Flow Fluctuations Research Articles

A three-directional stress-strain model-based physics-embedded prediction framework for metal tube full-bent cross-sectional characteristics

A metal tube system is known as the industrial blood vessel, among which the bent section is the most vulnerable part. The cross-sectional defects (CSDs) of the bent tube cause the flow fluctuation of the fluid inside the tube. The existing defect characterization methods are roughly presented by describing CSDs in some specific cross-sections, which results in the lack of the tube full-bent section (FBS) characteristic information. To comprehensively describe and predict the tube FBS characteristics, an advanced physics-embedded CSDs prediction framework is proposed. This framework includes an FBS-neutral layer displacement angle (NLDA) prediction module and an FBS-CSDs prediction module, which uses the method that integrates the analytical model and BiLSTM-based deep learning (DL) models to predict the CSDs in the FBS of the tube. A novel analytical model of CSDs that considers both three-directional stresses and strains during tube bending is embedded in the FBS-CSDs prediction module. The analytical model provides the initial predicted values of CSDs through the NLDA sequence obtained from the FBS-NLDA module. The inaccurate CSDs are then treated as physical information to be fed into DL models for further correction and prediction. The prediction performance of this framework is validated through numerical simulations and experiments. The results prove that the framework can accurately predict the CSDs in the tube FBS. The integration of DL models with the analytical model not only overcomes the limitations of the analytical model, but also improves the prediction accuracy and convergence speed of DL models.

Speed Strategy on High-Pressure Compressor for the Charging Process of Advanced Adiabatic Compressed Air Energy Storage During Dynamic Shutdown

Abstract Advanced adiabatic compressed air energy storage (AA-CAES) starts and shuts down frequently. A detailed charging process comprising three series of centrifugal compressors with intercoolers was constructed within the framework of UniSim® Design. The safety measures were meticulously considered by integrating anti-surge circuits, vent valves, and check valves. PI controllers were allocated to the primary component to govern the shutdown procedure. The speed strategy of the HP inverter motor during the load shedding stage is the focus of research. Six speed strategies, including decreasing speed, constant speed, and increasing speed, were discussed, respectively. The discussion focused on changes made to air injection, inlet mass flow of the HP, inlet and outlet pressure of both the middle-pressure compressor (MP) and HP, and energy efficiency. The study found that implementing the minimum allowable speed for the inverter motor speed (IMS) and increasing speed during the load shedding stage can cause fluctuations in the air injection. As IMS increases at the end of the load shedding stage, the pressure anomalies at the MP outlet and the HP inlet weaken, and the shutdown process's energy efficiency improves. The HP inlet flow fluctuations caused by various strategies were within an acceptable range. This study reveals that there is a mutual influence between components in the charging process of AA-CAES. An appropriate speed strategy for the HP inverter motor can mitigate the operational hazards. The results of this study can provide guidance for similar AA-CAES shutdowns.

River Flashiness in Great Britain: A Spatio-Temporal Analysis

Flashiness refers to the rapidity and frequency of fluctuations in river flow. It can provide insights into flooding, by capturing dramatic increases in river flow, as well as contaminant transport, relating to concentrations of diffuse pollution. Despite a very well gauged river system, there is limited research in Great Britain targeting this component of river flow. This study addresses that gap in knowledge, with a detailed spatio-temporal analysis of river flashiness in Great Britain. Using 513 gauging stations, with historical records of at least 30 years, the average Richards–Baker flashiness index (RBI¯) was calculated for 1990–2020, showing an overall west- (0.6–0.8) to east-coast (0.1–0.2) gradient, being higher in the west (with the exception of some gauges in the south-east). Employing random forest models, the main predictor for flashiness was found to be soil composition, with some additional region-specific predictors. These include flood attenuation by reservoirs and catchment areas, affecting flashiness in the north and west of Great Britain. Additionally, using a subset of 208 gauging stations with data recorded from 1970 to 2020, a temporal analysis examined significant breakpoints and/or trends in yearly flashiness, using the Pettitt test and Mann–Kendall trend test, respectively. Increases in flashiness were found mainly in the north-east and south-west of Great Britain, with implications in flooding and river health. On a seasonal scale, and using a monthly RBI¯, the timing of flashy events was found to oscillate between autumn and spring over the 50 years, gravitating around winter.

