Condensation Rate Research Articles

Estimating Phase Transition Rates in Shallow Cumulus Clouds from Mass Flux. Part II: Vertically Dependent Formulation

Abstract This work continued the investigation of the relationship between phase transition rates and mass flux in trade wind cumulus clouds. The latter was simulated by an LES model initialized with soundings from the Rain in Cumulus over the Ocean (RICO) field project. In Part I, we demonstrated that a very high correlation exists between integral phase transition rates and upward mass flux. In this study, we focused on the vertically dependent variables and showed that a similar high correlation exists between the condensation rate and the upward mass flux . Based on condensation theory, we showed that under quasi-steady approximation condensation rates can be calculated by a linear function of with the slope coefficient dependent only on temperature and pressure. The model data showed that the error of such approximation is less than a few tenths of a percent. The parameterization of the evaporation process is more complex, mostly because of the slow evaporation of raindrops as they fall through the cloud’s unsaturated areas. Nevertheless, it was possible to define the fraction of the evaporation to condensation rate as a function of vertical coordinate z and cloud thickness H. This function can be quite accurately approximated by the third-order polynomials of z and H. It is suggested that the proposed formulation of evaporation together with the quasi-steady formulation of condensation can serve as a parameterization of water phase transition rates in shallow cumulus clouds. Significance Statement This study investigated condensation/evaporation processes in tropical cumulus clouds. The energy exchanged during these processes is an important driving force behind a wide range of atmospheric phenomena. It was found that the vertical distribution of this energy source can be expressed as a linear function of cloud updrafts. This finding suggests a new approach to calculate cloud energy transformations in numerical weather prediction models.

Liquid-Cooled Thermoelectric Modules: Potential for Efficient Water Harvesting Through Air Condensation

Water is one of the essential natural resources for the sustaining life of all beings on this planet. In general, groundwater is used to meet daily needs, although the availability of this water source becomes a major concern, particularly in some areas with limited access to it. Air condensation is a solution for providing water in such areas. This study aims to explore the potential of utilizing the thermoelectric technology as an alternative solution for water provision. An experiment is conducted using a system consisting of single liquid-cooled thermoelectric cooling devices/modules (TECs). Three types/variants of TECs with different cooling capacities are tested at three different operating voltages. During the tests, changes in physical quantities are recorded for analysis, along with amount of water produced. The results demonstrate notable performance differences between all TEC variants. The highest cooling capacity is achieved by the TEC-1 variant, albeit with higher current usage. The TEC-3 variant delivers the lowest performance of all. TEC-2 obtains the highest water yield, producing 46.9 g of water at 12 V, while TEC-1 and TEC-3 produce 34.4 and 13.2 g, respectively. The highest condensation rate, i.e., 3.72%, is achieved by TEC-2, at 9 V, while the lowest energy consumption, i.e., 3.74 kWh/L, is shown by TEC-2, at 12 V.

EVALUATION OF ENERGY SAVING EFFICIENCY OF BOILER COMBINED WITH HEAT PUMP FOR SUPPLEMENTARY FEED WATER HEATING

This paper investigates the integration of heat pumps for heating boiler feedwater and evaluates the impacts of feedwater temperature and condensate recovery rates on fuel consumption, energy efficiency, and CO2 emissions. The results show that using heat pumps significantly reduces boiler fuel consumption, especially when the feedwater temperature increases and the condensate recovery rate is high. The COP (Coefficient of Performance) of the heat pump gradually decreases as the water temperature rises; however, heating the water at lower temperatures yields better economic and energy efficiency. Economically, heat pumps provide substantial benefits, with maximum cost savings achieved at a water temperature of 75°C. Additionally, integrating heat pumps reduces CO2 emissions, particularly in boilers without condensate recovery, with the highest emission reduction reaching 17.8 kgCO2 per ton of steam. These findings demonstrate that using heat pumps is not only energy-efficient and cost-effective but also contributes to environmental protection by reducing greenhouse gas emissions.

