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Enhancing critical heat flux (CHF) and heat transfer coefficient (HTC) by promoting the nucleation, growth, and departure of boiling bubbles has drawn significant attention owing to its wide applications. However, in‐depth understanding and comprehensive manipulation of under‐liquid bubble dynamics from in situ microscale perspectives remain challenging. Herein, in situ observations and analyses of the microsized boiling bubbles of ultra‐low surface tension fluorinated liquids (FLs) are conducted on the superaerophobic silicon surfaces with crisscross microchannels and selective nanowires. It is revealed that deep microchannels yet short nanowires enable ultrafast liquid spreading (<549.6 ms) and ultralow bubble adhesion (≈1.1 µN), while an appropriate spacing (240–600 µm) between microchannels minimizes the bubble departure time (<20.6 ms) due to timely coalescence. By verifying the above bubble dynamics principles through the collaborative enhancement of CHF and HTC, an optimized structure (microchannel depth ≈52.9 µm, microchannel spacing ≈362.9 µm, nanowire length ≈0 nm) is obtained and further implemented onto the exposed Si surface of a commercial CPU chip. Cooled by phase‐change of FLs, the average temperature of CPU maintains ≈64.9 °C even under extreme power loads (≈130 W), far below than those in conventional air‐cooling and water‐cooling operations. [ABSTRACT FROM AUTHOR]

We have developed a heat transfer correlation for saturated flow boiling of water in a helically coiled tube. Initially, we collected experimental data encompassing a broad spectrum of thermal-hydraulic conditions and geometric configurations, and examined the influences of key dimensionless parameters, such as the convection number and the boiling number. The data analysis showed that the observed trend aligns with previous studies on boiling heat transfer within a straight tube. Also, we investigated the influence of centrifugal force acting on the fluid in a helically coiled tube and confirmed its significant impact on boiling heat transfer. Based on our findings, we propose a new heat transfer correlation that incorporates a dimensionless number of the centrifugal force divided by gravitational force. The basic structure of this correlation was adapted from the Kandlikar correlation for saturated flow boiling. The new correlation demonstrated enhanced accuracy compared to existing ones. Additionally, we showed its applicability to boiling heat transfer within a straight tube as well. [ABSTRACT FROM AUTHOR]

Copyright of Automobile Technology & Material is the property of Automobile Technology & Material Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Metallic foams have become a cutting-edge solution for many thermal management problems. These are of interest by thermal research community because of the cellular structure and have gas-filled pores inside a metal matrix. Due to the uniqueness in their structure, they exhibit good performance in boiling heat transfer because of the properties such as higher specific surface area, large number of nucleation sites, wettability characteristics, and capillary action. The boiling heat transfer over metal foam is a complex phenomenon, greatly affected by the thickness, porosity, and pores per inch (PPI) of metal foam along with the thermo-physical properties of the foam and boiling liquid. By thoroughly examining recent research investigations, the paper explains the impact of open-cell metal foams on pool boiling of different liquids such as water, refrigerants, organic liquids, and dielectric liquids. This paper reviews the complexity and various influencing factors involved in flow boiling through metal foam in tubes. It also highlights findings that show metal foam significantly enhances jet impingement boiling heat transfer. Moreover, the discussion on gradient metal foams, offering insights into their potential to enhance boiling heat transfer. The comprehensive review also encompasses numerical modeling studies, such as the lattice Boltzmann method, contributing to a deeper understanding of the intricate flow and heat transfer characteristics within channels filled with metal foam. [ABSTRACT FROM AUTHOR]

Deionized water is replacing fluorinated liquids as the preferred choice for two-phase immersion cooling in data centers. Yet, insufficient bubble removal capability at low saturated pressure is a key challenge hindering the widespread application. To solve this issue, this study employs non-ionic surfactant (Tween 20) and asymmetric structures (expanding microchannel) to enhance the boiling performances of deionized water under sub-atmospheric pressure. The research examines the effects of pressure (8.8~38.5 kPa), surfactant concentration (0.1~0.5 mL/L), and heat flux density (10~180 W/cm2) on the boiling heat transfer characteristics and analyzes the mechanism of unusual temperature oscillations induced by surfactants. It was found that the trade-off between the sub-atmospheric pressure, surface tension coefficient, and reduced static contact angle results in pronounced intermittent boiling on the heated surface. Even with the addition of surfactants, the improvement in heat transfer requires demanding conditions. Boiling enhancement throughout all heat flux conditions was achieved when the surfactant concentration was higher than 0.2 mL/L for the expanding microchanneled surface. The heat transfer coefficient reached 6.89 W·cm−2·K−1 under 8.8 kPa, which was 45% higher than without the surfactant. Under the same heat flux and sub-atmospheric pressure, as the concentration increased from 0.1 to 0.5 mL/L, the amplitudes of temperature fluctuation of the plane surface and expanding microchanneled surface decreased from 10 K to 2 K and 18 K to 1 K, respectively. The onset of nucleate boiling and wall superheat of the expanding microchanneled surface gradually decreased with the increase in surfactant concentration, where the onset of nucleate boiling decreased by 10.54 K. When the heat flux is 160 W/cm2, the wall superheat is reduced by 12.8 K. [ABSTRACT FROM AUTHOR]

• New data of jet impingement boiling on surface modified metal foam were obtained. • Effects of metal foam wettability on boiling heat transfer were analyzed. • Influence on bubble dynamics behavior was analyzed. • New heat transfer coefficient correlation considering wettability was developed. Wettability may have significant influence on jet impingement boiling on metal foam, but the effect mechanism of metal foam wettability remains unclear. In this study, the boiling heat transfer characteristics of distributed jet array impingement on hydrophobic and hydrophilic metal foam covers were experimentally researched and compared with those on uncoated metal foam covers to analyze the influence of wettability. The experimental conditions cover contact angles of 14.0–158.7°, pore densities of 20–40 PPI, porosities of 92 %-97 %, thicknesses of 3.0–5.0 mm, and jet velocities of 0.5–4.0 m·s−1. The results show that, the obtained maximum heat flux and maximum heat transfer coefficient are up to 538.1 W cm−2 and 57.9 Kw m−2 K−1, respectively; the hydrophobic metal foam cover has a 4.8 K lower surface superheated degree at the onset of nucleate boiling, but a 7.5 % lower maximum heat transfer coefficient compared with the uncoated one; the hydrophilic metal foam cover shows a less deterioration after the departure from nucleate boiling but a 5.3 K higher surface superheated degree at the onset of nucleate boiling than those of the uncoated one. A new correlation for boiling heat transfer coefficients was developed with a mean relative error of 9.75 %. [ABSTRACT FROM AUTHOR]