On flow fluctuations in ruptured and unruptured intracranial aneurysms: resolved numerical study

Flow fluctuations have emerged as a promising hemodynamic metric for understanding of hemodynamics in intracranial aneurysms. Several investigations have reported flow instabilities using numerical tools. In this study, the occurrence of flow fluctuations is investigated using either Newtonian or non-Newtonian fluid models in five patient-specific intracranial aneurysms using high-resolution lattice Boltzmann simulation methods. Flow instabilities are quantified by computing power spectral density, proper orthogonal decomposition, and fluctuating kinetic energy of velocity fluctuations. Our simulations reveal substantial flow instabilities in two of the ruptured aneurysms, where the pulsatile inflow through the neck leads to hydrodynamic instability, particularly around the rupture position, throughout the entire cardiac cycle. In other monitoring points, the flow instability is primarily observed during the deceleration phase; typically, the fluctuations begin just after peak systole, gradually decay, and the flow returns to its original, laminar pulsatile state during diastole. Additionally, we assess the rheological impact on flow dynamics. The disparity between Newtonian and non-Newtonian outcomes remains minimal in unruptured aneurysms, with less than a 5% difference in key metrics. However, in ruptured cases, adopting a non-Newtonian model yields a substantial increase in the fluctuations within the aneurysm sac, with up to a 30% higher fluctuating kinetic energy compared to the Newtonian model. The study highlights the importance of using appropriate high-resolution simulations and non-Newtonian models to capture flow fluctuation characteristics that may be critical for assessing aneurysm rupture risk.

Mechanistic insights into how mixing factors govern polyelectrolyte-surfactant complexation in RNA lipid nanoparticle formulation

Hypothesis: Lipid nanoparticle self-assembly is a complex process that relies on ion pairing between nucleic acids and hydrophobic cationic lipid counterions for encapsulation. The chemical factors influencing this process, such as formulation composition, have been the focus of recent research. However, the physical factors, particularly the mixing protocol, which directly modulates these chemical factors, have yet to be mechanistically examined using a reproducible mixing platform comparable to the industry standard. We here utilize Flash NanoPrecipitation (FNP), a scalable rapid mixing platform, to isolate and systematically investigate how mixing factors influence this complexation step, first by using a model polyelectrolyte-surfactant system and then generalizing to a typical RNA lipid nanoparticle formulation.Experiments: Aqueous polystyrene sulfonate (PSS) and cetrimonium bromide (CTAB) solutions are rapidly homogenized using reproducible FNP mixing and controlled flow rates at different stoichiometric ratios and total solids concentrations to form polyelectrolyte-surfactant complexes (PESCs). Then, key mixing factors such as total flow rate, inlet stream relative volumetric flow rate, and magnitude of flow fluctuation are studied using both this PESC system and an RNA lipid nanoparticle formulation.Findings: Fluctuations in flow as low as ± 5 % of the total flow rate are found to severely compromise PESC formation. This result is replicated in the RNA lipid nanoparticle system, which exhibited significant differences in size (132.7 nm vs. 75.6 nm) and RNA encapsulation efficiency (34.0 % vs. 82.8 %) under fluctuating vs. steady flow. We explain these results in light of the chemical variables isolated and studied; slow or nonuniform mixing generates localized concentration gradients that disrupt the balance between the hydrophobic and electrostatic forces that drive complex formation. These experiments contribute to our understanding of the complexation stage of lipid nanoparticle formation and provide practical insights into the importance of developing controlled mixing protocols in industry.

