing melting. This approach, practically, adds to the role played by the inherently high thermal conductivity of Ga and results in effectively higher apparent thermal conductivity of Ga beyond its typical nominal value. Further, this vibration-enhanced mixing in­ creases the rates of convective heat transfer within the mushy region and subsequently to the solid Ga body below this region that is undergoing a solid–liquid phase change process. Furthermore, the vigorous corruga­ tions induced by applied vibrational excitations magnify the contact surface area between liquid Ga in the mushy region and the hot water, which is expected to result in faster transfer of the heat from the water down into solid Ga. Vibrational effects in the heat transfer area have been studied by testing heating wires [12,13] and standard regular shapes, such as plates [14,15] and cylinders [16,17]. The ideas have been developed further to include the influence of vibration on the heat transfer of flowing fluids. Cheng et al. [18] have highlighted the beneficial effect of flow-induced 2

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measure the acoustic pressure at the PCM’s elevated temperature [34]. Joshi et al. [35] studied the effect of vibration on a passive battery thermal management using a system which disposes PCM in an enclo­ sure that houses the battery pack. Ceramic cartridge heaters are used to mimic 2300 mAh 18,650 Lithium-ion batteries. The transient thermal behavior of the battery pack at different discharge rates and different vibrational parameters (20–30 Hz frequency and amplitude of 30 mm/s) were investigated. A Recent review by Chakravorty [36] presents techniques and ap­ proaches adopted over the past six decades to intensify the exchange rates in chemical engineering processes by implementing pulsation and vibrational effects. Given the above presented literature review on the areas related to implementing vibrational effects to heat transfer processes, to the best of the knowledge of the present authors, direct contact heat transfer under mechanical vibrational effects between a high thermal conductivity solid PCM undergoing phase change and a hotter immiscible liquid, with the PCM in this case acting as a heat sink material or energy storage medium, is not known in published literature. Nonetheless, the present authors, as highlighted earlier above, studied the enhancement of heat transfer occurring between high thermal conductivity solid PCM and other immiscible liquids but without applying vibrational effects [1,4–7]). Thus, utilizing vibrational effects to enhance heat transfer covers one of the following: (1) the cooling of hot solid objects, (2) the heat transfer of flowing fluid, and (3) the phase change of typical PCMs. In this work, we introduced vibrational effects to a heat sink used to cool down hot water brought into direct contact with a PCM, namely solid gallium (Ga), which has a low melting temperature and high thermal conduc­ tivity. We hypothesize that vibrating the whole heat sink involving the liquid to be cooled (hot water) and the PCM as the cooling material (solid Ga) and bringing them in direct contact with each other can be an energy-efficient method of facilitating faster heat transfer from the hot liquid to Ga. This is achieved by suppressing the tendency of melted Ga during the process to experience any significant superheating and by maximizing the heat transfer contact area by vibration between the two materials exchanging heat. Under these conditions, melted Ga in the mushy region contacting water would then not be expected to experi­ ence any significant superheating due to enhanced mixing effects attributed to vibrational excitations. This means that the vibration would put a threshold for the temperature boundary condition at the interface between the hot liquid water and melted Ga that is close to the nominal value of Ga’s melting temperature, namely 30 ◦ C, irrespective of the increased heat flux from the hot liquid water (the source) that is being intensified by vibrational effects. It should be re-emphasized that the low specific heat capacity of Ga would tend to support superheating melted Ga in the mushy region and would thus be expected to adversely affect the temperature difference between the hot liquid and the mushy Ga region. The present study attempts to determine the vibrational effect and shed light on how it can reverse such adverse effects caused by Ga’s low specific heat under different experimental vibrational settings. Finally, although vibration is known to enhance heat transfer as highlighted in the above literature review, to the best of our knowledge, none of the previous publications addressed vibration to enhance direct contact heat transfer at the interfacial region between two immiscible liquids, involving solid PCM undergoing melting.

saved in a computer through data acquisition (DAQ). Used thermocouple were calibrated using two-point calibration approach, which is a common way of rescaling the temperature output. It corrects both the slope and the offset errors, knowing that the ther­ mocouple output is reasonably linear within the measurements range. The calibration was performed by using two reference points typically ice-bath and boiling water. To excite the system to vibrational signals, a B&K LDS shaker was used. The device consists of different components, namely a field generator (to supply the shaker with the power required for operation), a power amplifier (to amplify the delivered input signals), controller/ DAQ (to control the displaced motion and save the data), a fan (to cool down the shaker), and two accelerometers, input and output, (to deliver the input signal and record the output signal). The process starts by entering the input signal through a desktop computer using Shaker Control software. The signal is then passed to the controller, to the power amplifier, and then to the shaker. Then, the input accelerometer gives a feedback signal to the controller to make the necessary adjust­ ments and pass the signal to the power amplifier in a loop. The output accelerometer sends the output data to the DAQ to be saved on the computer. A simplified illustration of the above process, including the names of the shaker’s components and a representation of the experi­ mental testing, is presented through the schematic diagram in Fig. 1. To ensure the firm fixture of the testing setup and to accommodate for its occupied space, a tapered aluminum (Al) plate (small diameter = 15.5 cm (see Fig. 2(b) and (c)); larger diameter = 25.5 cm (see (a)) was manufactured, and nine holes were drilled into it so that bolts and ac­ celerometers could be placed on the shaker’s base. Additional five holes were drilled in the Al plate to fix a 16.5 cm cylinder at which the 8.7 cm cylinder, the one that hosts Ga, was placed (see Fig. 2(a), (e)). It is worth mentioning that the larger cylinder was added to avoid any water leakage from the smaller cylinder or water spillage while water was poured on top of Ga. To achieve this, the base of the larger cylinder was manufactured to be thick enough, and four holes were drilled on the base so that the small cylinder could be firmly fixed in the large cylinder (see Fig. 2(d)). It should be noted that precautions, such as the drilled holes’ depth in both the Al plate and the large cylinder, were considered (e.g., they were not drilled through) to avoid any water leakage to the shaker’s basement. As depicted in Fig. 1, the thermocouples were given numbers, indi­ cating the locations at which they were placed. For the temperature measurement in the main body of the water, three thermocouples (not illustrated in the schematic in Fig. 1) were placed in the water so that their average value could be taken to minimize the experimental errors. A perforated plate was affixed at the top of the heat sink container; the thermocouple probes were allowed to penetrate through the relevant holes of the plate, and their tips reached the depths at the measuring locations in the water and Ga as highlighted in the schematic drawing presented in Fig. 1 (locations 1 to 4). Table 1 lists the locations of the thermocouples’ tips measured from the upper edge of the testing heat sink container. In this study, vertical sinusoidal vibrational signals were applied to the heat sink assembly (including both the to-be-cooled hot water and the sink material (Ga)). Two levels of frequency (20 and 50 Hz), and three values of the amplitudes (0.3, 0.5 and 0.7 mm) were adopted in the experiments. It should be noted that the values given for the amplitudes represent peak-to-peak displacements. Prior to any experiment, the testing container was placed on an ice bath to sufficiently reduce Ga’s temperature below its melting point. Then, Ga was allowed to heat up naturally under ambient conditions (in a room temperature of about 23 ◦ C) to about 15 ◦ C; the temperature at which the recording of the data started. Each test was repeated three times. The maximum standard deviation for water and Ga measurements were 0.2 ◦ C and 0.18 ◦ C, respectively. Measurements involved certain level of uncertainty, the main objective of the uncertainty analysis is to quantify the errors associated