Microchannel heat sinks (MCHS) are capable of removing exceptionally high heat fluxes through liquid-to-vapor phase transition, making them suitable for various applications, including the thermal management of high-power microelectronics. However, their commercial applicability is hindered by the flow boiling instability associated with chocking of the micro-passage as the vapor bubbles grow. The present study addresses the research gap in literature pertaining to the impact of microchannel depth on flow boiling instability in terms of amplitude of heated surface temperature and pressure drop oscillations, and their influence on heat transfer performance. Experiments are conducted using dielectric water boiling in multiple parallel microchannels with mass fluxes of 220 and 320 kg/m²s and wall heat fluxes ranging from 25 kW/m² to 338 kW/m². Two different MCHS, fabricated from oxygen-free copper substrate, were examined, each comprising 44 parallel microchannels with nominal depths of 500 µm and 1000 µm, and a consistent nominal width of 200 µm. Heat transfer coefficients were measured using an array of embedded T-type thermocouples on the substrate to measure temperature gradients. The findings reveal that increasing the microchannel depth results to a significant increase in the amplitude of wall temperature fluctuations under fixed wall heat flux conditions, which in turn diminishes heat transfer performance. Additionally, the study demonstrates a notable dependence of pressure drop on coolant flow and both microchannel sizes. This research provides new insights into optimizing MCHS design for enhanced thermal management, highlighting the critical role of microchannel depth in mitigating flow boiling instability and improving overall heat transfer efficiency.

This study investigates the boiling characteristics of graphene (GNP) nanofluids, graphene-copper (GNP-Cu) composite nanofluids, and graphene-iron (GNP-Fe) composite nanofluids with mass fractions of 0.001%, 0.002%, and 0.003%. The results indicate that GNP-Cu and GNP-Fe nanofluids can simultaneously enhance the critical heat flux (CHF) and heat transfer coefficient (HTC). Among different mass fractions, GNP-Cu nanofluids with a mass fraction of 0.003% exhibited the highest CHF and HTC. Through the observation of bubbles, the research elucidated that the presence of copper and iron elements is crucial in enhancing heat transfer. Based on the experimental results, this study modified the boiling curve equation of Rohsenow into a linear function. The modified model can predict the boiling curves of GNP-Cu, GNP-Fe, and GNP-Ag nanofluids at various concentrations. Furthermore, the experimental findings indicated a quadratic relationship between the boiling heat transfer coefficient and the heat flux in GNP, GNP-Cu, GNP-Fe, and GNP-Ag nanofluids. As a result, this study investigates the differences in heat transfer and bubble dynamics among GNP nanofluids modified with various metallic elements during boiling. It explores the underlying heat transfer mechanisms and proposes boiling curve equations that are applicable to a range of nanofluids. The findings suggest that acid-mixing treatment and metal-functionalization play a facilitating role in heat transfer of GNP nanofluids. Furthermore, nanofluids loaded with different metallic elements exhibit similar trends in their boiling curve equations. [ABSTRACT FROM AUTHOR]

This paper experimentally investigated the impact of the electric field strength (E), electrode installation heights (H), and the electrode shape on enhanced pool boiling heat transfer performance under a downward heating surface with an electric field. It is observed that the critical heat flux (CHF) generally increases with increasing electric field strength. For instance, for the mesh electrode, the CHF is increased by 100.0%, 240.0%, 340.0%, and 440.0% at E = 0.35 × 106 V/m, 0.70 × 106 V/m, 1.05 × 106 V/m, and 1.40 × 106 V/m, respectively, compared to E = 0 V/m. Furthermore, the electrodes hinder the detachment of vapor bubbles, which becomes more pronounced when the electrode installation height is low. At the same time, the more micro-ribs of the electrodes and the denser the distribution, the more uniform the electric field generated. Under this condition, the “pinch-off effect” caused by the non-uniform electric field is reduced, which is more conducive to enhancing boiling heat transfer performance. Ultimately, at H = 5.0 mm and E = 1.40 × 106 V/m, the CHF with grid electrodes improved by 101.1% compared with the horizontally upward without the electric field, which is a superior combination of working conditions and suggests that a more optimistic boiling heat transfer performance can be obtained in microgravity. This work provides guidance for enhancing boiling heat transfer in microgravity by an electric field. [ABSTRACT FROM AUTHOR]

The impact of the thickness on the boiling phenomena of the water film on the liquid metal surface is compared, and various mechanisms are analyzed, using a molecular dynamics simulation. The findings demonstrated that the best heat transfer performance between the liquid metal surface and water film is obtained when employing a thickness of 9.56 Å, along with a shorter boiling time. Additionally, the boiling time on each surface was further accurately characterized by considering and examining the water film motion and the temperature distribution, in addition to comparing the kinetic energy and potential energy of the system. Also, the surface thickness affected the fluctuation of the liquid metal, the interfacial thermal conductance, and the interfacial thermal resistance. The thicker the liquid metal, the greater the fluctuation. However, a liquid metal surface with a thickness of 9.56 Å is characterized by a larger average interfacial thermal conductance, a smaller average interfacial thermal resistance. Based on the analysis, the difference in boiling time among the different cases was due to the combined effect of fluctuation, interfacial thermal conductance, and interfacial thermal resistance. The results enlighten new ideas and methods for augmenting the efficiency of boiling heat transfer.

This study involves the fabrication and characterization of original, hydrophobic, superhydrophilic, superhydrophobic and hybrid biphilic pattern coupled with the flat and pillar-structured surfaces. The boiling performance of the seven wettability structured surfaces is experimentally and numerically investigated, aiming at analyzing the boiling mechanism of wetting pattern coupled with structures. The findings indicate that coupling superhydrophobicity pillar structure surface (SHO-PS) result in an excellent boiling performance, the superhydrophilicity have difficulty in improving the heat transfer coefficient and critical heat flux. Analysis of the bubble dynamics behaviors reveals a strong positive correlation between the bubble nucleation sites and bubble departure diameter, except for hydrophobic flat structured surface (HO-FS) and superhydrophobicity pillar structured surface (SHO-PS), which exhibit the negative correlation. The bubble departure frequency shows a linear correlation with the contact angle of all the modified surfaces. In the simulation, it is observed that the similar bubble dynamic behaviors in experiment.

