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In the case of products made of steel, the presence of an oxide layer, which is formed during the steel production process as a result of high temperature, has a significant impact on the process of heat removal from the surface of the cooled material. For this reason, it is necessary to take into account the presence of the oxide layer in mathematical and numerical models used to simulate the distribution of the temperature field in cooled steel products. These models are based on the boundary conditions identified for given production conditions. This paper presents a comparison of the results of the identification of the boundary condition during water spray cooling of Armco iron with the use of the inverse solution. Numerical calculations were carried out using two models of heat conduction. In the first model, the presence of an oxide layer with different thermophysical properties than the base material (Armco iron) was taken into account. The second model assumed no oxide layer on the cooled Armco iron surface. It was found that the inverse solution obtained in the case of the heat conduction model taking into account the thickness of the oxide layer is correct in time and as a function of temperature. Thus, the boundary condition model obtained as a function of temperature is universal. However, this model requires an additional layer of oxides with different thermophysical properties than the base material to be included in the finite element model (FEM). Based on the conducted uncertainty tests of the inverse solution, it was found that the results of the determined boundary condition in the absence of the oxide layer on the cooled surface are subject to an error higher than 10% in comparison to the maximum reference value of the heat transfer coefficient. [ABSTRACT FROM AUTHOR]

Regeneratively cooled scramjets are successfully used as propulsion devices in hypersonic vehicles. During operation, scramjets experience acceleration. This special process causes a dynamic flow process, and heat transfer in the cooling channel commonly occurs, which may cause hazards and control difficulties for scramjets. A dynamic numerical model with a modified heat transfer coefficient calculation method was established to study the transient flow and heat transfer processes in a cooling channel. The dynamic characteristics of the flow and heat transfer under different conditions were calculated and are discussed, including the changes in the inlet fuel mass flow, heat flux, and pressure working conditions. The results indicate that the stable time of the cooling channel outlet fuel temperature is related to the rate of change in the inlet mass flow and heat flux. The stable time of the outlet fuel temperature under decreasing heat flux working conditions was approximately 12.5 s. These results summarize the dynamic flow and heat transfer characteristics, which are significant for designing cooling channels in scramjets. [ABSTRACT FROM AUTHOR]

To investigate the spray cooling characteristics and the impact of spray parameters such as chamber pressure, spray height, and spray tilt angle on heat transfer efficiency, a mathematical model based on the Eulerian–Lagrangian frame was established for an R410A closed-loop spray cooling system. The results revealed that the spray pattern is conical, with the center velocity significantly higher than the edge velocity. The temperature distribution of the cooling surface and liquid film height both exhibit a "W" shape, and the surface temperature is lower where the liquid film is thin. There is an optimal liquid film height of approximately 5 μm, at which the cooling surface temperature is the lowest. The surface temperature increases with an increase in the spray chamber pressure. Considering average cooling surface temperature, the optimal tilt angle is 40° with an average surface temperature of 330.1 K. When considering wall temperature and wall heat transfer coefficient uniformity, however, the optimal tilt angle is 10°, leading to the average surface temperature of 332.6 K. When increasing the optimal spray height to 70 mm, the average surface temperature is 313.4 K. [ABSTRACT FROM AUTHOR]

To investigate the spray cooling characteristics and the impact of spray parameters such as chamber pressure, spray height, and spray tilt angle on heat transfer efficiency, a mathematical model based on the Eulerian–Lagrangian frame was established for an R410A closed-loop spray cooling system. The results revealed that the spray pattern is conical, with the center velocity significantly higher than the edge velocity. The temperature distribution of the cooling surface and liquid film height both exhibit a “W” shape, and the surface temperature is lower where the liquid film is thin. There is an optimal liquid film height of approximately 5 μm, at which the cooling surface temperature is the lowest. The surface temperature increases with an increase in the spray chamber pressure. Considering average cooling surface temperature, the optimal tilt angle is 40° with an average surface temperature of 330.1 K. When considering wall temperature and wall heat transfer coefficient uniformity, however, the optimal tilt angle is 10°, leading to the average surface temperature of 332.6 K. When increasing the optimal spray height to 70 mm, the average surface temperature is 313.4 K.