2. Experimental setup Two hundred milliliters of hot water was poured on top of a fixed amount of solid Ga (120 ml) either at a static condition or at the spec­ ified vibrational amplitude and frequency signals conditions. Ga and hot water were placed in a mild steel cylindrical container of a diameter of 8.7 cm and a height of 13.2 cm. The process was monitored by placing Ktype omega thermocouples (accuracy=±1.0 ◦ C) at the locations of in­ terest, and the recorded data at a sampling rate of nearly one sec were 3

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Fig. 1. Schematic diagram of the vibration testing process: a) desktop computer with Shaker’s software installed to collect the input vibrational signal, b) controller/ DAQ, c) power amplifier, d) field generator, e) fan, f) shaker, g) accelerometer, and h) desktop computer for temperature data collection.

Fig. 2. (a) and (b) Design Features of the Vibrating System: Top and Back Views of the Manufactured Tapered Al Plate respectively, (c) Shaker’s Base Fixture, (d) Big cylinder base, and (e) Assembled Fixture.

with the set of data acquired by measurements, and to identify how these uncertainties impact the experimental results’ accuracy. The true estimated value of a measurement can be obtained in terms of average value of the measurement and its uncertainty, as given below: Estimated True value = Average Value ± Uncertainty (P%)

Where T ‘: true estimated value T: average value of the measurement tv,P:is the “t-estimator” which is a function of probability P and de­ gree of freedom v = N – 1 N: measurements number S: The standard error of the mean P%: confidence (probability) level

(1)

For temperature values, the true estimated value can be obtained as: ′

T = T ± tv,P S; (P = 90%)

(2) 4

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Table 1 Thermocouple locations for vibration experiments. Thermocouple #

Measured Heights (cm)

Location

1 2 3 4

12.2 11.3 6.1 10.8

Middle of Ga Bottom Hot Water–Ga Interface (in Ga) Middle of Hot Water Upper Hot Water–Ga Interface (in the water)

Based on the above uncertainty analysis, error bars have been added to the reported temperature measurements and the estimated true value predications are given as follows: Gallium Temperature = T ± 0.43◦ C (P = 90%) Lower Interface Temperature = T ± 1.24◦ C (P = 90%) Upper Interface Temperature = T ± 1.28◦ C (P = 90%) The propagated uncertainties in the calculated quantities reported in the results are obtained as follows: (3)

Q = m c ΔT UQ = Q ′

Q′ = Uq = Q′ ′

√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ( )2 ( )2 UΔT Um + ΔT m

(4)

cp m ΔT t.A

(5)

√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ( )2 ( )2 ( )2 ( )2 UΔT Um Ut UA + + + ΔT m t A

(6)

Where Q: Heat transferred [kJ] Q′′ : Heat flux [W/m2] UQ: Heat transfer uncertainty Uq: Heat flux uncertainty U ΔT: Manufacturer uncertainty of thermocouples Um: Manufacturer uncertainty of weight scale UA: Manufacturer uncertainty of length scale Ut: Uncertainty in time measurement

Fig. 3. Water temperature history: (a) Group B (20 Hz), and (b) Group C (50 Hz).

results attained under static conditions in test 1A (cf. results of tests 1B and 1A, in Fig. 3a). By contrast, the influence of the vibrational effects commences and becomes evident as the vibrational amplitudes increase further and exceed 0.3 mm. This conclusion can be confirmed by noticing that in test 2B, the time needed to reduce the water temperature by about 35 ◦ C (from 76 ◦ C to 40 ◦ C) drops by approximately 33%, whereas the time reduction reaches 60% when the amplitude is increased to 0.7 mm in test 3B (compare results of tests 2B, 3B, and 1A in Fig. 3a). The water cooling rates increase immensely under the conditions of test group C, where the frequency and amplitude were 50 Hz and 0.7 mm, respectively. As compared with the static case (test 1A), Fig. 3b indicates that the time to drop the water temperature by about 35 ◦ C in test 3C is reduced by 90% (compare this percentage with 60% attained in test 3B; cf. Fig. 3a and b). However, even with the higher level of frequency of 50 Hz in test group C, effects of vibration on the cooling of hot water are not evident as long as the applied amplitudes are less than the threshold of 0.3 mm (cf. results of test 1C in comparison test 1A). To grasp and appreciate further the role played by vibration regarding heat transfer enhancement, a closer look into the details of the temperature history of the interfacial region between the water and Ga, as well as the main Ga’s body, are presented in Figs. 4–6. As can be seen in Fig. 4, when the water (with initial temperatures around 80 ◦ C) is poured on top of solid Ga, the temperature at the lo­ cations of the thermocouples rapidly increased. Because of the high thermal conductivity of Ga, the temperature of the Ga body rises in 10 s to levels approaching the melting temperature of Ga (about 30 ◦ C). The two temperature recordings in the immediate vicinity of the interfacial plane between water and Ga from the top and bottom sides of that plane