With the development of surface engineering, porous surfaces have emerged as a significant research subject in boiling heat transfer. The latter, in turn, plays a crucial role in various industries such as power plants, distillation plants, and microelectronic technology. In this paper, the Molecular Dynamics method is adopted to investigate the wicking dynamics and boiling dynamics of two porous surfaces: foam, which exhibits randomly distributed pores, and mesh, composed of ordered square wires with relatively uniform pore sizes. Three wettability, namely hydrophilic, neutral, and hydrophobic wetting states, are assigned to the two porous surfaces de-coupling the effect of wettability from surface structure. Results reveal that, during the wicking process, the foam surface shows better wetting ability as it absorbs liquid under both hydrophilic and neutral wettability. Comparatively, the mesh surface has the fastest wicking speed under hydrophilic wettability yet it becomes non-wetting under neutral wettability. During the boiling process, the boiling dynamics differ greatly under three wettability. More importantly, the difference in surface structure makes the foam surface possess a better heat transfer whereas the mesh surface causes gentle pressure variation. Our findings provide insights into the design of artificial porous surfaces for certain purpose and their potential application.

During a postulated accident in water-cooled nuclear reactors, such as loss-of-coolant accident, the reactor core can be partially or completely uncovered from coolant and consequently becomes overheated. The cold liquid is reinjected into the nuclear reactor core to effectively cool the superheated fuel rods. In this process, the quenching boiling will be encountered in the fuel rod surface. The reflooding quenching boiling of nuclear fuel rod is an important accident mitigation measure to avoid the core melting after the loss-of-coolant accident of the core of pressurized water reactor. In this work, quenching experiments of Zr-4 alloy with different roughness were performed in subcooled distilled water pool at atmospheric pressure. The surface of Zr-4 was polished by abrasive paper with different mesh numbers. The effects of Zr-4 surface roughness and coolant subcooling degree on cooling rate and boiling heat transfer during the quenching boiling were studied. The visualization experiments of quenching boiling were carried out on different surface roughness test sections, and the internal temperatures of test sections were measured at the same time. The image processing technique was used to obtain the evolution of vapor film thickness during quenching boiling of fuel rod and the inverse heat conduction problem was employed to obtain the surface temperature and heat flux during the quenching. The experimental results show that the surface roughness has little effect on the film boiling heat transfer. However, the surface with higher roughness triggers the surface-liquid contact earlier and strengthens the quenching boiling. When the roughness is small, the effect of roughness on quenching boiling is weak. When the roughness is further reduced, the duration of quenching boiling increases due to the increase of the surface contact angle. In addition, with the increase of the liquid subcooling, the vapor thickness of film boiling decreases, the minimum film boiling temperature to maintain stable vapor film increases, and the quenching rate increases. Based on the experimental data, the relationship between the minimum film boiling temperature (Tmin) and the coolant subcooling degree (Tsub) is established with the average error of 2.4%. This study provides a theoretical basis for the boiling heat transfer mechanism during the reflooding process of nuclear reactor core at a loss-of-coolant accident.

Abstract\nHIGHLIGHTSAutomobile air conditioning systems significantly contribute to vehicle energy consumption. The transition to new, environmentally sustainable refrigerants in place of traditional ones is a critical trend shaping the future of this industry. The prevalent refrigerant R134a, used in automotive air conditioning, is environmentally detrimental, necessitating the development of low Global Warming Potential refrigerants as viable long-term alternatives. This study examines the flow heat transfer characteristics of the proposed refrigerant blend R1234yf/R152a in porous microchannel tubes via numerical simulation. It assesses the impact of heat flux, mass flow rate, saturation temperature, and wall superheat on the Jakob number, vaporization core density, and boiling heat transfer coefficient. Furthermore, it compares these parameters with those of R134a and R1234yf to evaluate the potential of R1234yf/R152a as a substitute. The findings indicate that the Jakob number differences among the three refrigerants are negligible. Notably, R1234yf/R152a consistently exhibits higher vaporization core density and the highest boiling heat transfer coefficient, coupled with the lowest pressure drop, thereby affirming its suitability as a heat transfer-efficient alternative. These insights could inform the enhancement and gradual transition from R134a in automotive air conditioning systems.Flow heat transfer characteristics of R1234yf/R152a mixtures studied by numerical simulation.The critical heat flux of the mixture in the porous microchannel is 79 kW/m².R1234yf/R152a has better heat transfer performance compared with R134a and R1234yf refrigerants.Explore the long-term substitution of low-GWP refrigerants in automobile air conditioning. [ABSTRACT FROM AUTHOR]

Copyright of Atomic Energy Science & Technology is the property of Editorial Board of Atomic Energy Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

• A new eco-friendly alternative mixed working fluid to replace R245fa/R134a is proposed. • Boiling heat transfer characteristics of R1234yf/R1336mzz(z) were experimentally evaluated. • Sun & Mishima correlation and Kandlikar correlation has been appropriately modified. Due to the inclusion of 18 HFCs, including R134a and R245fa, in the Kigali Amendment as controlled working fluids, the search for excellent alternatives to R134a and R245fa is urgent. R1234yf and R1336mzz(Z) are potential alternative working fluids to R134a and R245fa, but most studies have focused on the comparison of thermodynamic performance and boiling heat transfer capability of these pure working fluids. There is limited research on the boiling heat transfer performance of their mixed working fluids. Therefore, this study focuses on the flow boiling heat transfer characteristics of the mixed working fluid R134a/R245fa under non-azeotropic conditions. Experimental methods were employed to investigate the boiling heat transfer performance of the alternative working fluids R1234yf/R1336mzz(Z) (including R245fa/R1234yf and R1234yf/R1336mzz(Z) mixed working fluids) and evaluate the feasibility of R1234yf and R1336mzz(Z) as substitutes for R134a and R245fa. The results indicate that among the three mixed refrigerants, R134a/R245fa exhibits the highest heat transfer coefficient, while R1234yf/R1336mzz(Z) shows the lowest heat transfer coefficient. However, the differences in heat transfer coefficients among these three are relatively small, and their overall trends under different operating conditions are similar. It is evident that R134a/R245fa, with its good thermodynamic performance and stability, still holds potential as a transitional working fluid. R1234yf/R1336mzz(Z), with similar physical and thermodynamic properties, is an excellent alternative to R134a/R245fa. [ABSTRACT FROM AUTHOR]