Nanofiber surface coating is a promising method for the enhancement of heat transfer during spray cooling. In the present work, the drop dynamics as well as local and overall heat transfer during single drop impact onto a heated wall covered with a polyacrylonitrile (PAN) nanofiber mat are investigated to obtain insight into the mechanisms governing the heat transport enhancement. The influence of wall superheat, drop impact velocity, and mat thickness on the hydrodynamics and heat transfer from the heated wall to the fluid is studied. The experiments were conducted inside a temperature-controlled test cell with a pure vapor atmosphere maintained with refrigerant FC − 72 (perfluorohexane). The temperature field at the solid–fluid interface was observed with a high-speed infrared camera, and the heat flux field was derived by solving a three-dimensional transient heat conduction equation within the substrate. The presence of the nanofiber mat on the heater surface suppresses the drop receding phase due to the pinning of the contact line at the end of the spreading phase. Two different heat transfer scenarios are observed depending on the wall superheat and drop impact velocity: scenario (I), in which the liquid drop completely penetrated through the porous nanofiber mat and made contact with the heater surface; and scenario (II) in which the vapor produced inside the pores of the nanofiber mat prevented the liquid drop from touching the heater surface. In scenario (I), an up 450% heat flow enhancement during the sessile drop evaporation stage has been observed. In scenario (II), a 80% heat flow enhancement at this stage has been registered. • Wall heat flux during drop impact on nanomat-covered hot substrates is measured. • The drop receding phase is suppressed in the presence of nanofiber mat. • Heat transfer scenario is determined by impact velocity and wall superheat. • Heat transfer in sessile drop phase is significantly enhanced by using nanomats. • Heat transfer enhancement is high at high impact velocities, low wall superheats. [ABSTRACT FROM AUTHOR]

This work presents the experimental investigation of droplet boiling characteristics on superhydrophilic surfaces. These surfaces are prepared on a copper substrate, and the boiling characteristics are studied and compared with the bare copper surface. Two types of superhydrophilic surfaces exhibiting needle-like (CuO-1) and sheet-like (CuO-2) nanostructures are prepared by the chemical etching oxidation technique. The hierarchical surface structures are characterized by carrying out SEM and XRD analysis. We employ high-speed imaging along with temperature measurement to characterize the heat transfer phenomenon. The surface temperature varies from 100 °C to 190 °C, and the Weber number is maintained constant at 2.78, corresponding to the gentle droplet impact regime. The effectiveness in the heat transfer performance of the different surfaces is characterized by measuring the critical heat flux (CHF) and the Leidenfrost point (LFP), and it is correlated with the surface properties viz. roughness, wettability, and porosity. The superhydrophilic surface alteration reduces the contact angle by about 99.7% compared to the bare surface. This reduction in contact angle corresponds to an increase in Critical Heat Flux (CHF) by 69.95% for CuO-1 and 47.17% for CuO-2, respectively, compared to bare copper. It is also seen that the LFP is delayed on the superhydrophilic surfaces, with an increase in the LFP temperature by 16.67% and 14.28% for CuO-1 and CuO-2 coatings, respectively. The effect of structures on the atomization and formation of secondary droplets is also presented. We report the contact coefficient (k w) for superhydrophilic surfaces for the first time, which is helpful in the theoretical prediction of CHF. These results show that significant improvement in heat transfer can be obtained in spray cooling and hot spot cooling applications without resorting to sophisticated microfabrication techniques. • Significant enhancement in droplet boiling by cost-effective wet etching technique. • 70% increase in CHF and 17% increase in the Leidenfrost temperature. • Atomization is strongly dependent on surface microstructure. • Contact coefficient is reported for the first time for superhydrophilic surfaces. [ABSTRACT FROM AUTHOR]

