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The Hadley circulation (HC) has been expanding poleward in recent decades. The Coupled Model Intercomparison Project Phase 6 (CMIP6) models predict that the expansion will accelerate in the future, more so in the Southern Hemisphere (SH). However, the extent of the expansion varies widely among the models. We investigate the mechanisms driving the intermodel spread in SH HC expansion predictions. The intermodel spread is obtained by an empirical orthogonal function analysis on the SH HC trend patterns of 16 CMIP6 model simulations using the historical and shared socioeconomic pathway 5–8.5 scenarios. The leading mode, showing a mean meridional stream function anomaly at the poleward SH HC extent, explains 49.73% of the variance and significantly correlates (r = 0.94) with the SH HC expansion. By analyzing the extended Kuo‐Eliassen equation, we find that the intermodel difference in the representation of diabatic heating is responsible for about 14% of the intermodel spread. The meridional eddy momentum and heat fluxes contribute to about 21% and 18% of the intermodel spread, respectively. The models simulating a relatively large SH HC expansion tend to show increased precipitation in the Southern Pacific Convergence Zone, reduced baroclinic instability in the subtropics, and an enhanced poleward shift of jet stream in the midlatitudes. This suggests that the uncertainty in the HC projection may be constrained by reducing the bias in the trend of the mean fields. Plain Language Summary: The Hadley circulation (HC), which affects global climate patterns, is expanding toward the poles. However, different climate models predict varying extents of this expansion, especially in the Southern Hemisphere (SH). We aim to understand why. By analyzing climate model data, we identified key factors influencing the spread in SH HC expansion. Our findings suggest that factors like diabatic heating and meridional eddy momentum play significant roles. Models showing greater SH HC expansion tend to simulate increased precipitation in specific regions and shifts in atmospheric jet streams. Addressing these model biases could help reduce uncertainty in future HC projections. Key Points: The first intermodel stream function trend mode effectively captures the spread of the Southern Hemisphere Hadley Circulation expansionThe intermodel spread in expansion is explained by the spread of the meridional eddy momentum, heat fluxes, and diabatic heatingThe spread of the eddy fluxes and diabatic heating are linked with the changes in precipitation, jet, and static stability [ABSTRACT FROM AUTHOR]

The "Emmons Problem" is a foundation of fire science and gives a mathematical boundary layer solution to the burning of a vaporizing fuel from the surface of a flat plate immersed in a uniform flow of oxidizing gas. It approximates the Navier–Stokes equations assuming infinitely fast chemistry and ignores differential diffusion and thermal radiation. This allows "similarity" solutions to be developed and expressed in terms of the classic Blasius function. The current paper extends the solution, in mathematical form, to the entire domain far from the boundary layer and upstream of the leading edge. The introduction of conformal parabolic coordinates and use of the Howarth transformation allows the solution for the stream function to be expressed in exactly the same form as that found by Emmons and furnishes an explicit recipe for the pressure perturbation. The same coordinate transformations allow the exact solution of the full elliptic mixture fraction equation to be obtained, and the representation of the velocity components in terms of the stream function guarantees that the continuity equation is also satisfied exactly. Further, an exact solution to the transverse momentum equation is also displayed permitting the introduction of a crossflow into the spectrum of results obtained. In short, an analytic solution is found for the Emmons problem in the entire elliptic domain - upstream and in the far field. [ABSTRACT FROM AUTHOR]