Abstract\nHIGHLIGHTSIt has been shown that wettability has an important effect on the surface’s heat transfer performance. In this article, the effects of different wettability of the surfaces of the micropillar array on the heat transfer performance under the same working condition (single-wettability and mixed-wettability surfaces) are compared by numerical simulation, the effects of the surface’s geometrical structure on the flow state of the workpiece and the behavior of the bubbles are also described. It is found that the mixed wettability surfaces combine the characteristics of hydrophilic and hydrophobic surfaces can effectively reduce the wall temperature. The microcolumn array further enhances the boiling heat transfer effect by perturbing the flow process of the workpiece while increasing the heated area. The surface structure of the hydrophobic top combined with hydrophilic sidewalls can significantly improve the heat transfer performance by 10%∼40% during the stable boiling process.Design of a rectangular channel with a square column array coupling different wettability distributions.Analysis of the coupling of geometric structure and non-uniform wettability distribution on bubble behavior.The effect of different wettability distributions on the mechanism of bubble behavior is analyzed by numerical simulation.Four structural arrangement options, hydrophobic top combined with hydrophilic sidewalls for the most significant increase in heat transfer efficiency.Design of a rectangular channel with a square column array coupling different wettability distributions.Analysis of the coupling of geometric structure and non-uniform wettability distribution on bubble behavior.The effect of different wettability distributions on the mechanism of bubble behavior is analyzed by numerical simulation.Four structural arrangement options, hydrophobic top combined with hydrophilic sidewalls for the most significant increase in heat transfer efficiency. [ABSTRACT FROM AUTHOR]

Prior studies have evidenced the potential for enhancing boiling heat transfer through modifications of surface or fluid properties. The deployment of nanofluids in pool boiling systems is challenging due to the deposition of nanoparticles on structured surfaces, which may result in performance deterioration. This study addresses the use of TiO2–water nanofluids (mass concentrations of 0.001 wt.% and 0.1 wt.%) in pool boiling heat transfer and concurrent mitigation of nanoparticle deposition on superhydrophobic laser-textured copper surfaces. Samples, modified through nanosecond laser texturing, were subjected to boiling in an as-prepared superhydrophilic (SHPI) state and in a superhydrophobic state (SHPO) following hydrophobization with a self-assembled monolayer of fluorinated silane. The boiling performance assessment involved five consecutive boiling curve runs under saturated conditions at atmospheric pressure. Results on superhydrophilic surfaces reveal that the use of nanofluids always led to a deterioration of the heat transfer coefficient (up to 90%) compared to pure water due to high nanoparticle deposition. The latter was largely mitigated on superhydrophobic surfaces, yet their performance was still inferior to that of the same surface in water. On the other hand, CHF values of 1209 kW m−2 and 1462 kW m−2 were recorded at 0.1 wt.% concentration on both superhydrophobic and superhydrophilic surfaces, respectively, representing a slight enhancement of 16% and 27% compared to the results obtained on their counterparts investigated in water. [ABSTRACT FROM AUTHOR]

External reactor vessel cooling (ERVC) is a key technology in the severe accident mitigation strategy of third generation pressurized water reactor nuclear power plants, and the critical heat flux (CHF) determines the pressure vessel integrity. Studies on ERVC boiling heat transfer enhanced by coating show that coating surface can significantly increase CHF, in order to investigate the aging effect of the real material of nuclear reactor pressure vessel SA508 steel surface on CHF characteristics of coating surfaces, experimental studies on boiling heat transfer characteristics of SA508 steel bare surface and TC4 titanium alloy porous coating surface based on SA508 steel under different aging conditions were carried out. The substrate of SA508 steel bare surface was made of copper block and 3 mm thick SA508 steel by explosive welding. The TC4 titanium alloy porous coating surface was prepared by spraying particles on the bare surface of SA508 steel by supersonic cold gas spray technology. The micro-scale (the diameter of particles is 10-50 μm) TC4 titanium alloy particles were accelerated to a high speed of 400-500 m/s by the propulsion from a stream of high-pressure inert gases with a much lower temperature than thermal spraying. Four kinds of aging experiments were carried out on the SA508 steel bare surface and three kinds of aging experiments on the TC4 titanium alloy porous coating surface at the inclination angle of 5°. The results show that the SA508 steel bare surface oxidizes rapidly in water, and the CHF tends to increase with the deepening of aging, within 20%. The scanning electron microscopy and EDS characterization were used to analyze the surface characteristic. The CHF enhancement is due to the generation of Fe3O4 magnetic micro-nano particle layers that improve surface wettability and added the nucleation sites by oxidation of SA508 steel. Nevertheless, the CHF increase due to oxidation is limited. Compared with the SA508 steel bare surface, the CHF of TC4 coating surface without oxidation increases more than 36.9%. The TC4 coating surface changes from super-hydrophilic to hydrophobic with the deepening of oxidation, the oxide generated by substrate SA508 steel is easy to clog the coating pores, and the CHF shows a deterioration trend. The application of porous coating technology to enhance the performance of ERVC needs to consider adding oxidation resistance layer between the SA508 steel substrate and the porous coating surface, and the problem of bonding strength and alternating stress of multilayer coating should be solved. This study helps to deepen the understanding of enhanced heat transfer technology for ERVC and lays the foundation for subsequent research.

In this paper, a mathematical model validated by in-situ temperature measurement data of the direct chill (DC) casting process has been established in order to study the domination and effect of multi-parameters including secondary cooling water flow rate (Q), casting speed (V), condition of primary cooling, and spraying water temperature (Tw) on DC casting index of sump depth (dsump), maximum and minimum temperature gradient (Tg,max and Tg,min) at mushy zone and shape of solidus line. Further, the height of impingement zone (Hip) is systematic quantitative analysis by a novel designed test (Hip=1.08865Q`+0.06272V−4.75597). The calculated temperature using the numerical simulation exhibits a good match with the actual temperature measurement data. The results of multi-factors on index by the designed orthogonal test indicate that V dominates the dsump (dsump=0.033+27.74V) and Tg,min (Tg,min=2569.15−766342.20V) at mushy zone, Q dominates the Tg,max (Tg,max=9195.12+2344770Q−27.83Tw) by analysing the range (R), variance (S) and significance (F). Likewise, by discussing the combination of R, S, F and microstructure observation, the priority influencing the shape of solidus line at center part was V. The Q dominates the shape of solidus line at the position between the center and edge part.