The heat transfer characteristics of two hydrophilic surfaces, SM-QS3100 and ZCP-0010, were investigated in single-phase and two-phase zones in comparison to a smooth surface concerning spray cooling. The results showed that in the single-phase zone, the SM-QS3100 and ZCP-0010 hydrophilic surfaces could not enhance heat transfer, and the ZCP-0010 surface with better hydrophilicity had the worst heat transfer characteristic. Compared with the smooth surface, the heat transfer coefficients of the two surfaces decreased by 11.5% and 28.8% at a heat flux of 58.0 W/cm2. Within the two-phase zone, both surfaces positively influenced heat transfer, with the ZCP-0010 surface, being more hydrophilic, exhibiting a more notable enhancing effect. The heat transfer coefficients exhibited 12% and 11.5% increments at a heat flux of 151.7 W/cm2. However, the contribution of hydrophilic surfaces to heat transfer tended to be consistent with the heat flux increasing. Although the temperature homogeneity of each surface became worse, the temperature uniformity on the hydrophilic surfaces was better in both the single-phase and two-phase zones. [ABSTRACT FROM AUTHOR]

• The effect of flow rate and electric field intensity on electro-spray morphology is investigated. • The formation and transformation mechanism of each electro-spray jet mode are clarified. • The enhanced heat transfer strategy of electro-spray phase change cooling technology at elevated flow rates is proposed. • At a flow rate of Q = 800 ml/h and an applied voltage of V = 6 KV, the critical heat flux ( CHF ) can reach 100.8 W/cm2. This study has enhanced the application prospects of electro-spray in the cooling field. The advancement of semiconductor and microelectronics technologies has underscored the increasing importance of efficient heat management in electronic devices. To overcome the shortcoming of low flow rates of electro-spray, the present study is motivated by using visualization and heat transfer performance experiments to reveal the morphology evolution and heat transfer characteristics of electro-sprays with high flow rates. The results indicate that the morphology of electro-sprays is closely related to the electric field intensity and the flow rate, and can be classified into six modes: dripping mode, spindle mode, cone jet mode, multi-cone jet mode, simple jet mode, and oscillating jet mode. Furthermore, the formation mechanisms and transition rules of these modes are discussed in detail. In addition, the effects of the flow rate, voltage, and spray morphology on the heat transfer performance of electro-sprays was investigated, and strategies for enhancing heat transfer were subsequently proposes. At a flow rate is 800 ml/h and an applied voltage is 6 KV, the critical heat flux ( CHF ) can reach 100.8 W/cm2, and the maximum heat transfer coefficient ( h max ) can reach 14416.55 W/m2K. This study not only enhances the comprehension of high flow rate electro-spray technology, but serves as a vital reference for the design and application of electro-spray cooling devices. [ABSTRACT FROM AUTHOR]

This study introduces a methodology to compute spray cooling in the nucleate boiling regime. It examines the cooling of a horizontal circular tube, although the approach is not restricted to this geometry. While numerous investigations have considered nucleate boiling in the past, these are usually restricted to spray impingement onto a flat plate and not onto more complex surfaces. Furthermore, most prior studies are highly empirical in nature. The present study circumvents both of these restrictions. On the one hand, with more complex surfaces additional factors must be considered, in particular the influence of the local impingement angle on the number flux of impinging drops. On the other hand, the heat transfer for single droplets is first computed using existing theoretical solutions and then the principle of superposition is used to compute the global heat transfer from the surface over which the spray impinges. Accompanying this computation, a drop size distribution is specified in order to also investigate the influence of not only one representative drop size, but also the variance of drop size distribution on the heat transfer, an influence seldom reported on. Furthermore, the probability of drop-drop interaction on the surface has been estimated and the heat transfer correspondingly adjusted. This approach of computing total net heat transfer on a surface is first validated using available measurements in which the heat transfer in the nucleate boiling regime from a flat plate were used for comparison. The heat transfer from a circular tube was then computed as a function of mass flow rate, drop size distribution (expectation and variance) and wall temperature. Conditions for maximum heat transfer, corresponding to the critical heat flux, were identified. In all cases the net heat transfer was limited by the onset of drop-drop interaction on the substrate, i.e. the net coverage of liquid on the surface. The results of these parametric studies indicate clearly how the mass flow rate can be adjusted to maximize heat transfer while avoiding excess fluid consumption. Furthermore, the Sauter mean diameter is shown to be an appropriate drop size to use, if no further information is available concerning the size distribution. • A non-empirical methodology to computing heat transfer in the nucleate boiling regime. • Spray cooling computation taking into account explicitly the size distribution of drops. • Insight into spray conditions, which maximizes heat transfer while minimizing liquid consumption. • Consideration of highly varying number density of drops when cooling a surface of complex geometry. [ABSTRACT FROM AUTHOR]