Amos, C.L.; Kassem, H.; Petrie, B.; Shaw, J., and Ivaldi, R., 2024. An evaluation of the Bagnold (1956) theories for sediment transport in Northumberland Strait, Canada. Journal of Coastal Research, 40(6), 1019–1036. Charlotte (North Carolina), ISSN 0749-0208. This study examines the seabed stability and sediment transport in the region of a proposed fixed link (bridge) across Northumberland Strait, Canada. The region is dominated by strong semidiurnal and diurnal tides that have eroded, transported, and deposited material that modify the character of the local seabed morphology. The seabed comprises rippled fine sand interspersed with a shelly gravel lag. The study provides an opportunity to examine the theories of R.A. Bagnold on sand transport that were deficient in the prediction of the transport of fine and very fine sand. A further purpose was to determine the mechanisms of the sand transport (waves, currents, or both). Representative sediment samples were collected and subjected to hydrodynamic forcing in a laboratory flume (Lab Carousel); relationships were derived between the applied stream power and sediment transport rates as bedload and in suspension. In addition, a multiparameter benthic lander (Ralph) was deployed at two sites in the nearshore regions of the fixed link for a total duration of 33 days. Flow velocity measurements derived from the lander were used to assess the transport potential using calibrations derived from the flume studies. The results showed that the total immersed bedload transport measured herein corresponded well to Bagnold's dimensionless stream power function when normalized to flow depth and grain size. They also showed that the tidal currents coupled with the mean flow in the region are sufficient in magnitude to erode and transport sand to the SE, where they are deposited to form a tidal delta. The sand transport in the shallow margins (depth < 10 m) took place mainly as bedload, although periodic suspension also took place. The nature of the predicted sand transport indicates that the seabed is in a continued state of evolution subject to the present-day hydrodynamic forcing. [ABSTRACT FROM AUTHOR]

We consider the problem of maximizing a non-negative submodular function under the b-matching constraint, in the semi-streaming model. When the function is linear, monotone, and non-monotone, we obtain the approximation ratios of 2 + ε , 3 + 2 2 ≈ 5.828 , and 4 + 2 3 ≈ 7.464 , respectively. We also consider a generalized problem, where a k-uniform hypergraph is given, along with an extra matroid or a k ′ -matchoid constraint imposed on the edges, with the same goal of finding a b-matching that maximizes a submodular function. When the extra constraint is a matroid, we obtain the approximation ratios of k + 1 + ε , k + 2 k + 1 + 2 , and k + 2 k + 2 + 3 for linear, monotone and non-monotone submodular functions, respectively. When the extra constraint is a k ′ -matchoid, we attain the approximation ratio 8 3 k + 64 9 k ′ + O (1) for general submodular functions. [ABSTRACT FROM AUTHOR]

The slip flow behavior in nanofluid is necessary in industrial and engineering systems. Thermal and concentration slip is very important to enhance the heat and mass transport in micro-channels, artificial heart valves polishing, emulsion, suspended substances, foaming, internal heart cavities, and polymerization treatments. The movement of the fluid in the slip flow pattern is quite distinct from the conventional flows. The main aim of present research is to examine the thermal and concentration slip effects on heat and mass transport of magneto-nanofluid across stretchable surface in the presence of viscous dissipation and thermal density. The mathematical model is developed in terms of partial derivatives and converted into ordinary form by using similarity variables and stream functions. By using similarity and stream variables, the significant physical parameters such as Eckert number, modified buoyancy parameter, Prandtl parameter, density parameter, Brownian factor, and slip factors are generated. The numerical outcomes are elaborated by using Keller–box scheme with Newton–Raphson method. The velocity of nanoparticles, temperature, and concentration distributions are the main key findings of this research. It is noticed that the temperature distribution exponentially increases as density parameter increases. It is examined that the significant slip behavior in thermal and concentration increases as Eckert number increases. It is found that significant variations in slip velocity and slip temperature are examined for each slip parameter. The magnetic-driven stretchable surface is very beneficial in cooling strips, microelectronics, heat insulation, energy storage devices, micro-MHD pumps, oil reservoirs, and metal extraction. [ABSTRACT FROM AUTHOR]