A traffic-weather generative adversarial network for traffic flow prediction for road networks under bad weather

Traffic flow prediction is pivotal in providing reliable information for intelligent traffic systems. Unexpected events, such as bad weather, unavoidably impact the precision of traffic flow prediction. Therefore, to achieve accurate traffic flow prediction results in road networks under bad weather, a novel Traffic-Weather Generative Adversarial Network (TWeather-GAN model) is developed. This model comprises a Generator and a Discriminator. The Generator incorporates both the traffic and weather modules to extract the spatiotemporal patterns hidden in traffic flow and weather data. In the traffic and weather modules, the gated convolutional layer, Encoder-Decoder architecture, and attention mechanism are established. In the Discriminator, the gated convolutional layer and bidirectional long short-term memory neural network are introduced. Traffic flow data under fog, strong wind, and heavy rain are selected to test the seven baseline models and the proposed model, and the ablation experiments are conducted to analyze the mechanism of the proposed model. The experiments demonstrate that the TWeather-GAN model outperforms the baseline models under bad weather, and makes the prediction error have an average reduction of 0.20%–34.81%, 3.21%–35.22%, and 9.46%–39.10%, respectively, under one-step prediction, three-step prediction, and six-step prediction. Furthermore, establishing the gated convolutional layer and the weather module enhances the accuracy of traffic flow prediction under bad weather. Results show that traffic flow fluctuations and distributions differ under fog and strong wind, and heavy rain affects the trend of traffic flow over one day.

Research on positioning control strategy of hydraulic support pushing system based on multistage speed control valve

The precise position control of the hydraulic support pushing system in the coal mining face is a key technical support for intelligent coal mining. At present, the hydraulic support pushing system uses the electro-hydraulic directional valve as the control element. However, the electro-hydraulic directional valve has problems such as discrete input values, low switching frequency, delay, inability to adjust flow, and large flow fluctuations during the switching process, which results in relatively low positioning control accuracy of the hydraulic support pushing system. Therefore, this study introduces a multi-stage speed control valve that is suitable for underground coal mine conditions and can achieve flow regulation. At the same time, a segmented control strategy combining Bang-Bang control and online predictive control is proposed. Bang-bang control is used for fast propulsion with large flow rate, large range, and short time. Online predictive control method is used to achieve precise positioning control with small flow rate and small range, thereby solving the problem of low positioning control accuracy caused by the imperfect characteristics of electro-hydraulic directional valves. Finally, this study verified the effectiveness of the proposed scheme through simulation and experiments. The results showed that compared with existing logic positioning control methods based on electro-hydraulic directional valves, the proposed scheme can improve the accuracy of single cylinder positioning control from 62 mm to within 10 mm.

Analysis and identification of gas-liquid two-phase flow pattern based on multivariate multi-scale dispersion entropy and interconnected dispersion pattern complex network

Gas-liquid two-phase flow is polymorphic and unstable. The investigation of the flow behavior of two-phase flow is vital for the application of gas-liquid transport in ocean engineering areas. We propose an analytical framework that combines multivariate multi-scale dispersion entropy (mvMDE) and interconnected dispersion pattern complex networks (IDPCN) for flow patterns. The resistance sensor array is used to capture the two-phase flow fluctuation signals in the riser, and the dimensionally reduced time series are nonlinearly mapped into a multivariate symbolic sequence. The mvMDE of the multivariate symbolic sequence is computed to measure the complexity of the flow pattern signals at the level of amplitude variation. In addition, a new multis-cale complex network based on the symbolic sequence is proposed to study the pseudo spatial coupling behavior of flow patterns. The evolution of the flow pattern from bubble to churn flow is quantitatively characterized using the mean value of the complex network indices in the optimal scale range. Finally, we construct the joint plane of mvMDE and two network indices to complete flow pattern identification. The research results show that the framework can effectively fuse multi-channel flow pattern information at different time scales to reveal the evolution mechanism of gas-liquid two-phase flow.