Cooling systems often rely on numerical calculations with precise heat transfer boundary conditions (HTBC), usually expressed as average values. The value of the average HTBC depends on the area in which they are determined. The paper presents a new approach showing the influence of the choice of the method of supplying liquid onto the surface on the non-uniformity of energy transfer from the cooled surface, which is important in the selection of the determination domain on the HTBC. The tests were carried out for two full-cone nozzles with different spray angles and two materials with different thermal properties. The local and average heat fluxes were determined for various distances of the nozzles from the surface and various liquid supply pressures. Cooling capacity, unevenness of energy transfer from the surface and quenching characteristics were evaluated and assessed using cooling curves. The study concludes that adopting HTBC based on average heat flux variation does not cause a significant error in the assessment of energy transfer during cooling with a nozzle with spray angle of 60° for EN 1.4845 steel. However, for Inconel and a nozzle with spray angle of 45°, the noticeable non-uniformity requires the application of a local HTBC. • Unevenness the spray cooling process. • Possibilities of using the average heat transfer boundary condition. • Recommendations for the use of local heat transfer boundary condition. [ABSTRACT FROM AUTHOR]

• The high temperature cylindrical surface cooled by spray was simulated. • The axial tilt spray can effectively solve the hot spot problem and improve the cooling uniformity. • The temperature and wall heat flux distribution of the cooling area under different spray angles were analyzed. • Only when the spray boundary is tangent to the cylindrical surface (H = 70 mm), the circumferential tilt Angle has a positive effect on the wall heat flux. In the hot-rolled seamless steel tube production process, quenching is a crucial process. Spray cooling technology can achieve uniform and high-intensity cooling during the steel tube production process, which is expected to improve production efficiency and product quality. This study performs numerical simulations to explore the effects of spray cooling on a heated cylindrical surface. The influence of spray angles is focused on the cooling efficiency, while the spray height is also found to be another crucial variable. In the simulation, the axial tilt angle and circumferential tilt angle vary between 0 ∼ 30°, and the spray height changes within 50 ∼ 150 mm. A high-temperature steel tube is selected as the test object. The detailed analysis is discussed on the variations in the cooling area and wall heat flux under different spray angles. The results indicate that the axial tilt angle can effectively solve the hot spot. With an increase in axial tilt angle and spray height, the cooling area expands gradually. Meanwhile, the wall heat flux decreases with an increasing axial tilt angle and spray height. However, when the spray height is too high (H > 100 mm), the excessive axial tilt angle will have a negative influence on the wetting region. Although the circumferential tilt angle greatly changes the shape of the cooling area, it has a smaller effect on the size. It is worth noting that the spray boundary is just tangent to the cylindrical surface at H = 70 mm. Only at this moment does the circumferential inclined spraying exhibit a positive influence on the wall heat flux. [ABSTRACT FROM AUTHOR]

• The heat transfer enhancement and surface temperature non-uniformity are numerically studied. • The radial groove surface has a stronger heat transfer capability than the straight groove surface. • There is an optimal groove width and optimal groove number on the radial groove surface. • A novel enhanced surface achieves maximum heat flux with a small heat transfer area. • The design of the enhanced surfaces should focus on the flow and distribution of the liquid film more. A numerical model of spray cooling for enhanced surfaces in the non-boiling regime is created with deionized water as cooling medium. This model is validated by contrasting the simulated data with the corresponding experimental data, and the relative deviation is within 12 %. Compared with a smooth surface, the area of the enhanced surface is expanded, the cooling performance is significantly improved, but the surface temperature distribution is less uniform. Compared to the straight groove surface with the same area, the heat flux of the radial groove surface is higher because its surface structure is more conducive to the spreading and leaving of the liquid film. Studies of the effects of the structure parameters (groove width and groove number) of the radial groove surface on the heat transfer show that there is an optimal groove width (0.2 mm) and groove number (45) for the strongest cooling capacity, and both the velocity and thickness of the liquid film are significant factors in cooling performance. The faster the liquid film velocity, the thinner the liquid film and, thus, the better the heat transfer. Motivated by these findings, three novel enhanced surfaces are machined to increase liquid film fluidity and heat transfer area even further. The cooling performance of the three novel enhanced surfaces is further improved, and the slope groove surface acquires the strongest cooling capacity due to the acceleration of liquid film flow by gravity, although its heat transfer area is not the largest. Research on all enhanced surfaces indicates that thinner liquid film and faster liquid film flow should be the primary design goals of the enhanced surface, followed by an increase in heat transfer area. [ABSTRACT FROM AUTHOR]