Optimizing solar still performance: A response surface methodology approach to evaporation and condensation enhancement

Water crisis is a major problem across the world. It is significant to migrate for effective methodologies to meet future water demand. Solar-based desalination system is environmental friendly and suitable method for potable water yield production from saline/brackish water and also cost effective than other methods. The role of optimization study in maximizing the water yield is paramount for the performance enhancement of solar-based desalination system and its effect was insufficiently addressed. In present study, a new approach of waste scraper and double fan arrangement is introduced inside the conventional solar still (SS). Then, using response surface methodology, Box–Behnken design (BBD)-based optimization is performed to determine optimal solution for the influence of input parameters (operating Time interval, Time duration and voltage of scraper and dual fan) on the output parameter relative humidity (RH) to increase the condensation and evaporation rates of a SS, which helps to enhance the water yield productivity. Experiment is conducted at 9.672° (North) and 77.994° (East) Madurai, Tamil Nadu, India. Validation of experiment results is done using the BBD method. Result reveals that the analysis of variance model with double-fan arrangement inside the still shows better with optimal performance with a coefficient of determination R2 = 97.78%, adequate precision = 46.22, RH = 76.515% than that with scraper arrangement ( R2 = 96.7%, adequate precision = 35.76, RH = 76.327%). The optimized model exhibit promising results with statistically significant P-value less than .0001 for the both methods and its F-value is noticed that 126.96 (for a SS with scraper) and 190.66 (for a SS with double fan).The outcome of this study helps to enhance the condensation rate to produce the more amount of fresh water from hybrid photovoltaic with thermal system.

Molecular dynamics simulation of heat and mass transfer in a nano-grooved heat pipe: Focusing on filling ratios' effect.

Managing the heat generated in microprocessors and other similar heat-generating devices requires the design and construction of superconductors with high reliability. For this purpose, heat pipes (HPs) are a very good option. Nano-grooved micro flat plate heat pipes (FPHPs), which are in the group of vapor chambers (VCs), have received attention due to their suitable structure. In this research, an FPHP with a length of 1050nm is investigated using molecular dynamics (MD) simulation. The effects of using three metals for walls including platinum (Pt), copper (Cu), and aluminum (Al) as well as three working fluids including argon (Ar), water (H2O), and ethanol (EtOH) were investigated. Focusing on the filling ratio of the interior space, mass and heat transfer inside the HP has been fully investigated. Evaporation rate, condensation rate, temperature, density, and velocity distribution as well as heat flux have been studied. The results show that although Ar shows better mass transfer results (due to its monoatomic nature), EtOH has better thermal performance. Among the three metals used, Cu has the best thermal performance. The maximum heat flux is obtained by using Cu and EtOH and is equal to 1819 W/cm2. The optimal filling ratio is reported in different states. The maximum mass transfer rate relates to Ar and at FR = 0.3; which equals 32.5%. The highest phase change rate is obtained using platinum and water, which is equal to 74%.

Design and development of wire-mesh packed bed liquid desiccant dehumidifier to reduce pressure-drop and carryover

In response to the high air-pressure drop and desiccant carryover experienced in liquid desiccant-packed bed dehumidifiers, which adversely affect the room environment and system economics, this study explored various modified wire-mesh packed bed designs. It experimentally evaluated dehumidification efficiency, and thermal performance across different corrugated wire-mesh packings, introducing a new design for cost-effective moisture removal while reducing pressure drop and desiccant carryover. Three specially designed packings (P-1, P-2, and P-3) were tested against standard commercial options like Celdek (7090, 6090, 5090) and Mellapak 250Y, focusing on optimizing performance. At a constant optimal concentration of the desiccant solution, the effects of airflow rates (ma), solution flow rates (ms), and solution temperatures (Ts) on the performance of the system was analyzed. The findings indicated that P-1 performed better than others, particularly in terms of condensation rate (CR) and moisture effectiveness (εm). Specifically, it outperformed the acrylonitrile butadiene styrene (ABS) (benchmark) packing by 22.1 % and 8 % respectively at a solution concentration of 40 wt% and ma of 0.025 kg/s under ambient conditions of nearly 0.02921 kg/kg specific humidity and 31 °C temperature. Increasing the void fraction led to a reduction in air pressure drop while enhancing the wettability, and dehumidification efficiency. The packing, P-1, made of stainless steel (SS340) with 0.3 cm mesh was finally proposed to obtain better performance for dehumidification applications in buildings. Additionally, its potential to reduce air-pressure drop and desiccant carry-over can provide improved energy efficiency and enhanced air quality, making it a practical choice for sustainable building cooling solutions.