Inventory of Pollution Sources for The Lakes of Universiti Tun Hussein Onn Malaysia

Eutrophication affects freshwater systems worldwide. Eutrophication can occur naturally, but man-made causes are also common. Human activities that release phosphorus and nitrogen lead to anthropogenic eutrophication, which increases organic matter production. Lake eutrophication affects surface waters all over the world. Water pollution can be assessed regarding point sources (PS) and non-point sources (NPS). PS is the intentional or unintentional release of pollutants from industrial and wastewater facilities into waterways. Agriculture, urban development, and natural processes in the lake's catchment area can cause NPS pollution. NPS pollution has many causes, including precipitation, airborne deposition, infiltration, drainage, and fluctuations in water flow in the catchment. The pollution inventory was conducted in UTHM lakes such as Tasik Kemajuan, Tasik Teknologi (FKAAB), Tasik Teknologi (FPTV), and Tasik Pembangunan. The PS and NPS in the study area were assessed through an on-site investigation. The UTHM water discharge plan is being analyzed to determine the inflow sources into the lake. The PS pollutant inventory revealed that the cafeteria wastewater, business buildings, and faculty drainage systems pollute all lakes. Tasik Teknologi (FPTV) identified runoff from palm oil plantations as a source of pollutants that can increase the nutrient content of the lake. Leaves, grass clippings, and other garden waste were in the water in all the lakes analysed. The Tasik Kemajuan, the Tasik Teknologi (FKAAB), and the Tasik Teknologi (FPTV) received water discharges from other lakes transporting pollutants. The assessment of pollutant sources revealed that most NPS originate from surface runoff. Road runoff contains several pollutants. Stormwater runoff or surface runoff can carry these pollutants from roads into waterways. Stormwater washes fertilizers into storm drains and lakes. To summarise, all pollutant sources that contributed to the eutrophication of the Tasik Kemajuan, Tasik Teknologi (FKAAB), Tasik Teknologi (FPTV), and Tasik Pembangunan were identified through a pollutant source inventory.

Assessing the performance of three experimental methods to investigate air path inside wall assemblies

Air leakages in buildings’ envelopes can lead to an over-consumption of energy and to additional issues such as moisture damage and poor indoor environment. The leakage air flow rate is usually assessed at the building scale using a pressurization test and leakage locations are commonly detected by infrared thermography or smoke. However, little is known about the air paths within wall assemblies, despite the need for detailed experimental data to validate numerical models for the coupled heat, moisture and pollutants transfers. One of the reasons is the difficulty to find adapted and robust experimental methods.In this paper, three experimental laboratory approaches are tested on simple light-wall assembly configurations: the implementation of three-dimensional grids of thermocouples and relative humidity sensors within the wall, and the use of a micro-particle tracer. The results are compared with each other as well as with numerical simulations.It was found that thermocouple grid has limited intrusiveness, good accuracy and response time but results are subject to flow fluctuations. Moreover, heat capacity and conductive transfer within materials complicate the correlation between heat and air transfers. Humidity sensors grid avoids the latter issue but is intrusive, overestimating air dispersion. The micro-particle tracer has the advantage of being non-intrusive and less impacted by flow fluctuations but its ability to track the air flow is strongly linked with the insulation filtration properties and the flow velocity. Overall this method seems to provide the best results but it is also the most complex and time-consuming one.

Efficient nitrogen removal of decentralized rural sewage: Pilot-scale study of a novel push-flow coupled bio-ecological system