• The high temperature cylindrical surface cooled by spray was simulated. • The effect of spray spacing on cooling was simulated, and the best spray spacing range was obtained. • The temperature and wall heat flux distribution of the cooling area under different nozzle array forms were analyzed. • It is pointed out that the unidirectional inclined array spray can obtain better cooling effect. Spray cooling technology is an efficient cooling method. In the industrial application, the large area cooling requires the multi-nozzle spray design. Reasonable selection of nozzle array form is particularly important. Therefore, the simulation is applied in this study to investigate the effect of the nozzle array on the spray cooling of steel pipes after the model is validated. A steel pipe with a diameter of 140 mm, a wall thickness of 20 mm, and a length of 350 mm is employed as the research object, with an initial temperature of 900 °C. The scheme has four options for double spray spacing: OLR = −15 %, 0 %, 15 %, and 30 %. The results show that when the OLR grows, the cooling area gradually diminishes, and the cooling area's average temperature and average surface heat flux fall and subsequently increase. When OLR=30 %, the best cooling zone shape is obtained. The minimum average temperature, 231 °C, is obtained when OLR = 15 %. After comprehensive analysis, the ideal spray spacing range is found at OLR = 15 %∼30 %. In order to study the nozzle array, spray nozzles are arranged in multiple rows according to OLR = 30 %. This study also explores the strategies of unidirectional inclined spray and opposite inclined spray for lessening the area of the hot spot. There are six nozzle array arrangements in total. By comparing the results, it is discovered that the inclined spray increases the cooling area and accelerates the surface cooling of steel pipes. Under the side-by-side unidirectional inclined spray and the staggered unidirectional inclined spray, the cooling areas are 146,868 mm2 and 142,914 mm2 respectively, the average temperatures are 157.09 °C and 154.28 °C respectively. It is indicated that side-by-side inclined spray and staggered inclined spray are the better nozzle array arrangement to obtain the maximum cooling efficiency. [ABSTRACT FROM AUTHOR]

There is an urgent need to quantify the heat transfer features of spray cooling involving high-temperature transition and film boiling regions. To meet this need, this study proposes integrating inverse heat-transfer computation with sparse regression for estimating the cooling heat flux of high-temperature spray cooling. A series of physical and numerical experiments was performed to verify and validate the proposed algorithm. The preliminary results indicate that the first-order Tikhonov regularization combined with the conjugate gradient algorithm is an efficient way to solve nonlinear inverse heat-conduction problems. Sparse regression is helpful to formulate time-varying boundary heat fluxes by filtering out appropriate functions from a library of candidate functions. The reconstructed boiling curves show that the high-temperature spray cooling experienced five heat transfer regions: the onset of spray cooling, the film boiling region, the transition boiling, the nucleate boiling region, and the single-phase liquid cooling region. Particularly, the film boiling dominates the high-temperature spray cooling, which accounts for, in our case, >80% of the cooling time. [ABSTRACT FROM AUTHOR]