Discrete element method model of soot aggregates.

Soot aerosols emitted during combustion can affect climate by scattering and absorbing the sunlight. Individual soot particles are fractal aggregates composed of elemental carbon. In the atmosphere, these aggregates acquire coatings by condensation and coagulation, resulting in significant compaction of the aggregates that changes the direct climate forcing of soot. Currently, no models exist to rigorously describe the process of soot restructuring, reducing prediction accuracy of atmospheric aerosol models. We develop a discrete element method contact model to simulate restructuring of fractal soot aggregates, represented as assemblies of spheres joined by cohesion and by sintered necks. The model is parametrized based on atomic force spectroscopy data and is used to simulate soot restructuring, showing that the fraction of necks in aggregates determines the restructuring pathway. Aggregates with fewer necks undergo local compaction, while aggregates with nearly full necking prefer global compaction. Additionally, full compaction occurs within tens of nanoseconds, orders of magnitude faster than the timescale of soot aging through condensation. An important implication is that the rate of condensation determines how many necks are fractured simultaneously, affecting the restructuring pathway, e.g., producing more compact soot at lower condensation rates than at faster condensation rates for comparable amounts of condensate formed on soot.

CFD Modeling of Film Condensation from a Steam-Air Mixture in Vertical Channels

Steam condensation in the presence of a noncondensable gas is of vital importance for passive cooling containment systems. The noncondensable gas causes a significant reduction in the condensation rate and heat transfer across the containment, which is important for postulated loss-of-coolant accidents in a nuclear reactor. In this work, computational fluid dynamics models of condensation and the adjacent single-phase steam-air mixture flow are developed for laminar and turbulent flow in vertical channels by two distinct wall condensation modeling approaches using the commercial code STAR-CCM+. The first is the fluid film model available in STAR-CCM+, which solves liquid layer governing equations with connections to the adjacent gas mixture flow. The second is a user-defined wall condensation model that neglects the fluid film and instead accounts for mass, momentum, and heat transfer via user-defined volumetric sink terms adjacent to the cold wall. The condensation models are assessed by first comparing the calculated results with the numerical solution of laminar flow, solved using a complete two-phase model that solves parabolic equations based on conservation of mass, momentum, energy, and species for each phase. Next, the results of a two-dimensional analysis are compared with COPAIN experiments and existing numerical solutions from three-dimensional analyses. The comparisons include new, detailed results that have not been reported in previous analyses of a COPAIN case. These new results include local field profiles of velocity, temperature, and air mass fraction, and local mass flux.

Controlled fabrication of hierarchical porous carbon nanospheres with high doped nitrogen content for high-performance adsorbent of biomacromolecule