Boiling is known as an effective mode of heat transfer at low-temperature differences, due to the rapid vaporization of liquid. The performance of boiling heat transfer can be enhanced by reducing surface wettability and modifying surface structures. In this study, polished copper (bare) substrates were modified by composite coatings of TiO2 and SiO2 nanoparticles. Four different samples were prepared using electrophoretic deposition and by varying the coating duration to 5, 10, 15, and 20 min, which were named S5, S10, S15, and S20, respectively. The surface characteristics of bare and coated samples, such as morphology, wettability, surface roughness, and coating layer thickness, were investigated. The contact angle measurements of the bare surface were 65.7°, whereas the coated samples S5, S10, S15, and S20 were 112.9°, 103.6°, 100.3°, and 96.8°, respectively. The coating layer thickness of the samples S5, S10, S15, and S20 was 2.46, 4.76, 9.86, and 14.58 microns, respectively. The pool boiling performance was examined in demineralized (Milli-Q) water on bare and coated surfaces. The onset of nucleate boiling (ONB) temperature was reduced for all composite coated surfaces. The largest reduction in ONB was observed for S15, which was ~ 3.5 °C less than the bare surface. The maximum enhancements in the boiling heat transfer coefficient (BHTC) recorded for S10 and S15 were 38% and 62%, respectively. The optimum coating layer thickness was observed to be ~ 10 µm, up to which heat transfer performance was improved. [ABSTRACT FROM AUTHOR]

An active method for heat transfer enhancement is proposed and thoroughly characterized for the first time for cryogenic quenching, in which mechanical vibrations are directly induced onto the sample to be quenched, employing a compact modular system composed of a pneumatic plunging device along with a DC motor/eccentric cam mechanism, generating oscillations on three different axes at a wide array of amplitude-frequency combinations. The quenching performance was investigated from both flow-field and thermal standpoints, through numerical simulations of the flow behavior, high-speed imaging of the process, and experimentally generated transient quenching and boiling curves under the influence of the governing parameters, underlining their combined effect on the mechanism of heat transfer augmentation. Under optimal conditions of amplitude and frequency, a remarkable CHF enhancement of 270% was obtained and the quenching time was reduced from 5 seconds to 1.8 seconds compared to the non-vibration case, where the vibration frequency was found to be the primary factor involved in the increase of oscillation-driven pressure drop and subsequent cavitation-induced CHF enhancement. Consequently, we are providing researchers in the field of cryogenics a method that not only provides enhanced performance but also offers flexibility enabling active control of the governing parameters of the system. [ABSTRACT FROM AUTHOR]

Mixture fluids have the advantage of a flexible adjustment of the physicochemical properties by actively tuning the composition and concentrations, showing promising potential in thermal and power-related applications. However, mixtures are mainly zeotropic with heat transfer deterioration during the boiling process, resulting in a challenge to gain a comprehensive understanding of their microscopic phase change. In this study, molecular dynamics simulations were employed to investigate the nanoscale behavior of CO 2 , R32 and CO 2 /R32 mixtures. The equilibrium molecular dynamics (MD) method and the non-equilibrium MD method was utilized to study the vapor-liquid interface characteristics and the boiling heat transfer characteristics of zeotropic mixture, respectively. The results revealed that the thickness of the vapor-liquid interface was linearly related to the temperature, and the surface tension displayed significant fluctuations in both solid-liquid and vapor-liquid interfaces, which indicated a potential barrier for molecular transport. Compared to the pure components, the inception of nucleation boiling and vapor film formation of the mixture fluid was significantly delayed. The heating and evaporation rate, heat flux of mixture were lower, while the thermal resistance was significantly higher. Moreover, the time required for bubble nucleation and the formation of vapor film decreased notably with the enhanced wetting characteristics. The findings in this study provide a molecular-scale insight into zeotropic mixture boiling heat transfer and the possible wettability regulation to improve the heat transfer performance of zeotropic mixtures and promote their wider applications. [ABSTRACT FROM AUTHOR]

External reactor vessel cooling (ERVC) is a key technology in the severe accident mitigation strategy of third generation pressurized water reactor nuclear power plants, and the critical heat flux (CHF) determines the pressure vessel integrity. Studies on ERVC boiling heat transfer enhanced by coating show that coating surface can significantly increase CHF, in order to investigate the aging effect of the real material of nuclear reactor pressure vessel SA508 steel surface on CHF characteristics of coating surfaces, experimental studies on boiling heat transfer characteristics of SA508 steel bare surface and TC4 titanium alloy porous coating surface based on SA508 steel under different aging conditions were carried out. The substrate of SA508 steel bare surface was made of copper block and 3 mm thick SA508 steel by explosive welding. The TC4 titanium alloy porous coating surface was prepared by spraying particles on the bare surface of SA508 steel by supersonic cold gas spray technology. The micro-scale (the diameter of particles is 10-50 μm) TC4 titanium alloy particles were accelerated to a high speed of 400-500 m/s by the propulsion from a stream of high-pressure inert gases with a much lower temperature than thermal spraying. Four kinds of aging experiments were carried out on the SA508 steel bare surface and three kinds of aging experiments on the TC4 titanium alloy porous coating surface at the inclination angle of 5°. The results show that the SA508 steel bare surface oxidizes rapidly in water, and the CHF tends to increase with the deepening of aging, within 20%. The scanning electron microscopy and EDS characterization were used to analyze the surface characteristic. The CHF enhancement is due to the generation of Fe3O4 magnetic micro-nano particle layers that improve surface wettability and added the nucleation sites by oxidation of SA508 steel. Nevertheless, the CHF increase due to oxidation is limited. Compared with the SA508 steel bare surface, the CHF of TC4 coating surface without oxidation increases more than 36.9%. The TC4 coating surface changes from super-hydrophilic to hydrophobic with the deepening of oxidation, the oxide generated by substrate SA508 steel is easy to clog the coating pores, and the CHF shows a deterioration trend. The application of porous coating technology to enhance the performance of ERVC needs to consider adding oxidation resistance layer between the SA508 steel substrate and the porous coating surface, and the problem of bonding strength and alternating stress of multilayer coating should be solved. This study helps to deepen the understanding of enhanced heat transfer technology for ERVC and lays the foundation for subsequent research. [ABSTRACT FROM AUTHOR]