• The combined heat transfer enhancement method is proposed for electrospray cooling. • The CHF is increased by 63 % with cubic-pin-fin surface as compared to the flat one. • The surface modification dominates heat transfer enhancement at 51 °C < T s < 119 °C. • The superior CHF of 7.93 W/cm2 is achieved for cubic-pin-fin surface at T s = 145 °C. • The superior heat transfer performance is achieved with an area ratio of 0.79. Electrospray (ES) cooling is promising to achieve the high-heat-flux thermal dissipation with a low fluid consumption when using structured surfaces as heat sinks of micro-size and high-power electronics. Nevertheless, available research is still limited in the fundamental of combined heat transfer enhancement owing to the macro-structured surface and electric field. In this study, four macro-structured surfaces machined with cubic pin fins, conical pin fins, wavy fins and straight fins are compared to one flat surface under electric field to shed lights on the combined heat transfer enhancement mechanism during ethanol ES cooling. The experimental results demonstrate that both electric field and surface modification can elevate the critical heat flux (CHF) and heat transfer coefficient. A CHF of 7.93 W/cm2 is achieved by the cubic-pin-fin surface with an applied voltage of 4.5 kV at T s = 145 °C, corresponding to a 63 % enhancement over the flat surface. The CHFs at first increase and then decline with the increased area ratio (f), and the superior heat transfer performance is achieved when f = 0.79. In the low temperature region (30 °C < T s < 51 °C), the enhanced convection and bubble formations caused by electric field are deemed as the dominated heat transfer mechanism. The increase in nucleation sites triggered by macro-structured surfaces governs the heat transfer in the mid-temperature region (51 °C < T s < 119 °C). Whereas, the heat transfer enhancement due to macro-structured surfaces declines in the high temperature region (T s > 119 °C), possibly as a consequence of the large thermal resistance induced by the Leidenfrost phenomenon. [ABSTRACT FROM AUTHOR]

• Application of MCrAlY coating to increase heat transfer during water spray cooling. • The use of the coating intensifies heat transfer compared to the uncoated surface. • The thickness of the coating affects the intensity of the heat removal. The main purpose of the paper was to determine the influence of NiCoCrAlY coating application and its thickness on the heat transfer during water spray cooling under surface boiling conditions. The scope of the research included: sensor preparation, measurements of the sensor temperature during cooling, and numerical calculations to determine the intensity of sensor cooling. The intensity of heat removal was determined by the average values of the heat flux on the cooled surfaces. The inverse method for the heat conduction equation was used to determine the heat transfer boundary conditions. Temperature measurements during cooling were carried out for an initial sensor temperature of 500°C, 700°C and 900°C and a liquid pressure 0.1 MPa, 0.2 MPa. Due to this, it was possible to select a coating thickness that contributed to the greatest extent to the increase in the intensity of heat dissipation from the hot surface. The highest values of the heat flux were obtained during the cooling of the sensor with a 134.5 μm coating. [ABSTRACT FROM AUTHOR]

This paper examines the performance of a heat sink that combines an evaporator and an expansion device into a single component within a compact vapor compression refrigeration system designed for applications with high heat fluxes. The liquid refrigerant at high pressure expands through orifices, generating a spray that impacts a copper heater. The heated surface is enhanced with laser-micromachined micropillars featuring a square cross-section to improve the thermal conductance of the boiling liquid film. Qualitative evaluations of the enhanced surfaces using interferometry analyses determined the heat transfer surface area and assessed the effectiveness of the fabrication technique. The experiments involved using R-134a, a two-orifice expansion device, and enhanced surfaces with pillar edge sizes ranging from 200 to 600 μ m. This analysis encompasses the cooling system's thermodynamic performance, including compressor power and coefficient of performance, as well as steady-state heat transfer parameters such as convection coefficient and critical heat flux. The system achieved a cooling capacity of 230 W (35.9 W/cm 2), with the heater surface temperature staying below 22.9 °C and the highest average heat transfer coefficient reaching as high as 55 kW/(m 2 -K). This represents a 129% increase in thermal conductance compared to mirror polished surfaces, leading to a significant reduction in the temperature of the heated surface. Additionally, the area-corrected heat transfer coefficient is computed to verify the thermal resistance reduction unrelated to the surface area enhancement, and a 60% reduction is found. Furthermore, although this heat transfer enhancement shows minor to no influence on the thermodynamic performance of the refrigeration system, the heater cooling efficiency, defined as the ratio of the enthalpy rise delivered by the heat source to its ideal maximum, increased by 13%. The findings are supported by high-speed video sequences illustrating the boiling heat transfer features. • Compact refrigerator combines evaporator and expansion device in new spray heat sink. • Laser-micromachined surfaces provide two-fold enhancement during flow boiling. • Two-orifice expansion device produced cooling capacity of 230 W (35.9 W/cm 2). • Maximum recorded average heat transfer coefficient of 55 kW/(m 2 K). • The thermal conductance increased by 129% compared to a polished surface. [ABSTRACT FROM AUTHOR]