Constructing nitrogen-doped porous carbons with high specific surface area, rapid mass transfer channels, and positive charge is a crucial requirement for high-performance adsorbents. Herein, by the kinetic self-assembly synthesis strategy, we prepared nitrogen-doped hierarchical porous carbon spheres (N-HPCS) with adjustable pore structure, high specific surface area, and high nitrogen doping content (8.88 %). By using ethylenediamine as an assisted polymerization and assembly agent, the hydrolysis and condensation rate of tetraethyl orthosilicate (TEOS) as the silica source and the condensation rate of 3-aminophenol and formaldehyde as the phenolic resin precursor were controlled by adjusting ammonia volume as the alkaline catalyst to tune kinetic self-assembly of silica and phenolic resin components, thus achieving their simultaneous or sequential nucleus and growth. After carbonization and selective silica etching, three types of carbon nanospheres with center-radial pores, hollow center-radial pores and hollow structure were obtained. High nitrogen doping content endowed the nanospheres with positive charge. Through adsorption experiments on the bovine serum albumin (BSA) and Hemoglobin (Hb) as typical biological macromolecules, hollow carbon nanospheres with center-radial pores exhibited excellent adsorption performance for BSA(622.34 mg g−1) and Hb(759.96 mg g−1). Our fabricated N-HPCS may become a potential candidate for high-performance adsorption materials.

Removal of moisture from air by cooling method

Moisture removal from air is a critical aspect of climate control in various industrial and residential applications. The cooling method, which relies on the condensation of water vapor by lowering air temperature below its dew point, is one of the most commonly used techniques for dehumidification. This study investigates the principles, effectiveness, and limitations of the cooling method in different environmental conditions. By examining the impact of factors such as ambient temperature, humidity levels, and cooling system design, this research aims to identify strategies for optimizing energy efficiency in dehumidification processes. Experimental results highlight the correlation between cooling temperature and condensation rates, emphasizing the need for advanced cooling technologies to reduce energy consumption. The findings contribute to the development of more sustainable and cost-effective dehumidification systems, offering valuable insights for enhancing HVAC performance and reducing environmental impact.

3D numerical investigation of bubble upflow condensation behaviors during subcooled flow boiling in mini-channel with VOSET

In the subcooled flow boiling process, bubble condensation is an inevitable basic phenomenon. This paper studies the condensation phenomenon of the single, double vertical/horizontal saturated bubbles rising in a three-dimensional mini-rectangular channel based on the interface capture method VOSET (coupled volume-of-fluid and level set method) and the phase transition model. Bubble condensation behaviors are investigated at different initial diameters, inlet velocity distributions, subcooling temperatures, bubble gaps, and arrangement for the two-bubble condensing system especially. The effects of these parametric on bubble motion trajectory, shape evolution, volume variation, and condensation rate are presented. The numerical results indicated that the initial bubble size and liquid subcooling play an important role in influencing the shape and volume variation of condensing bubble behaviors significantly, while the inlet velocity distribution only affects bubble motion trajectory. Furthermore, the interaction and coalescence between the bubbles will affect the bubble behaviors and the condensation rate. Finally, the condensation heat transfer coefficients at the bubble surfaces for different cases simulated in this paper are presented, seemingly first in the literature.

ExoLyn: A golden mean approach to multispecies cloud modeling in atmospheric retrieval

Clouds are ubiquitous in exoplanets' atmospheres and play an important role in setting the opacity and chemical inventory of the atmosphere. Understanding clouds is a critical step in interpreting exoplanets' spectroscopic data. The aim is to model the multispecies nature of clouds in atmospheric retrieval studies. To this end, we developed -- a 1D cloud model that balances physical consistency with computational efficiency. solves the transport equation of cloud particles and vapor under cloud condensation rates that are self-consistently calculated from thermodynamics. is a standalone, open source package capable of being combined with optool to calculate solid opacities and with petitRADTRANS to generate transmission or emission spectra. With we find that the compositional structure of clouds in hot Jupiter planets' atmospheres is layered with a cloud dominated by magnesiumsilicates on top of an iron cloud. This finding is consistent with more complex cloud formation models but can be obtained with in only a few seconds. The composition of the cloud particles can be constrained from the spectrum, for example MgSiO3 and Mg2SiO4 components give rise to an absorption feature at $8-10\ m $. We investigate the dependence of the cloud structure on the bulk elemental composition of the planet and find that SiO2 -dominated clouds form on metal-rich planets and Fe clouds with a strong extinction effect form on C-rich planets. Designed toward maximum flexibility can also be used in retrieval analysis of sub-Neptunes and self-luminous planets. The efficiency of opens the possibility of joint retrieval of exoplanets' gas and cloud components.