The performance and mechanisms for pollutant removal were investigated in an extended pilot-scale operation. Results demonstrated that the PF-EFB system maintained stable and efficient performance after over 450 days of continuous operation. Under various operating conditions, the total nitrogen (TN) concentration was reduced to <2 mg/L, and the removal rate exceeded 90 %. The effluent chemical oxygen demand (COD) concentration remained below 40 mg/L. Additionally, a combination of nitrogen transformation and molecular biology analyses was conducted to explore the mechanisms. The key bacterial groups driving system performance were aerobic and anoxic nitrifying bacteria, which dominated the microbial population. Microbial community analysis showed that the abundance of aerobic denitrifying bacteria in the middle of the system was 40.5 %, while the abundance of anoxic denitrifying bacteria at the end was 19.0 %. This spatial variation in the distribution of aerobic and anoxic denitrifying bacteria along the flow direction inside the reactor, driven by environmental factors, is key to the system's efficient denitrification. Overall, the PF-EFB system effectively addressed challenges posed by water flow fluctuations and enhanced nitrogen removal efficiency. This innovative system offers significant benefits and serves as a valuable reference for rural sewage treatment.

Numerical simulation study of the influence of stirred vessel structure on particle suspension characteristics in dilute solutions

The Euler-Euler/RANS approach has been used to simulate the particle suspension in solid–liquid stirred vessels, with experimental validation conducted through the Electrical Sensing Zone Method (ESZ). An innovative evaluation method has been introduced to quantify the critical impeller speed Nc required for particles to achieve a specific uniform suspension state in dilute solutions. The impact of different vessel bottom shapes (flat, round, and W-shaped) on particle suspension characteristics is examined. The results indicate that optimizing the bottom shape to align with flow streamlines markedly enhances particle suspension, a conclusion supported by the Online Micro-sized Particle Analyzer (OMiPA). Further analysis shows baffle configurations transform the tangential and radial velocities into the axial velocity, which is not conducive to providing initial conditions for particle suspension but improves overall suspension uniformity. Overall, effective particle suspension relies on the interaction between main flow and turbulent fluctuations, with tangential and radial flows playing critical roles.

Unsteady measurement in a transonic axial compressor with optimized axial slot casing treatment

Casing treatment has been widely adopted to enhance the operating range of compressors by extending the stall margin. In this article, a high-precision experimental investigation was conducted in a transonic compressor. Unsteady pressure is measured in the casing wall using a cluster of time-resolved transducers with axial and circumferential spatial resolution. The experimental data show that the optimized axial slot casing treatment improves the stall margin without peak efficiency penalty for all measured speedlines. A comprehensive flow field analysis indicates that the surge boundary of transonic compressor is sensitive to the position of shock wave and tip leakage flow. After the application of optimized axial slot casing treatment, the flow structure can be significantly modified, which specifically manifests as both the mitigation in shock wave detachment and redistribution of tip leakage flow trajectory toward the trailing edge of the blade. Furthermore, power spectral density analysis is conducted to examine the unsteady effect. The amplitude of characteristic frequency band induced by the unsteady fluctuation of tip leakage flow and shock wave is considerably suppressed, which can also be regard as the stability enhancement mechanism of casing treatment.

The randomness and determinacy of wall pressure fluctuations in incompressible flow

Wall pressure fluctuations caused by turbulent boundary layers have a significant impact on aircraft structural vibration and cabin noise. This study aims to investigate the mechanism of turbulence-induced pressure fluctuations by focusing on the randomness of wall pressure fluctuations, analyzed in both the time–frequency and spatial-wavenumber domains using measured data obtained from a phase array in a wind tunnel. Three roughness elements were designed and installed upstream of the plate to manipulate the turbulent boundary layer at a specific Mach number. The results of the investigation demonstrate that the disturbance strength induced by the roughness element influences the randomness of wall pressure fluctuations, in addition to the parameters utilized for data analysis. Generally, stronger turbulence fluctuations tend to decrease the randomness of pressure fluctuations. Moreover, wall pressure fluctuations also exhibit certain statistical principles that cannot be precisely calculated using mathematical expressions, highlighting their inherent randomness. Further investigation into randomness in the spatial-wavenumber domain revealed the hydrodynamic modes of turbulence fluctuations with varying convection velocity analyzed through wavenumber maps computed using the beamforming algorithm. These modes with variable convective speed significantly contribute to the generation of randomness in wall pressure fluctuations. Both the time–frequency domain and the spatial-wavenumber domain affect the randomness characteristics of wall pressure fluctuations. However, such effects are not easily discernible through a rudimentary analysis of the space–time correlation of turbulence fluctuations.