This study examines spray cooling of horizontal, circular tubes when the surface temperature exceeds the Leidenfrost point, and the individual drop impacts are in the film boiling regime. Although film boiling is not an optimal condition for heat transfer, it is encountered in transient cooling processes or when high temperatures persist along the tube. The goal of the study is to apply existing models for drop impact and heat transfer to surfaces more complex than flat plates and to determine the overall steady state heat removal rate as an essential parameter for heat exchanger design. The spray characteristics are prescribed by a local number flux and drop size, assuming a random distribution in space and a uniform velocity of all drops. The angle of individual drop impingement on the cylindrical tube is accounted for through the maximum spreading diameter of the drop on the surface and the normal component of impact velocity. Furthermore, drop-drop interaction on the heated surface is accounted for at high local number flux values through an effective coverage area coefficient. The results are expressed in the form of a local heat transfer coefficient. These results confirm that the most influential parameters regarding heat transfer are the liquid mass flow rate in the nozzle and the drop diameter; however, they also indicate that the non-normal impact of drops over portions of the cylindrical tube leads to a highly reduced number flux; hence heat transfer. This oblique impact angle arises for one from the local spray angle, but more drastically from the curved, cylindrical surface; the latter leading to a dramatic sharp decrease in heat transfer. This is important information when considering the use of multiple spray nozzles, either circumferentially or longitudinally along the tube, since it dictates the optimal spacing between neighbouring nozzles. [Display omitted] • A methodology for predicting spray cooling in the film boiling regime is introduced. • The predication of heat transfer is based on theoretical analysis; only one empirical factor is introduced. • The local impingement angle of drops has been considered in the hydrodynamics of impact and in the influence on the local number flux. • Parametric studies indicate the influence of droplet size, substrate temperature, and mass flow rate on the heat transfer. • This study lays the basis for simulation of practical spray cooling scenarios involving multiple nozzles and/or nozzle arrays. [ABSTRACT FROM AUTHOR]

• Droplet flow and misty flow are observed in long distance spray. • The maximum heat transfer coefficient is obtained in droplet flow stage. • Surface drying appears and the critical heat flux is reached in misty flow stage. • Increasing the spray pressure can increase the critical heat flux by 59.5 %. • Recommended spray operating parameters are obtained. Spray cooling has substantial potential for wide application, given its unique characteristics, including high heat transfer coefficient, absence of contact thermal resistance, and the elimination of cooling hysteresis. In this study, a visualized experimental system featuring a gas-liquid two-phase cyclonic nozzle was constructed to study both the heat transfer and fluid morphology features pertaining to the wall. With the increase of wall superheat, a progressive transition across four distinct stages of heat transfer – liquid film, stream flow, droplet flow, and mist flow can be found. Of these, the droplet flow stage outperforms others in terms of heat transfer performance and is thus advocated as the preferred mode of application. In response to increasing spray pressure, the droplets generated on the wall during the droplet flow stage undergo a reduction in size, yet become more densely distributed. A notable increase in critical heat flux by 59.5 % is observed when spray pressure is elevated from 0.2 to 0.4 MPa. While raising the spray flow rate leaves the heat transfer performance during the liquid film stage largely unchanged, it effects a significant augmentation in critical heat flux. Our experimental results ultimately obtain the optimal operating parameters that facilitate the wall surface's retention in the droplet flow stage. These experimental results are poised to contribute meaningfully to the engineering practices associated with spray cooling applications. [ABSTRACT FROM AUTHOR]