Optimizing cord pyramid solar distillers: A comprehensive study on square baffles, reflectors, and phase transition materials

Limited access to safe drinking water is a critical global issue, particularly in areas with inadequate infrastructure. Solar stills offer a promising alternative for such regions. This study investigates the influence of square baffles within a modified solar still design on its overall efficiency. Additionally, the integration of reflectors is explored to enhance both evaporation and condensation rates. Furthermore, the effectiveness of a paraffin wax phase change material (PCM) combined with silver nanoparticles is assessed within the modified still. Thermo-economic analyses are conducted to evaluate the economic feasibility of the proposed system. The findings demonstrate a significant improvement in distillation yield. The modified still with square baffles achieved a yield of 9800 mL/m2.day compared to 3550 mL/m2.day for the reference still, representing a 193 % increase. Moreover, incorporating the nano-PCM at an optimal configuration (25 cords) resulted in a further 265 % productivity increase for the modified still with both square baffles and reflectors. This configuration also achieved an efficiency of 63 %. Economic analysis revealed a minimal cost difference between the reference still (0.014 $/L) and the modified still with square baffles and nano-PCM (0.01 $/L). In terms of environmental impact, the modified still exhibited a lower annual CO2 emission of 28.8 tons.

Thermodynamic and Condensation Rate Modeling in Abandoned Wells: Assessing Potential Corrosion Risks in CCS Applications

Summary Carbon capture and storage (CCS) is considered one of the most suitable solution strategies for decarbonization in energy-intensive industries. While the examples of commercial-scale CCS projects are steadily growing worldwide, monitoring and success of such projects require mitigating several risks at the field scale. One of the challenges lies in assessing wellbore integrity issues in nearby abandoned wells, where wellbore corrosion caused by the condensation of acidic gases could be a potential integrity hazard. In this work, we develop a modeling framework to assess this issue by analyzing the underlying physical process of acid gas condensation through thermodynamics and heat transfer models to predict the acid gas condensation rates. We assess the effects of reservoir conditions of salinity, temperatures, and pressures on the resulting condensation rates, pH of the condensed liquid, and semi-empirically derived corrosion rates (CRs) across the well height. The study highlights the need to develop an assessment framework to identify and assess such integrity risks at an early stage for CCS projects.

Thermal-hydraulic analysis of wetted airside plain fin flat tube heat exchangers and the role of vortex generators

This study addresses the demand for efficient and compact heat exchange solutions in industrial applications. Unlike previous studies that predominantly focused on round tube configurations, this research investigates the impact of vortex generators and geometrical parameters on plain-fin flat-tube designs. Using ANSYS Fluent, the study evaluated the effects of fin geometry, vortex generators, and flow conditions on thermal–hydraulic performance. The key findings revealed that vortex generators enhanced heat transfer by 5–48% by promoting fluid mixing and turbulence but also leading to an increment in friction losses reaching 35–62%, depending upon the number of vortex generators. Condensation rates increased downstream of vortex generators due to enhanced mixing with cooler surfaces. In terms of thermal–hydraulic performance, specific plain-fin configurations outperformed others, offering efficient heat transfer with relatively lower friction losses, even when compactness was considered. Some configurations were recommended for applications where heat exchanger size is less important, but high heat transfer is crucial. Lastly, it was discovered that the effect of vortex generators is more pronounced for lower to intermediate pumping powers per unit area. New empirical correlations were also derived to predict thermal–hydraulic behavior based on geometry and vortex generator placement. A comparison with the literature revealed significantly higher performance as compared to convex/concave vortex generators. Lastly, it was discovered that the effect of vortex generators is more pronounced for lower to intermediate pumping powers per unit area. Empirical correlations for “j” and “f” were correlated with all geometric parameters.