The temperature rise characteristics of PMSM (permanent magnet synchronous motor) during operation were studied under the condition of BHT (boiling heat transfer) in cooling water. The subcooling boiling heat transfer model, RPI (Rensselaer polytechnic institute), was used to calculate and improve the computational accuracy of simulation results. The experiments have shown that, when the motor was tested and simulated after preheating, the temperature rise characteristics were similar to test data because the boiling heat transfer phenomenon of the motor was taken into account, with an error of 1.7%, which was more accurate than the error of 7.5% without boiling. Therefore, from the results obtained from the experiments, the phenomenon of boiling heat transfer in cooling system has a significant effect on the temperature rise characteristic of the motor, which should be regarded as an important factor. Due to the influence of two-phase flow boiling heat transfer, the temperature rise of the motor in the plain areas is 4–5 °C higher than that in the high altitude areas. Consequently, if the motor is operated in high altitude areas, its temperature rise characteristic has better effect compared with plain area. Additionally, when BHT in cooling water is considered, the temperature of the motor drops as the rate of flow increases. In the meantime, the temperature difference between the minimum flow rate and the maximum flow rate is about 1 °C, which means that the increase in rate of flow can enhance the boiling heat transfer effect. [ABSTRACT FROM AUTHOR]

The paper discusses how the vapour bubbles growing during boiling under the near-triple point pressure influence the heat transfer coefficient when the refrigerant level is lower than the bubble departure diameter. The experiments were carried out for liquid levels of 0.57 to 1.89 cm, saturated pressure range between 0.9 and 4 kPa (saturation temperatures between 5.5 and 29℃). Boiling occurred on a plain surface with wall heat flux densities between 0.43 and 5.93 Wcm-2. We determined boiling curves for the low-pressure process and analyzed the changes in wall superheat for different filling levels. The experimentally obtained heat transfer coefficient (HTC) was compared with the theoretical values produced by the most popular mathematical expressions used at higher pressures. We also prepared the boiling map, where we specified two boiling regimes: the regime of convection or small popping bubbles and the regime of isolated bubbles. The results indicate that the level of liquid can be neglected within the heat flux range analyzed in this study. The main mechanism of heat transfer under measured conditions is heat convection and conduction, rather than evaporation. The experimentally determined difference between the heat transfer coefficients for different levels of liquid is under 100 Wm-2K-1 (for the same heat flux and pressure at the wall). [ABSTRACT FROM AUTHOR]

Fructooligosaccharides (FOS) is a functional food additive. FOS syrup produced by biological methods can be easily transported, stored and used after drying. In this study, the effects of operating pressure, heating temperature and initial moisture content of FOS syrup on the drying characteristics during vacuum drying were studied. With a visual system, the state changes of the material during the drying process were recorded. The specific heat, viscosity and thermal conductivity of the FOS at different temperatures and moisture contents were measured. From the perspective of drying characteristics, the whole drying process can be divided into four periods: the increasing drying rate period AB, the first falling drying rate period BC, the second falling drying rate period CD and the third falling drying rate period DE. The heat transfer mode in AB and BC was boiling heat transfer, with the material viscosity less than 267.9 Pa·s. In CD period, the heat transfer mode was convection heat transfer with the material viscosity of 267.9 Pa·s to 501.6 Pa·s. In DE period, the material viscosity was greater than 501.6 Pa·s and did not have fluidity, and the heat transfer mode was heat conduction. A multivariate model for the convection heat transfer coefficient was obtained based on the heat balance. The maximum error between the simulation value by the model and the experimental value of the material moisture content during the vacuum drying process was 4.18 %. [ABSTRACT FROM AUTHOR]

Computational fluid dynamics was used and a numerical simulation analysis of boiling heat transfer in microchannels with three depths and three cross-sectional profiles was conducted. The heat transfer coefficient and bubble generation process of three microchannel structures with a width of 80 μm and a depth of 40, 60, and 80 μm were compared during the boiling process, and the factors influencing bubble generation were studied. A visual test bench was built, and test substrates of different sizes were prepared using a micro-nano laser. During the test, the behavior characteristics of the bubbles on the boiling surface and the temperature change of the heated wall were collected with a high-speed camera and a temperature sensor. It was found that the microchannel with a depth of 80 μm had the largest heat transfer coefficient and shortest bubble growth period, the rectangular channel had a larger peak heat transfer coefficient and a lower frequency of bubble occurrence, while the V-shaped channel had the shortest growth period, i.e., the highest frequency of bubble occurrence, but its heat transfer coefficient was smaller than that of the rectangular channel. [ABSTRACT FROM AUTHOR]

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Microscale electronic devices offer promising application capabilities in various fields, such as information, aeronautics and astronautics, energy, and chemical engineering. Specifically, the exceptional performance of high-integration and high-frequency devices leads to a significant heat flux enhancement. Conventional air and liquid cooling techniques struggle to meet the efficient heat dissipation requirement, affecting the reliability and safety of microscale electronic devices significantly. Many types of passive heat transfer process intensification strategies have been proposed recently, such as those based on adjusting element structure, surface roughness, surface hydrophobicity, and channel dimension. However, these passive strategies increase flow resistance to some extent, limiting their applicability. Ultrasound has several unique characteristics, including low cost, simple operation, flexible control, strong penetrability, and good biocompatibility. These characteristics make ultrasound a promising candidate for use in national defense, biomedical theranostics, agriculture, food, the environment, and materials. Researchers have paid considerable attention to the integration of ultrasound with heat transfer techniques, which has gradually become one of the key research directions for heat transfer enhancement. This paper aims to provide a comprehensive overview of the research progress on the intensification of the ultrasound-excited heat transfer process. First, the principles of ultrasound-excited heat transfer enhancement are introduced, and two major acoustic phenomena, acoustic cavitation and acoustic streaming, are highlighted. Theoretical and experimental studies on ultrasound-excited single-phase gas convection, single-phase liquid convection, pool boiling, and flow boiling heat transfer process intensification are then summarized, and typical studies in these fields are categorized and discussed in depth. Finally, current challenges and future directions are presented, such as simple numerical simulation models that should consider multiphysics and multidomain constraints for accurately representing the practical heat transfer process, lack of sufficient characterization methods that should develop new and integrated visualization techniques for precisely monitoring heat transfer performance, limited focus on other acoustic phenomena other than acoustic streaming and acoustic cavitation that should provide a comprehensive analysis for revealing the in-depth heat transfer mechanisms, and few attempts and pathways to industrialization that should demand researchers from different disciplines to work together and collaboratively. It is hoped that this review article will not only reveal the unprecedented functionality of ultrasound for heat transfer enhancement but will also provide critical guidelines for the rational and practical design of robust ultrasound heat transfer platforms.