Reducing flow fluctuation using deep reinforcement learning with a CNN-based flow feature model

Flow control and shape optimisation are fundamental problems in fluid mechanics, particularly in certain scenarios involving ocean engineering. Attempts to manage the flow field via reinforcement learning are based on newly developed deep-learning techniques. By utilising an adaptive optimisation process in the flow around two square cylinders (the main square cylinder with a smaller square cylinder in the front) for the position of the front square cylinder, the flow state that minimises the oscillation of the flow field in the wake can be obtained through deep reinforcement learning. Furthermore, as the training process for this reinforcement learning is time consuming, the flow simulation component of the process is replaced with a feature detection model based on a convolutional neural network, which effectively accelerates the training process. This approach to simulating the optimal position-finding procedure with acceleration can be extended to other similar situations and practical engineering projects.

The Effect of Covid-19 Vaccines on Menstrual cycle in selected Bangladeshi Female Population

The pandemic associated with the coronavirus disease hit Bangladesh in the year of early 2020, which was a part of the global pandemic caused by SARS-CoV-2. Six vaccines, namely Moderna, Pfizer, Covishield, Sinopharm, Sinovac and Janssen out of the eight vaccines approved by WHO, were received by the Bangladeshi people. A cross-sectional online survey comprising a descriptive questionnaire was carried out to find the effect of Covid vaccine on menstrual cycle. The longer, shorter or absence of menstrual cycles and any changes in menstrual flow were taken under consideration during the survey. The majority of the respondents (82.5%) was of 20-30 years old females. Among the total 309 responders, 210 women experienced vaccine associated side effects while fever was experienced by 36.5%, 19.1% experienced fatigue and 21.4% was reported to suffer from headache. Muscle and joint aches as well as pain, swelling and redness were noted to be 38.5% (most common) and 26.4%, respectively among others. Statistically significant (p&lt;0.01) fluctuation was observed in menstrual cycle although mostly persisting for only one cycle. About 70% of the women noted to have regular menstrual cycle before vaccination, which was decreased to 56% including about 10-14% females experiencing different fluctuation in menstrual flow. Medications taken to alleviate the vaccine-related side effects as well as to regulate normal menstrual cycle were also recorded in the survey. This study attempted to identify the impact of COVID vaccine on menstrual cycle and no significant conclusive negative effect on women's reproductive health was recorded. Bangladesh Pharmaceutical Journal 27(2): 149-157, 2024 (July)

Numerical investigation on dynamic flow characteristics of methane condensation in microchannels

Microchannel condensers play an essential role in cryogenic two-phase heat management systems due to their efficient heat transfer characteristics. Thus, it is worth conducting an in-depth study on microscale condensation characteristics of cryogenic fluids. This paper delves into the flow condensation process of methane in microchannels. A two-dimensional transient model with high accuracy for cryogenic fluids has been developed by combining a self-defined program for the source term of the phase transition model. The model fully considers the boundary layer thickness and accurately explores the mesh accuracy. The complete condensation flow patterns are captured for various vapor quality, mass flux, and wall subcooling degrees. The injection flow is a unique flow regime for condensation in microchannels. The decrease in wall subcooling degree and increase in mass flux leads to the separation point at the neck of the injected flow moving towards the exit, while the annular flow region is expanding and the flow pattern transition is lagging. The mass flux improves the heat transfer coefficient more significantly at high vapor quality. During injection and bubble flow, the wall shear stress and local heat transfer coefficient are subject to bouncing and oscillations, which may induce fluctuations in the upstream annular flow. The prediction performance of six classical heat transfer correlations is evaluated. The results indicate that the Nie et al. correlation has the highest comprehensive prediction accuracy with MRD and MARD of -5.00 % and 15.83 %, respectively.