Enhancing conical solar still performance using high conductive hollow cylindrical copper fins embedded by PCM

The present study aims to enhance the efficiency of the conical solar distiller in producing water during both day and night. This will be achieved through design enhancements, such as increasing the surface area of the distiller to maximize solar energy absorption and improve condensation rates. High thermal-conductivity cylindrical fins have been used, and their role will be investigated. These fins may be hollow and extended, with or without the inclusion of phase change material (PCM). Consequently, copper tubes are positioned at the base of the distiller basin, both with and without the inclusion of phase-changing paraffin wax material inside the hollow tubes. A comparison is made between the performance of three configurations: the first configuration is traditional, the second configuration includes fins without the incorporation of PCM, and the third configuration includes PCM-based fins. This comparison is crucial as it provides a clear understanding of the impact of each design enhancement on the distiller’s performance. The study findings indicated that the arrangement with hollow fins filled with PCM had the highest level of freshwater output. Furthermore, the results showed that the combined output of conical solar distillers equipped with fins made of copper tubes, both with and without PCM, were 7.50 and 6.75 L/m2/day, respectively. The cumulative production of conventional conical distillers is 4.85 L/m2/day. Freshwater output improved by 54.64 and 39.17 % when using hollow copper tubes with and without PCM within 24 h, compared with the conventional configuration. During night-time hours, it was observed that the freshwater output of distilled water from salt water significantly improved by 550 % when utilizing copper tubes loaded with PCM, compared to distillation using empty copper tubes. The maximum daily efficiency of conical distillers with fins with and without PCM were 73.6 % and 80.3 %, respectively. These results showed that conical distillers using copper tubes hollow filled with PCM represent good options for obtaining higher performance than distillation.

A unifying bubble-layer-based theoretical model for flow boiling and application to a rod bundle

Current analyses of flow boiling primarily utilize two−/three-dimensional numerical simulations or one-dimensional empirical correlations/models. To develop a quasi-two-dimensional theoretical model, a unifying bubble-layer-based theoretical model is proposed, which can be applicable to the entire flow boiling process, from the single-phase liquid flow to the dryout point. This model considers bubble behaviors in each region and heat and mass transfer at the interfaces of two regions, consisting of conservation equations of mass, momentum, and energy, supplemented by a few empirical correlations. A sensitivity analysis of these correlations is conducted, revealing that the slip ratio correlation and bubble condensation rate correlation have the most significant impacts. Using experimental data on void fraction, the most accurate combination of empirical correlations is identified, with a total absolute error of 27.9 %. The verification ranges are 0.1-8Mpa for pressure, 182-1700 kW/m2 for heat flux, 240-2200 kg/m2s for mass flux, 0.83–1.76 for Prandtl number, and 4.4e3–2.98e5 for Reynold number. Finally, this model is applied to the analysis of the NHR200-II rod bundle, revealing the variations of several two-phase parameters under micro-boiling conditions and the influence of operating conditions on the length proportion of different flow sections, serving as important references for analyzing the impact of boiling on reactor reactivity.

Efficient Fog-Harvesting Origami Fan.

Fog harvesting represents a promising strategy to address the global freshwater shortage. To enhance the water collection efficiency, diverse geometric structures that can effectively drive water droplet movement are essential. Inspired by the Livistona chinensis leaf, which naturally facilitates directional droplet motion through its unique gradually varying V-groove structure, we have developed a novel origami fan structure for fog harvesting through theoretical analysis. A key feature is that we can modulate the speed of droplet transport by adjusting the opening angle of the V-shaped grooves positioned at the outer circumference. Interestingly, the water collection efficiency exhibits a linear correlation with the opening angle. The highest efficiency of the origami fan can reach 5.75 times that of the control group calculated by the projected area and 3.76 times that of the control group calculated by the real area, showcasing its significant potential for enhancing water collection from fog. The simulations demonstrate that the hollow structure enhances the condensation rate of droplets, the geometric gradient of the gradual-variation V-groove drives the condensed droplets to move rapidly on the surface, and the Janus membrane permits the aggregated droplets to transit to the fan's rear side. The synergistic action of these three components ensures a clean surface for the subsequent water-collecting cycle, contributing to the high fog-harvesting efficiency. Given its simple fabrication and superior water transfer efficiency, the origami fan holds substantial promise for widespread application in the field of droplet manipulation.