3. Results and discussion A reference baseline case under static conditions will be used to assess the extent to which vibration affects the rate of cooling of the used hot source (i.e., water). Table 2 summarizes the different experimental runs conducted and their operating conditions. In Table 2, the baseline run is marked as test 1A. The rest of the runs are classified based on the vibration parameters, namely frequency and amplitude (displacement). Fig. 3 illustrates water temperature history with time during the conducted experiments. Fig. 3a compares the results of the runs of test group B with the results of the baseline case without vibrational effects (static conditions; test 1A). For test 1B with a frequency of 20 Hz and amplitude of 0.3 mm, Fig. 3a indicates no clear improvements over the Table 2 Summary of the conducted vibration experiments. Hot water amount: 200 ml Test group A Frequency (Hz) 0

B 20

Test number Amplitude (mm)

1B 0.3

1A N/A

C 50 2B 0.5

3B 0.7

1C 0.3

2C 0.5

3C 0.7

5

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Fig. 4. History of the interfacial region and Ga body temperature for the static case without vibrational effects (Test 1A).

Fig. 6. History of the interfacial region and Ga body temperature with vibra­ tional effects (Test Group C: Frequency 50 Hz; Amplitude: 0.3 mm, 0.5 mm, and 0.7 mm).

also indicate a very rapid temperature rise in the first 10 s. The upper interfacial region (on the water side) experienced a very sharp temper­ ature rise and overshot temperatures around 65 ◦ C before this upper interfacial temperature started to decline as heat was transferred from the water to the Ga body. Similar temperature overshooting took place at the bottom side of the interfacial plane with lower peak levels at 40 ◦ C recorded about 10 s after the start of the test. After approximately the initial 10 s of the test time, the bottom side interfacial temperatures started to decline to the levels close to those attained in the middle of Ga’s main body, which are only slightly higher than the nominal melting temperature value of Ga of 30 ◦ C (cf. Fig. 4). Contrarily, the temperatures of the upper interfacial region, though they still continued to decline after the first 10 s of the test time, maintained clearly higher levels close to 40 ◦ C over the period displayed in Fig. 4. When compared with the interfacial region temperature results under vibration, these comparatively higher interfacial temperatures in test 1A have a direct adverse impact on the temperature difference between the water and Ga that drives the heat transfer from the water to Ga and thus on the cooling rates of water.

Fig. 5. History of the interfacial region and Ga body temperature with vibra­ tional effects (Test Group B: Frequency 20 Hz; Amplitude: 0.3 mm, 0.5 mm, and 0.7 mm). 6

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Fig. 5 presents the temperature results for the test group B under vibration. Fig. 5 qualitatively indicates the same trend observed in Fig. 4 for the case with no vibration (test 1A). When it comes to the temper­ ature history for the main body of solid Ga, the results of group B cases are both qualitatively and, to a good extent, quantitatively similar to those of their counterpart, in Fig. 4 for Test 1A with no vibration. More specifically, solid Ga temperature rapidly increased to around 30 ◦ C (the nominal Ga’s melting temperature) in the first 10 s by conduction heat transfer before melting of Ga started to take place. After that, Ga’s temperature settled to almost a constant level around 30 ◦ C, indicating that for this absorption stage, mainly latent heat is transferred from water to Ga. As the vibrational amplitudes increased (0.5 mm and 0.7 mm), the rate of heat exchange between the water and molten Ga in the mushy region increases progressively, resulting in the increased melting of solid Ga. Hence, this caused a more pronounced drop in hot water tempera­ ture. The more vigorous vibrational dynamics leads to faster convective heat transfer from water to molten Ga in the mushy region and, subse­ quently, from the upper parts to the lower parts of the mushy region. The effective passing of heat across the mushy region in the downward di­ rection toward solid Ga resulting from the vigorous vibration hence the resulting active mixing and agitation effects restricted the extent of superheating molten Ga in the mushy region; hence it supported main­ tenance of a large temperature difference and thus higher heat transfer rates between water and the Ga’s main body. The agitation and the resulting interfacial surface area increase due to corrugations caused by vibration also contribute to the observed enhancement in heat transfer between water and molten gallium in the mushy region. Evidence on above arguments can be confirmed form the lower temperature levels recorded in the middle of the water body and in the upper and lower interfacial regions for the tests with vibration, especially as the vibra­ tional amplitude increased (cf. results of Figs. 3–5). For test 1B with amplitude of 0.3 mm, there is no significant differ­ ence in the peak levels of the upper and lower interfacial temperatures from those attained in test 1A (cf. Figs. 4 and 5); neither is there a dif­ ference in the time at which these peaks are attained. These peak tem­ peratures, especially the one corresponding to the bottom interface (on the Ga side) start showing clearly lower temperature levels as the vibrational effects are progressively increased. Even though it is still slightly noticeable, in the first 100 s of the test time displayed in Figs. 4 and 5, one cannot clearly see in test 1B much difference between tem­ peratures of the upper interfacial region and the levels attained in Fig. 4 with no vibration. This is in line with the water temperature results for the middle of the water body given in Fig. 3, where the middle water temperatures in test 1B are not significantly different from those in the results of test 1A. Here the vibrational excitations imposed in test 1B are not sufficient to cause any additional impact beyond what is achieved already by the transport phenomenon taking place at the molecular level in conventional heat conduction setting. It should be noted that since the heat source is applied form above the heat sink, contribution to the heat loss form water to the gallium sink will be greatly dominated by pure conduction. The difference between the case with no vibration (test 1A) and the other tests in test group B, namely tests 2B and 3B, becomes more evident after the first 10 s of the test time. Here, the upper and lower interfacial region temperatures in tests 2B and 3B are at lower levels and indicate lower rates of decline with time; this is an indication of the faster heat removal rates from water in these tests. This argument is in line with the water temperature results presented in Fig. 3a. Fig. 6 presents the temperatures of the middle of Ga and interfacial region temperatures for test group C. The same observations reported above for test group B are still applicable qualitatively for test group C. For tests 1C and 2C, the peak temperature levels in the early stages of the tests are somewhat higher than their counterpart tests 1B and 2B. The more active vibrational effects in the tests of test group C cause more heat to pass from the main hot water body toward the lower mushy