There are a series of complex physical phenomena in once-through steam generators (OTSG), such as full-regime flow boiling and phase-change heat transfer from supercooled water to superheated steam, coupled heat transfer between tube side and shell side. At the same time, the structure of OTSG is also very complex. There are a large number of slender heat exchange tubes in the OTSG, and the difference between the radial size and the axial size is very large, that is, the size span is large. These problems and characteristics lead to the problems of high computational difficulty, low solution efficiency and poor solution stability when using computational fluid dynamics (CFD) and threedimensional refined modeling methods to analyze the three-dimensional temperature field of OTSG with large-scale heat exchange tube bundles. Based on the full-regime flow boiling, phase-change heat transfer model and the criterion model of boiling flow regime, a one-dimensional full-regime flow boiling and phase-change heat transfer analytical model were stablished in this paper. With appropriate parameter transfer, the cross-scale coupling solution between the one-dimensional boiling heat transfer analytical model on the tube side and the three-dimensional refined CFD model on the shell side was realized. This crossscale coupling calculation method can realize the independent coupling between each heat exchange tube on the water side and the threedimensional fluid domain on the sodium side. The proposed crossscale coupling numerical model was applied to the oncethrough steam generator of the Indian fast reactor to realize the independent coupling between each OTSG heat exchange tube and the shell side threedimensional sodium fluid domain, and the plugged tube condition analyses were carried out. The effectiveness of the proposed cross-scale coupling model was verified by comparison with experimental data. The study results show that the established crossscale coupling numerical analysis model between tube side and shell side can accurately predict the temperature distribution and the main heat transfer characteristic points of each heat exchange tube over the entire height. The calculation results can also give the temperature of different heat exchange tubes and the temperature difference between the tube walls of each heat exchange tube in detail. This method is also very convenient to realize the analysis of plugging conditions. The crossscale coupling solution method avoids the direct solution of complex threedimensional multiphase flow equations, and greatly improves the efficiency and stability of the numerical solution of the OTSG threedimensional temperature field. This study provides an efficient threedimensional refined analysis method for the design and safety verification of OTSG.

A numerical study on transient heat transfer of shell and tube type ice thermal storage system is carried out based on the concept of a single u-tube borehole thermal network. Two tubes are arranged in the thermal storage tank in which glycol solution flows in one of the tubes, while a refrigerant flows in the other tube. In this study a boiling heat transfer of the refrigerant is considered to model the heat exchange among the ice storage, the refrigerant and the glycol solution which can be used for air-conditioning application. Temperature variation of all the three substances of the ice thermal storage system (i.e. the ice/water, glycol solution and the refrigerant) with depth has been determined for specified times. Also temperature history of all the three substances has been determined at specific depth of the thermal storage system. Finally the effect of mass flow rate of the refrigerant on the solidification process has been investigated with the numerical method. The transient boiling heat transfer of the refrigerant in the saturated region, the transient single-phase heat transfer process of the glycol solution and the refrigerant at the superheated region, and the solidification process of the ice thermal storage system were all investigated in this study.

Enhancement in boiling heat transfer performance is significant for addressing thermal management bottlenecks of advanced electronic systems. Reduced graphene oxides (rGO) are regarded as promising candidates for thermal management due to their excellent thermal properties, chemical stability and adjustable wettability. In this study, rGO coatings with micron pores and controllable oxygen contents are prepared on Al substrate via cathodic electrophoretic deposition and subsequent thermal annealing, leading to enhanced pool boiling performance. The heat transfer coefficient for Al/rGO450 is 37.2 kW m−2 K−1, which is increased by 112.6% compared with bare Al, also outperformed previously reported Al based substrates. It is assumed that the hydrophilic and aerophobic rGO coatings effectively promote the liquid infiltration and bubble departure during pool boiling process. Importantly, repeatability tests indicate the durable stability of vertically oriented rGO nanosheets. Reverse none-quilibrium molecular dynamics simulation indicates that the interfacial transmission coefficients of Al/rGO increase after thermal annealing, indicative of the enhanced heat transfer performance of heterogeneous interface. Our study opens a new avenue for endowing metal substrates with high pool boiling performance using porous carbon coating nanoengineering strategy with controllable morphology and components. [ABSTRACT FROM AUTHOR]

The immersion phase-change cooling technology utilizes the latent heat of the cooling liquid to dissipate heat by directly contacting the cooling liquid with the heat-generating electronic chip, which can meet the cooling requirements of current high heat flux density data centers. In this paper, the effect of different factors on the heat dissipation performance of immersion phase-change cooling technology was explored through numerical simulation. The results show that, under certain power conditions, the inlet temperature and flow rate of the cooling water in the condensation module, as well as the different arrangement of servers, have a significant impact on the heat dissipation performance of the entire system. The inlet water temperature mainly affects the chip temperature after stabilization. With the decrease in the inlet temperature, the chip surface temperature decreases significantly. The inlet water flow rate mainly affects the time required for the heat exchange to reach the desired temperature. With the increase in the inlet flow rate, the required cooling time is shortened. As the spacing between servers increases, the thermal safety and stability of the entire system increase. When the spacing between servers increases from 5 mm to 15 mm, the highest temperature and the temperature uniformity coefficient between the systems decrease significantly. When the spacing increases from 15 mm to 25 mm, the highest temperature and the temperature uniformity coefficient decrease slightly. These results can provide useful information for the designers of immersion phase-change cooling systems to improve the cooling efficiency of data centers, save energy, and ensure the safe operation of related computers, servers, and communication systems. [ABSTRACT FROM AUTHOR]