Experimental investigation of the swirling steam jet condensation at low mass flux

Swirling steam jet condensation holds significant applications in industrial processes such as nuclear safety and gas–liquid mixing in the oxygen transmission pipeline of the liquid rocket engine. However, due to its involvement with complex flow and phase-change heat transfer, the application and optimization of related condensation technologies still face challenges. Therefore, this paper aims to investigate the condensation characteristics of the swirling steam jet by numerous experiments. The steam mass flux is 15–45 kg/(m2·s), and the water temperature ranges from 40 to 85 °C. A novel X-type swirl pressure nozzle is selected to achieve the swirling flow of the steam jet. A comparative analysis is conducted on the interface behavior and evolution of condensation parameters of the non-swirling and swirling steam jets during condensation processes. Results show that the swirling jet condensation includes three flow patterns, namely, chugging regime, smooth grown bubble regime, and rough grown bubble regime. Compared with the non-swirling steam jet condensation, swirling steam jets exhibit a 10.36% increase in the smooth grown bubble regime region and a 14.63% decrease in the rough grown bubble regime. Swirling bubble morphology evolves steadily, and the surface is smoother and more rounded. Simultaneously, irregular deformation behaviors can also occur in the swirling bubble condensation process, such as spiral growth of jet bulge, neck torsion, and the corolla pattern. This deformation helps to increase the contact area and prolongs the bubble lifetime, allowing for more adequate heat transfer at the steam–water interface. The swirling motion of the steam jet will reduce the bubble collapse frequency. As the water temperature rises from 60 to 80 °C, the bubble condensation rate and collapse frequency decrease. The bubble radius increases and the condensation time is extended. With the increasing steam mass flux, the collapse frequency gradually increases. The condensation rate and the bubble radius vary nonlinearly. At the higher steam mass flux, the swirling motion can effectively release the heat that accumulates inside the bubble after reaching the condensation equilibrium state.

On the non-linearity of rheological film condensation

Condensation of non-Newtonian fluids is a less explored research field but has tremendous potential in the industry. We propose a mathematical theory to model the behaviour of non-Newtonian film condensation on vertical surfaces. The simple theory can contribute to understanding the operation of many engineering appliances using motor oils, polymeric liquids, and fuels. The well-known power-law model approximates the viscosity of condensate. We vary the power-law index (n) within 0.8≤n≤1.2 to encompass the behaviour of shear-thinning, Newtonian and shear-thickening films, while the flow consistency index (μ0) remains constant throughout the study. Since the film flow is gravity-driven, stream-wise advection is expected to dominate over cross-stream advection. We, however, establish the subtle role of cross-stream advection within the thin condensate film. We have identified a thinner film, a lower condensate drainage rate and a greater average heat transfer coefficient (hm) as an influence of the cross-stream advection. An exclusion of cross-stream advection transforms temperature distribution across the film from non-linear to linear. The linear temperature distribution is unrealistic for Ja≥0.5. We illustrate approximately 5% error incurred for neglecting cross-stream advection in estimating hm at Ja=0.81 and n=0.8. The error increases with a further decrease in n values or an increase in the Ja. The exclusion of cross-stream advection affects the film-thickness and average heat transfer disproportionately in shear-thinning and shear-thickening regimes. Finally, we propose mathematical expressions to estimate heat transfer coefficient and Nusselt number, which would be helpful for field engineers.