region and subsequently to Ga beneath it, resulting in these higher mushy region temperature levels observed in tests 1C and 2C, compared with tests 1B and 2B. For test 3C, which is associated with much more intensive heat transfer activity from the water to the mushy region, the much faster heat transfer from the mushy region to Ga beneath it due to more vigorous vibrational activity leads to suppressing reaching higher temperature peaks in the mushy region in test 3C. Moreover, after the initial 10 s, where melting of Ga in the mushy region starts to be clear, the rate of interfacial temperature decline is more noticeable in the case with much vibrational activities, namely test 3C. This is in line with the arguments laid down above to explain the lower peak levels of tem­ perature in the mushy region in test 3C. It should be noted that vibra­ tional effects are expected to act on the interfacial region leading to enhancement in heat transfer from the mushy region down to the Ga body, causing further intense melting as more and more Ga melting takes place and, hence, as the mushy Ga layer becomes thicker and thicker with time. The temperature of solid Ga’s main body in test group C does not indicate much difference from those reported in the other tests, both qualitatively and, to some good extent, quantitatively. This is attributed to the quite high thermal conductivity of Ga which leads to fast con­ duction of heat throughout the solid Ga causing solid Ga to reach its melting temperature namely about 30 ◦ C and to stay at it all the time while receiving heat from the upper Ga’s mushy layer, irrespective of applied vibrational levels. During the early stages of the tests (10 s), almost no melting of Ga in the interfacial region between water and Ga has happened yet. In this case, the main cause of the initial temperature rise in Ga temperature is heat transfer from water to the solid surface of Ga in contact with the water and subsequently heat conduction throughout the solid Ga body. Apparently, from the test results reported in Figs. 4–6, vibration only has little impact on the above initial stage of sensible temperature rise in Ga. Once melting commences effectively after the initial period of the test, Ga’s temperature does not encounter any significant changes with time, and (as mentioned above) owing to the comparatively high thermal conductivity of Ga, Ga attains almost uniform temperature distribution at any subsequent instant while continually receiving heat from the hotter water. We may expect vibrational effects to play a more decisive role when more and more appreciable amounts of molten Ga are present in the mushy region interfacing Ga and hot water. At that instant, it is expected that these vibrational effects facilitate more intensive heat transfer to take place across the mushy region, thus resulting in more effective water cooling. This argument may be confirmed by the results of test 3C. Fig. 7 illustrates the total molten Ga as measured at the end of each of the conducted tests. Each test was ended when the temperature of the cooled water was very close to 30 ◦ C (the nominal melting temperature of Ga). Once again, each test started from a hot water temperature very

Fig. 7. Effect of vibrational parameters (frequency and amplitude) on molten Ga as the water temperature decreases from 76 ◦ C to 30 ◦ C. 7

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closely matching 76 ◦ C (see Fig. 3). The results reported in Fig. 7 are given vs. the vibrational signal amplitude and frequency. For instance, for a frequency of 50 Hz and vibrational amplitude of 0.7 mm (test 3C), the measured total melted Ga amount is larger than the total melted Ga amount measured under static heat transfer conditions (test 1A) by 70%. This higher amount of melted Ga in test 3C also indicates the larger latent heat transferred from water to Ga across the mushy region in this test. The absence of vibrational effects in test 1A after Ga reached its nominal melting temperature (about 10 s from the start of the test) clearly highlights the favorable role played by vibrational effects regarding heat transfer across the mushy region in test 3C. This indicates that the enhancement in the rate of heat transfer across the mushy re­ gion by vibrational effects (hence, the reduction of thermal resistance across the mushy region, as discussed later) is the most dominant factor associated with the overall enhancement of cooling immiscible hot water in direct contact with Ga. The vigorous dynamic motions and the intensive area corrugations, resulting in the increase in the surface area at the contact sites between the water and molten Ga, are so decisive in enhancing the rate of heat transfer from the water to the mushy region and to solid Ga beneath it. The enhancement in heat transfer from the water to Ga is not very well pronounced for vibrational amplitudes below 0.3 mm (test 1C). This conclusion is confirmed from Fig. 7, which compares the total amount of melted Ga under static conditions in test 1A with that in test 1B. For the vibrational frequency of 20 Hz, as the amplitude increases to 0.7 mm (test 3B), the amount of Ga melting increases by 50% over the amount attained in the static case in test 1A. Much more pronounced Ga melting is observed as the frequency increases to 50 Hz, at which (as mentioned earlier) in test 3C, the amount of melting increases by 70% over the rates observed in test 1A. It should be noted that with the in­ crease in the total melting amount in the tests with vibration, the instantaneous rates of melting also increase where the time of the whole process becomes shorter as well. Before proceeding with further discussions on the impact of vibration on the heat transfer processes in the conducted tests, in what follows we present more in-depth insights into the instantaneous events taking place in these tests. To achieve this goal, in what follows it is sufficient to focus only on test group C results and compare them with test 1A under static conditions. Fig. 8 presents the instantaneous heat removal rate from water over the first 100 s for each of the conducted tests in test group C. Clearly, test 3C is the one with the highest water cooling rates. Fig. 8 confirms the existence of a threshold for the applied vibrational amplitude, below which vibrational effects do not have any noticeable superiority over those in the test conducted under static conditions (cf. results of tests 1A and 1C in Fig. 8). Fig. 9 illustrates the instantaneous temperature difference across the

Fig. 9. Instantaneous temperature differential across the water/Ga interface.