The heat transfer process is an important part of energy utilization and conversion, and boiling heat transfer is one of the most significant and effective heat transfer modes in use. Enhancing boiling heat transfer can directly improve energy use efficiency and promote the sustainable development of the energy industry. Surfaces with mixed wetting topologies have been proven to possess the potential to enhance boiling heat transfer. However, the heat transfer promoting mechanism of these types of surfaces requires further clarification on actual heat exchanger surfaces with macroscale heat transfer enhancement structures, such as millimeter-scale pillars. In this study, the boiling heat transfer enhancement mechanism and the performance of the hybrid wetting surfaces with an array of macropillars were explored using both experimentation and numerical simulation. In the experiment, the single bubble growth dynamics at the onset sites of nucleation of these hybrid wetting surfaces in the initial boiling stage were recorded using a CCD camera with a top view. The boiling heat transfer coefficient was also measured at the stable boiling stage. Within the entire tested range of heat flux (3.75–18 W/cm2), the hybrid wetting surfaces significantly enhanced the boiling heat transfer, and the HPo(bottom)–HPi(top) surface (surf-2) exhibited the best heat transfer performance. At the representative heat flux 12.5 W/cm2, the boiling heat transfer coefficient of the HPo (bottom)–HPi (top) surface (surf-2) and the HPi (bottom)–HPo (top) surface (surf-3) were more than 33% and 18% higher than the pure copper flat surface, and more than 16% and 3% higher than the uniform HPi surface (surf-4), respectively. On the one hand, due to the view field of camera being blocked by the fiercely growing bubbles in the stable boiling stage, it was difficult to record bubble numbers and gather statistics at the onset sites of nucleation in order to correlate the bubble dynamics with the mechanism of boiling heat transfer enhancement. On the other hand, the single bubble growth dynamics recorded during the initial boiling stage lacked information about the hybrid wetting surfaces in the vertical cross-sectional plane. Therefore, a two-dimensional VOF-based numerical simulation was adopted to supplement the contribution of hybrid wetting surfaces in the vertical plane. The simulation results indicated that the hybrid wetting surfaces with macropillars can inhibit bubble overgrowth and accelerate bubble departure compared with spatially uniform hydrophobic surface. The bubble radius and departure time on surf-2 were smaller than those on surf-3. These are believed to be the reasons why the surf-2 surface exhibited the best heat transfer performance in the experiment. Both the experiment and numerical analysis proved that the hybrid wetting surfaces with macroscale pillars can promote the boiling heat transfer, thus demonstrating potential applications in actual horizontal or vertical tube boiling heat exchangers. [ABSTRACT FROM AUTHOR]

Introduction. Copper foam material has various advantages. It has been proved effective in enhanced boiling heat transfer, but also increases pump power consumption. Grooved copper foam is a solution to achieve good balance between boiling heat transfer characteristics and pump power consumption. Material and Methods. Grooveless and grooved copper foam in open space was studied. Copper foam specifications comprised the combination of porosities of 70, 80 and 90%, and pore densities of 90 and 110 PPI. The grooved copper foams have two specifications: 11 and 17 grooves. The corresponding rib widths are 2 and 1 mm, with groove depth 2.9 mm and width 0.6 mm. The flow boiling experimental system of copper foam sample includes four parts: a heating water reservoir, pump, a test section, and a data acquisition system. In the test section, liquid water turns into vapor and carries the heat away from a copper block surface, and then vapor condenses into liquid water in the terminal reservoir. Results. Grooved copper foam samples presented significantly higher efficiency than grooveless ones. Grooved copper foams can increase the critical heat flux and heat transfer coefficient, compared with grooveless ones. Seventeen-grooved samples showed more excellent performance than 11-grooved ones. Visual observation disclosed that the stratified flow pattern dominated in moderate and high heat flux for grooved copper foam with open space. Covering vapor mass was more effective to be formed above 17-grooved samples, compared with 11-grooved ones. It indicated more vigorous boiling behavior occurs in 17-grooved sample. Discussion and Conclusion. The number of grooves has a significant impact on boiling heat transfer. Grooved copper foam samples present a significantly higher critical heat flux and heat transfer coefficient. Structural parameters such as porosity and pore density, play a relatively secondly role in heat transfer argumentation. Visual observation shows there exists a cyclic alternation of flow patterns: bubbly flow, annular flow and mass vapor formation for grooved samples. Forming vapor mass is more effective to be formed in 17-grooved samples, compared to 11-grooved ones. It indicates more vigorous boiling behavior occurs in 17-grooved samples.

In this paper, the interaction mechanism between the solid–liquid–gas interface phenomenon caused by nanostructure and surface wettability and boiling heat transfer is described, and the heat transfer theory of single wettable nanostructure surface and mixed wettable nanostructure surface is proposed. Through molecular dynamics simulation, the thermodynamic model of the wettable surface of nanostructures is established. The nanostructures are set as four rectangular lattice structures with a height of 18 Å. The solid atoms are platinum atoms, and the liquid atoms are argon atoms. The simulation results show that with the increase of surface hydrophilicity of nanostructures, the fluid temperature increases significantly, and the heat transfer at the interface is enhanced. With the increase in surface hydrophobicity of nanostructures, the atoms staying on the surface of nanostructures are affected by the hydrophobicity, showing a phenomenon of exclusion, and the evaporation rate in the evaporation area of nanostructures is significantly increased. In addition, the mixed wettable surface is influenced by the atomic potential energy and kinetic energy of the solid surface, and when compared with the pure wettable surface under the nanostructure, it changes the diffusion behavior of argon atoms on the nanostructure surface, enhances the heat transfer phenomenon compared with the pure hydrophobic surface, and enhances the evaporation phenomenon compared with the pure hydrophilic surface. This study provides insights into the relationship between the vapor film and the heating surface with mixed wettability and nanostructures. [ABSTRACT FROM AUTHOR]

A numerical investigation has been made on transient heat transfer modeling of an ice on coil type thermal storage system based on a double u-tube borehole thermal network concept. Four distinct concentric tube has been considered inside a milk storage tank, where a refrigerant streams inside the inner tubes of the concentric tubes, while an ice will be formed at outer tube to store a cold energy. The complex boiling heat transfer of the cooling refrigerant has been performed by utilizing a set of empirical equations with iterative process. The cooling refrigerant cools down the milk inside the storage tank as well as it freezes the water inside the outer concentric tubes at the same time. In this analysis, temperature profile of the working fluids along the vertical position has been determined for specified times. Also temperature history of the working fluids has been determined at specific position of the thermal storage system. Finally the temperature variation of the refrigerant at the exit of the tubes is determined, and it is found that for the first 400 s the refrigerant leaves the exit of the tubes as superheated state, while the refrigerant exits the tubes as saturated state afterwards. [ABSTRACT FROM AUTHOR]