Evaluation of the prediction capability of mesoscale CFD models on velocity fluctuations in liquid-solid flows

Mesoscale CFD models are of great importance in multiphase flow studies due to their acceptable computational cost and great numerical fidelity. However, the evaluations of mesoscale models on velocity fluctuation predictions are still limited. An evaluation of the predictive capability of current CFD models on velocity fluctuations in liquid-solid flows is presented. Numerical simulations are carried out with both the Eulerian-Eulerian Two-Fluid Model (TFM) and the Eulerian-Lagrangian Discrete Phase Model (DPM), and compared with the available experimental data. Together with the proper models in both phases, the TFM satisfactorily predicts two-phase velocity fluctuations. A diffusion-based coupling method is implemented to mitigate the grid dependency problem in the DPM. The diffusion-based coupling method greatly improves the predictive fidelity of the particle volume fraction for DPM. However, it overpredicts velocity fluctuations for both phases. Further research is required to enhance the fidelity of velocity fluctuation prediction in fluid-particle flow simulation models.

Numerical study of MHD flow over stretching cylinder with variable Prandtl number and viscous dissipation in ternary hybrid nanofluids with velocity and thermal slip conditions

Industrial applications in domains such as warm rolling, crystal development, thermal extrusion and optical fiber illustration are seeing a significant increase. These applications specifically focus on addressing the challenge of a cylinder in motion inside a fluid environment. Elevated temperatures may affect the viscosity and thermal conductivity of fluids. Understanding the relationship between temperature and the properties of fluids is crucial. In light of these presumptions, the primary goal of this study is to examine, under transverse magnetic field, shape factor, velocity, thermal slip conditions and viscous dissipation, how temperature-dependent fluid properties could enhance the heat transfer efficiency and performance evolution of ternary hybrid nanofluid. In order to study flow fluctuations, the impact of nanoparticle addition and improvements in heat transfer, a variable Prandtl number is also included. The use of similarity variables converts the controlling flow model from partial differential equations (PDEs) to ordinary differential equations (ODEs). Mathematica’s shooting strategy solves ODEs using the fourth-order Runge–Kutta (RK-IV) method. Numerical calculations were done after setting parameters to acquire the desired results. Analytical data are provided in tables and graphs for convenient usage. The results showed that the velocity profile increases as the values of [Formula: see text], Pr, M, Re and S grow, and decreases when the values of [Formula: see text] decrease. Re, Pr and S lower the temperature profile, whereas [Formula: see text], [Formula: see text] and Ec raise it. The skin friction profile steepens as [Formula: see text], S, Re and M increase relative to the stretched cylinder, and flattens as [Formula: see text] and [Formula: see text] decrease. The Nusselt number profile rises as [Formula: see text], Pr, S and Re decrease with [Formula: see text], Ec and [Formula: see text]. When the Prandtl number goes from 3.0 to 6.2 in a ternary hybrid nanofluid with brick-shaped nanoparticles, the Nusselt number goes up by around 55.7%.

SME Failures Under Large Liquidity Shocks: an Application to the Covid-19 Crisis

Abstract We study the effects of financial frictions on firm exit when firms face large liquidity shocks. We develop a simple model of firm cost-minimization, where firms’ borrowing capacity to smooth temporary shocks to liquidity is limited. In this framework, firm exit arises from the interaction between this financial friction and fluctuations in cash flow due to aggregate and sectoral changes in demand conditions, as well as more traditional shocks to productivity. To evaluate the implications of our model, we use firm level data on small and medium sized enterprises (SMEs) in 11 European countries. We confirm that our framework is consistent with official failure rates in 2017–2019, a period characterized by standard business cycle fluctuations. To capture a large liquidity shock, we apply our framework to the COVID-19 crisis. We find that, absent government support, SME failure rates would have increased by 6.01 percentage points, putting 3.1% of employment at risk. Our results also show that in the presence of financial frictions and in the absence of government support, the firms failing due to COVID have similar productivity and growth to firms that survive COVID.