interfacial region between the water and Ga. It should be recalled that this temperature difference expresses the measured temperature differ­ ence between two interfacial points (one on the water side, and another on the Ga side), separated by a total distance of approximately 5 mm. Clearly, test 3C is the test associated with the smallest such temperature difference among all tests reported in Fig. 9. This obviously reflects the much smaller thermal resistance in the path of heat transfer across the interfacial region for test 3C. Tests 1A and 1C indicate the highest temperature difference and, hence, the largest resistance to heat transfer across the interfacial region. Fig. 10 presents the corresponding instantaneous thermal resistance results calculated based on the heat transfer rates and the interfacial temperature difference data reported in Figs. 8 and 9, respectively. The following equation was used to calculate the thermal resistance (R) across the interfacial region: R=

∆Tinterface Q˙ water

(7)

Where, ΔTinterface is the temperature difference across the hot water‑gallium interfacial region (with thickness of about 5 mm) measured by ther­ mocouples 2 and 4, as indicated in both Fig. 1 and in Table 1 above, while Q˙ water is the rate at which heat is removed form the hot water. In above equation, we assumed that the interfacial region is thin enough for us to ignore unsteady thermal energy storage effects within the body of that thin interfacial region. This approach may be justified by considering the relatively small distance between the points where the interfacial temperature difference measurements are made in our experiments. Further, this may also be justified by considering the comparatively high thermal conductivity of Ga (30 W/m K), which may

Fig. 8. Instantaneous heat removal rate from water.

Fig. 10. Instantaneous temperature differential across the water/Ga interface. 8

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lead to almost very close to isothermal temperatures in the thin inter­ facial region from its bottom side (the mushy Ga side). This latter argument may practically further reduce the thickness of the interfacial region to an even smaller value compared to the actual distance between the two measuring points in our experiments, rendering the effective thickness of the interfacial layer to be around 2–3 mm, thereby war­ ranting treating it as very thin surface when we applied the above equation. Notably, we assumed that at any instant of time, all the heat removed from the water was captured by Ga, and none was dissipated into the outer surroundings. However, the amount of heat transferred to the outer surroundings is much smaller than the amount captured by Ga, especially for the cases with properly selected vibrational parameters (i. e., tests 2C, 3C, and 3B in this work). Nevertheless, this conclusion is less valid for cases under static conditions or when vibrational parameters do not exceed the minimum amplitude threshold level of 0.3 mm. For such cases, ignoring the heat transferred to the outer surroundings during the experiments leads to under predicted values of the thermal resistance of the interfacial region. This under prediction still further highlights the favorable role of the vibrational effects (as is the case in test 3C in this study) when it comes to the enhancement in heat transfer from water to Ga in the heat sink. More specifically, by accounting for heat dissipation into the outer surroundings for cases such as tests 1A, 1B, and 1C, the actual interfacial thermal resistance would be even higher than the levels reported in Fig. 10. This will then further strengthen the under­ standing of the importance of vibration in regard to reducing the interfacial thermal resistance once the vibrational parameters are carefully selected. The latent heat absorption results that correspond to molten Ga amounts given in Fig. 7 are presented in Fig. 11 for the different am­ plitudes and frequency levels tested. Moreover, the combined total latent and sensible heat uptake of Ga from water is presented in Fig. 12, as a function of vibrational amplitude for the frequency levels studied. Once again, the results presented in Figs. 7, 11, and 12 are attained at the end of the test period, during which the water temperature drops from its initial value of about 76 ◦ C to about 30 ◦ C. Fig. 11 clearly demonstrates the significant increase in the latent heat uptake of Ga from the water when vibrational effects are applied with proper parameters (frequencies and amplitudes), as is the case in test 3C. Recall that some of the heat removed from water and absorbed by Ga will be received by Ga first as sensible heat to raise the temperature of Ga to Ga’s melting point (around 30 ◦ C), and the rest will be received as latent heat that melts Ga. From the results presented in Figs. 11 and 12, it can be concluded that the effect of the latent heat part on cooling water is by far more significant than the sensible heat part. In other words, we highlight hereby that solid Ga as a PCM can effectively cool down hot liquids in our experiments. The sensible heat absorbed by solid Ga before Ga starts melting is

Fig. 12. Combined latent and sensible heat uptake of Ga from water as a function of vibrational amplitude and frequency.

obtained by knowing the initial solid Ga temperature, the total mass of used solid Ga at the beginning of the test, and the melting temperature of Ga (30 ◦ C). After completing the stage of sensible heat addition to Ga, the amount of latent heat absorbed by Ga to melt it is a direct indication of the significance and impact of the applied vibrational excitations on the heat exchange process taking place within the mushy Ga layer. Apparently, this latent heat amount is very pronounced for the tests under vibrational effects that have amplitudes above 0.3 mm, particu­ larly in tests 2C, 3C, and, to some good extent, 3B (cf. Figs. 11 and 12). In the context of the discussions about the melting of Ga, it is interesting to refer once again to Figs. 4–6 and reflect back on the overshooting temperature of the interfacial region measured in the mushy Ga layer only a few millimeters (2 mm) below the interfacial plane separating the water from Ga. As can be seen from Figs. 4–6, it takes a very short time for the lower interfacial temperature to cross the border of the nominal melting point of Ga (30 ◦ C). This indicates that in a very short time after subjecting Ga to the water heat source, Ga at the interfacial plane starts melting. However, the temperature of that melting interfacial region does not stay at the nominal melting tem­ perature of 30 ◦ C; instead, it continues to increase, causing some superheating of the molten Ga to take place up to peak temperatures that vary from test to test, depending on the level of vibrational excitations applied (cf. Figs. 4–6). The level of enhancement of the vibrationinduced mixing, thus the resulting enhancement in heat exchange be­ tween the water and molten Ga within the mushy layer and subse­ quently between molten Ga and solid Ga below it, decides the level of water temperature decline rates in subsequent stages during the heat exchange process. The role played by vibration in corrugating the interfacial contact area between water and molten Ga is so evident where the intermingling between these two immiscible liquids and thus the resulting significant increase in the heat exchange area between them is obvious. Not only the effect of increased contact surface area between water and the molten Ga that is expected to lead to the enhanced heat transfer but also the induced activity at the molecular level between the water and molten Ga when vibration is applied. Fig. 13 presents the percentage of the sensible heat absorbed by Ga as compared to the total heat removed from the water. Recall that the total heat removed from water consists of three components. The first is the sensible heat transferred to Ga to raise its temperature from the initial value (15 ◦ C in all tests conducted) to the melting temperature of Ga (30 ◦ C). The second component is the latent heat uptake of Ga after reaching the melting point. The third component is the heat that directly escapes the heat sink container to the ambient surroundings through the outer sink boundaries. The total heat removed from the water is calcu­ lated from the instantaneous water temperature data presented in Fig. 3. As inferred from Fig. 13, the sensible heat uptake by Ga is only a small fraction of the total heat removed from the water. Most importantly, its

Fig. 11. Effect of vibrational parameters (frequency and amplitude) on the latent heat uptake of Ga as the water temperature dropped from 76 ◦ C to 30 ◦ C. 9

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little chance for the heat to be dissipated into the outer ambient sur­ roundings. This will lead to significantly reduced thermal pollution to the environment and, concurrently, allows for the efficient capture and storage of the thermal energy removed from hot sources into a sink material such as Ga, which is used in this study as a non-limiting example of a high thermal conductivity heat sink PCM. Fig. 15 illustrates heat flux results, which reflect the overall ability of the vibrating Ga heat sink to remove heat from water for the different vibrational frequency and amplitude parameters tested. Under static conditions (test 1A), the heat flux levels are very limited to a compar­ atively very low level of 0.5 W/cm2. As the vibrational effects commence, a significant increase in heat flux removal abilities is observed, especially under the high frequency and amplitude levels tested in test 3C, where 4 W/cm2 is attained. This represents an increase of 700% over the levels attained without vibration. This heat flux improvement in the tests with vibration is due to the enhanced uptake of latent heat into the mushy liquid Ga interfacial region attributed to the induced vibrational effects in the mushy Ga region. It is worth noting that the above heat flux results are overall the ones attained for the whole test time. In the early stages of the tests, while the temperature difference between the water and Ga is large, much higher instanta­ neous heat flux levels are attained, especially in the case of the tests with effective vibrational parameters, particularly test 3C. Below we give final remarks that are perhaps worth highlighting before we conclude our discussion: We made use in this study of solid gallium as a heat sink material, thereby benefiting from the following features that it possesses: (1) Its latent heat storage capacity, (2) its comparatively high thermal con­ ductivity, and (3) its low melting point. Clearly, we may still anticipate further improvements in the heat dumping rates from the source (the hot water in our case) into the solid gallium sink, should higher levels of the vibrational parameters are implemented in the process. This is an interesting area to explore further but surely suitable experimental setup and operational precautions would need to be taken into consideration before attempting to pursue such research explorations. With the above said, seeking higher heat exchange rates by applying more vigorous levels of vibrational parameters (frequency and ampli­ tude) might lead to adverse results, contrary to what may be anticipated at first glance. This may lead to chunks of liquid water and molten gallium to get disintegrated and be disengaged from each other leading to a loss of intimate contact between them as well as with the solid gallium beneath them. Such scenario may lead to some of the hot water finds its way (at least temporarily or at intermittent time intervals during the process) and seep and get sandwiched between fragments and

Fig. 13. Percentage of the sensible heat uptake of Ga to the total heat loss of water as the water temperature decreased from 76 ◦ C to 30 ◦ C as a function of vibrational amplitude and frequency.

value is not affected by the level of vibration applied to the sink, where for all vibrational tests conducted, it does not indicate much difference from the value attained under static conditions. Fig. 14 presents the percentage of total heat (both latent and sensi­ ble) absorbed by Ga to the total heat removed from water in each of the conducted tests. When vibrational effects are not applied (test 1A), the total heat that Ga will absorb from water is around 60% of the total heat lost by the water as the water cools from around 76 ◦ C to 30 ◦ C. The rest of the lost heat is dissipated into the outer ambient surroundings through the heat sink container boundaries exposed to the outer envi­ ronment, mainly by convection. By contrast, Ga heat sink becomes much more effective in capturing the heat from water when vibrational effects are applied. This appears to be the case, especially under the high range of amplitudes and frequencies tested in this study. For example, in test 3B, the percentages of the heat absorbed by Ga from the water and that directly dissipated into the outer ambient surroundings are 84% and 16%, respectively (compared with 60% and 40% under static conditions of test A). Under test 3C conditions, the percentage of total heat captured by Ga from water approaches 99%, leaving only 1% dissipated in the outer surrounding environment. Recall from Fig. 13 that for all tests, only a fixed percentage of 10% is received by Ga in the sink as sensible heat. As illustrated in Fig. 3, the time to remove the total amount of heat from the water and drop the water temperature by about 45 ◦ C is also drastically reduced when the vibrational effects are introduced properly; cf. Fig. 3. This means that the overall cooling process for the water will be accomplished in a significantly shorter time, and there will, hence, be

Fig. 15. Total heat flux removed from water (including total heat uptake by Ga (both latent and sensible) and the heat dissipated directly into the outer ambient surroundings (while dropping the temperature of the water from 76 ◦ C to 30 ◦ C)) as a function of vibrational amplitude and frequency.

Fig. 14. Percentage of the total heat uptake of Ga (both latent and sensible) to the total heat loss of water as the water temperature decreased from 76 ◦ C to 30 ◦ C) as a function of vibrational amplitude and frequency. 10

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pieces of the molten gallium and the solid gallium beneath them. This would be expected to have a serious negative impact on the heat transfer process where the chunks of molten gallium that were splashed up would find themselves surrounded by a hot water bath and, given the gallium’s low specific heat capacity, would consequently experience rapid temperature rise and superheating so they quickly approach thermal equilibrium with the hot water. If this happens as described above, the heated chunks of liquid gallium would then lose their po­ tential to act as coolant for the hot water, suppressing thereby the per­ formance of the heat sink as a whole. Moreover, the hot water that could leak between the solid gallium and the above described superheated liquid gallium chunks, may form a kind of bellow and hence blanket the surface of the solid gallium. As a result, the water, in cooperation with the heated gallium chunks, may then lead to establishing some addi­ tional thermal resistance in the path of heat transfer from the main body of hot water at the top into the solid gallium, jeopardizing thereby the overall performance of the heat sink system. In conclusion to the above arguments, it is to be highlighted here that one needs to be cautious before anticipating and ever increasing heat exchange rates as the vibrational parameter levels are increased and to expect reaching an optimum range beyond which a decline in the cooling performance might be expected, instead. One further note might be worth reflecting at namely let us hy­ pothesize a heat sink that holds completely liquid gallium as its cooling medium into which a hotter immiscible liquid (e.g. the water used in our experiment) would dump its heat. Let us hypothesize further that we implemented a vigorous mechanical stirring approach (e.g. a paddle wheel shaft-based stirring mechanism) to cause vigorous agitation for both the liquid gallium and the hotter water targeting getting them intimately contacting each other at a very small scale. In this case, heat transfer between the two liquids would be expected to be immense, especially when considering the high thermal conductivity of the liquid gallium. Hence, this mechanical shaft-based mixing scenario might at first glance look appealing. However, by reflecting deeper on the low specific heat capacity that characterize gallium, we may easily antici­ pate that gallium would get easily superheated and consequently would lose its potential to act as coolant for the hotter liquid (the hot water in our research). This approach would cease out to be feasible, unless some kind of dedicated cooling mechanism is implemented to relief the heated liquid gallium form the heat it captured. Obviously, this is a much more demanding and complex to build and implement of an approach, as compared to the much simpler approach we are proposing in this study benefiting from the latent heat and low melting temperature of solid gallium while subjecting them to mechanical vibration in the way we implemented in this research.

vibrational effects allowed for the rapid capture of almost 99% of the total heat removed from hot water and storage of the majority of this heat in the form of latent heat in the Ga sink. This means that only 1% of the total heat removed from the water was directly dissipated by con­ vection into the surrounding environment. By contrast, under static nonvibrating conditions, only 60% of the total heat removed from the water was captured and stored in the Ga sink; thus, we effectively increased the captured heat by 65%. Our results confirmed that introducing vibration to speed up the heat transfer process between two immiscible liquids is an efficient strategy of capturing and storing thermal energy from hot liquid sources and reducing thermal pollution. Yet, further optimization testing under higher levels of frequency and amplitude conditions, beyond those tested in this study, can be expected, provided that the structural sta­ bility of the experimental setup and the required measures of avoiding spillage of the involved liquids during operation are secured. Thus, our work may further inspire future studies to enhance cooling rates for energy-efficient cooling systems development. Declaration of Competing Interest The authors declare no conflicts of interest. Acknowledgments This work was supported by the Research Affairs Office of the United Arab Emirates University (Grant Code G00002972). References [1] S.-A. Al Omari, Enhancement of heat transfer from hot water by co-flowing it with mercury in a mini-channel, Int. Commun. Heat Mass Transf. 38 (2011) 1073–1079. [2] A.-R. Khaled, Heat transfer enhancement in a vertical tube confining two immiscible falling co-flows, Int. J. Therm. Sci. 85 (2014) 138–150. [3] A.-R. Khaled, K. Vafai, Heat transfer enhancement by layering of two immiscible co-flows, Int. J. Heat Mass Transf. 68 (2014) 299–309. [4] S. Al Omari, A numerical study on the use of liquid metals (Ga and mercury) as agents to enhance heat transfer from hot water in a co-flow mini-channel system, Heat Mass Transf. 48 (10) (2012) 1735–1744. [5] S. Al Omari, E. Elnajjar, Experimental study on the enhancement of heat transfer between water interfaced with higher thermal conductivity liquid, Int. Commun. Heat Mass Transf. 45 (2013) 95–99. [6] S. Al Omari, A. Ghazal, E. Elnajjar, A new approach using un-encapsulated discrete PCM chunks to augment the applicability of solid Ga as phase change material in thermal management applications, Energy Convers. Manag. 158 (2018) 133–146. [7] S. Al Omari, A. Ghazal, E. Elnajjar, A novel concept to enhance the applicability of solid Ga as phase change material for heat sinks by integrating within it discretely distributed chunks of un-encapsulated PCM, Int. Commun. Heat Mass Transf. 91 (2018) 274–281. [8] Kh. Hosseinzadeh, M.A. Erfani Moghaddam, A. Asadi, A.R. Mogharrebi, D.D. Ganji, Effect of internal fins along with hybrid Nano-particles on solid process in star shape triplex latent heat thermal energy storage system by numerical simulation, Renew. Energy 154 (2020) 497–507. [9] Salma Gharbi, Souad Harmand, Sadok Ben Jabrallah, Experimental comparison between different configurations of PCM based heat sinks for cooling electronic components, Appl. Therm. Eng. 87 (2015) 454–462. [10] B. Praveen, S. Suresh, Thermal performance of micro-encapsulated PCM with LMA thermal percolation in TES based heat sink application, Energy Convers. Manag. 185 (2019) 75–86. [11] Kh. Hosseinzadeh, A.R. Mogharrebi, A. Asadi, M. Paikar, D.D. Ganji, Effect of fin and hybrid nano-particles on solid process in hexagonal triplex latent heat thermal energy storage system, J. Mol. Liq. 300 (2020) 112347. [12] R. Lemlich, Effect of vibration on natural convective heat transfer, Ind. Eng. Chem. 47 (1955) 1175–1180. [13] W. Penney, T. Jefferson, Heat transfer from an oscillating horizontal wire to water and ethylene glycol, J. Heat Transf. 88 (4) (1966) 359–363. [14] K.K. Prasad, V. Ramanathan, Heat transfer by free convection from a longitudinally vibrating vertical plate, Int. J. Heat Mass Transf. 15 (6) (1972) 1213–1223. [15] A. Pilli, R. Narayanaswamy, J. Jewkes, A. Lucey, Convective heat transfer from a vertically-mounted vibrating heated plate, in: Fluid-Structure-Sound Interactions and Control, Springer, 2016, pp. 289–294. [16] A. Dawood, B. Manocha, S. Ali, The effect of vertical vibrations on natural convection heat transfer from a horizontal cylinder, Int. J. Heat Mass Transf. 24 (1981) 491–496. [17] C.-H. Cheng, H.-N. Chen, W. Aung, Experimental study of the effect of transverse oscillation on convection heat transfer from a circular cylinder, J. Heat Transf. 119 (1997) 474–482.

4. Summary and conclusions We investigated the effect of vibration on the heat exchange between solid Ga and water in direct contact with each other. The generated vibrational excitations were applied in the form of sinusoidal waves in the vertical direction with three levels of peak-to-peak amplitudes (0.3, 0.5, and 0.7 mm) and two levels of frequencies (20 Hz and 50 Hz). The obtained hot water cooling results under vibration were compared with their counterparts under static conditions. The results revealed significant improvements in the rate of heat removal from water when the vibrational effects were introduced and the applied amplitudes were above 0.3 mm. The best heat removal from the water was attained at an amplitude of 0.7 mm and a frequency of 50 Hz. The time to drop the water temperature from 76 ◦ C to 40 ◦ C was reduced from 550 s under non-vibrating static conditions to only 60 s when vibrational excitations were applied at an amplitude of 0.7 mm and a frequency of 50 Hz. This improvement is due to the increase in the total flux of heat removal from hot water from 0.5 W/cm2 under no vibration to 4 W/cm2 when vibration was introduced at the given pa­ rameters. Furthermore, the shortened heat removal time due to 11

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International Communications in Heat and Mass Transfer xxx (xxxx) xxx [27] T. Boziuk, M. Smith, A. Glezer, Enhanced boiling heat transfer on plain and featured surfaces using acoustic actuation, Int. J. Heat Mass Transf. 108 (2017) 181–190. [28] L. Quan, Z. Zhang, M. Faghri, Experiments on contact melting under vibration within rectangular enclosures, J. Thermophys. Heat Transf. 13 (1999) 166–168. [29] L. Quan, Contact Melting of Phase Change Material with Effect of Vibration, Ph.D thesis, University of Rhode Island, 1999. [30] K. Choi, J. Hong, Experimental study of enhanced melting process under ultrasonic influence, J. Thermophys. Heat Transf. 5 (1991) 340–346. [31] M. Oka, Heat transfer enhancement of a direct contact melting process by oscillating motion, Adv. Cold-Reg. Therm. Eng. Sci. (1999) 91–102. [32] Y. Oh, S. Park, Y. Cho, A study of the effect of ultrasonic vibrations on phasechange heat transfer, Int. J. Heat Mass Transf. 45 (2002) 4631–4641. [33] H.D. Yang, Y.K. Oh, Experimental and numerical study on enhanced heat transfer of solid-liquid PCM by ultrasonic wave, in: Key Engineering Materials, 2006, pp. 1145–1148. [34] H.D. Yang, Y.K. Oh, Effect of ultrasonic vibrations on accelerating heat transfer of pcm, Int. J. Modern Phys. B 20 (2006) 4341–4346. [35] N. Joshy, M. Hajiyan, A.R.M. Siddique, S. Tasnim, H. Simha, S. Mahmud, Experimental investigation of the effect of vibration on phase change material (PCM) based battery thermal management system, J. Power Sources 450 (2020) 227717. [36] A. Chakravorty, Process intensification by pulsation and vibration in miscible and immiscible two component systems, Chem. Eng. Process. Process Intensif. 133 (2018) 90–105.

[18] L. Cheng, T. Luan, W. Du, M. Xu, Heat transfer enhancement by flow-induced vibration in heat exchangers, Int. J. Heat Mass Transf. 52 (3–4) (2009) 1053–1057. [19] W. Liu, Z. Yang, B. Zhang, P. Lv, Experimental study on the effects of mechanical vibration on the heat transfer characteristics of tubular laminar flow, Int. J. Heat Mass Transf. 115 (2017) 169–179. [20] D. Li, X. Yang, S. Wang, D. Duan, Z. Wan, G. Xia, W. Liu, Experimental research on vibration-enhanced heat transfer of fin-tube vehicle radiator, Appl. Therm. Eng. 180 (2020) 115836. [21] M.M. Sarafraz, J. Harta, E. Shrestha, H. Arya, M. Arjomandi, Experimental thermal energy assessment of a liquid metal eutectic in a microchannel heat exchanger equipped with a (10 Hz/50 Hz) resonator, Appl. Therm. Eng. 148 (2019) 578–590. [22] A. Hosseinian, A. Meghdadi Isfahani, E. Shirani, Experimental investigation of surface vibration effects on increasing the stability and heat transfer coeffcient of MWCNTs-water nanofluid in a flexible double pipe heat exchanger, Exp. Thermal Fluid Sci. 90 (2018) 275–285. [23] P. Naphon, S. Wiriyasart, Experimental study on laminar pulsating flow and heat transfer of nanofluids in micro-fins tube with magnetic fields, Int. J. Heat Mass Transf. 118 (2018) 297–303. [24] M.M. Sarafraz, V. Nikkhah, S.A. Madani, Mohammad Jafarian, F. Hormozi, Lowfrequency vibration for fouling mitigation and intensification of thermal performance of a plate heat exchanger working with CuO/water nanofluid, Appl. Therm. Eng. 121 (2017) 388–399. [25] M. Zheng, B. Li, Z. Wan, B. Wu, Y. Tang, J. Li, Ultrasonic heat transfer enhancement on different structural tubes in LiBr solution, Appl. Therm. Eng. 106 (2016) 625–633. [26] Y. Zheng, J. Chen, Y. Shang, H. Chang, H. Chen, S. Shu, Numerical analysis of the influence of wall vibration on heat transfer with liquid hydrogen boiling flow in a horizontal tube, Int. J. Hydrog. Energy 42 (52) (2017) 30804–30812.

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