We study theoretically the steady Newtonian flow in confined and hyperbolic long tubes (symmetric channels and axisymmetric pipes) considering slip along the walls. Using a stream function formulation, and the extended (or high-order) lubrication method in terms of the square of the aspect ratio of the tube, ε , the solution for the stream function is found analytically up to twentieth order in ε. At the classic lubrication limit, i.e. i.e. for a vanishing small aspect ratio, and for perfect slip conditions, the analysis predicts a plug-like velocity profile and a constant strain-rate on the midplane/axis of symmetry of the tube. A constant strain-rate is also predicted for the non-slip case. Furthermore, the high order asymptotic results for the stream function and fluid velocity are post-processed with an acceleration technique to investigate the convergence and accuracy of the solution. The results reveal the existence of a boundary layer at the inlet of the tube, the influence of which diminishes in a very short distance from the entrance. We discuss the effect of the contraction ratio of the tube and the dimensionless slip coefficient on the midplane/centerline and wall (slip) velocities, as well as on the average pressure-drop, required to maintain a constant flow-rate. The acceleration of converge technique on the solution for the pressure-drop revealed a remarkable convergence at a value slightly larger (∼1 %) than the value predicted by the classic lubrication theory. Finally, we comment on the common practice in the literature for approaching the velocity profile with the velocity profile at the classic lubrication limit, and we compare the high-order results for the strain rate at the midplane/centerline with the effective strain rate previously derived in the literature by Housiadas & Beris, J. Rheology, 68(3), 327–339, 2024. [ABSTRACT FROM AUTHOR]

The motivation of this recent article is to study dusty Walter's B fluid flow due to its wide range of applications in biology and polymer industry. The fluid is traveling peristaltically through an asymmetric channel with wall slip. A discussion is also presented to examine heat transfer effects with thermal radiation and slip. The regular perturbation technique is employed to evaluate the mathematical model of the problem, which is first simplified by using stream functions. Mathematical results are simulated to illustrate flow characteristics of fluid and solid particles in salient quantities. Also, graphs of temperature distribution of fluid and dust particles have been discussed to study the impacts of various parameters. Walter's B fluid parameter reduces speed of both fluid and dust particles. By increasing thermal slip parameter, temperature transference becomes slower through the fluid, while Brinkman number significantly raises the temperature profile of both fluid and particles. This article presents a theoretical analysis of the problem. Moreover, the characteristics of liquids involved in the plastic industry and medical science can also be understood using the current analysis. Walter's B fluid with dust particle suspension has not been investigated for slip and thermal radiation effects. [ABSTRACT FROM AUTHOR]

Woody debris (WD) stabilizes riverbeds, creates habitats, supports biodiversity, and enhances water quality in ecosystems. This study investigates the impact of WD on sediment characteristics and particulate organic matter (POM) accumulation in the Roztoka stream, located within a forested catchment in the Polish Carpathians. The focus is on the influence of different WD types: coarse (CWD, length > 1 m and diameter > 10 cm), fine (FWD, length < 1 m and diameter < 10 cm), and mixed (MWD, a combination of CWD and FWD) on sediment differentiation and POM accumulation. Stand age, ranging from 20 to over 120 years (in 20-year intervals), was also analyzed as a factor affecting WD structure and POM deposition. Results indicate that MWD had the greatest effect on sediment differentiation, with mean grain size (Mz) ranging from -3.91 phi to -0.95 phi. Stand age significantly influenced POM accumulation, with the highest content (19.51%) observed in age classes III and VI. Older stands (> 120 years) had a diminished effect on both WD structure and POM accumulation. This study underscores the critical role of WD in sediment differentiation and provides insights for improving the ecological function of natural streams. Although the findings are region-specific, they have broader implications for similar temperate mountainous forests. [ABSTRACT FROM AUTHOR]

A steady Newtonian fluid flow through annular region in curved pipes is studied in this paper. The flow takes place due to an axial pressure gradient and it is three-dimensional in nature. The equations governing the flow are highly coupled and nonlinear. The solutions are obtained, analytically, using a regular perturbation method. The effects of curvature ratio (δ) , Reynolds number (Re) and the radius ratio (l) on the axial velocity and stream function are presented graphically. It is observed that, along with curvature ratio and Reynolds number, radius ratio highly affects the fluid flow in annular curved pipes. [ABSTRACT FROM AUTHOR]

The article "Two-dimensional turbulence on the ellipsoid" in the Journal of Fluid Mechanics explores the behavior of two-dimensional turbulence on ellipsoids, emphasizing the impact of domain geometry on energy transfer. The study demonstrates that energy transfer is influenced by angular momentum conservation, with spheres restricting energy flow into certain modes, while spheroids and triaxial ellipsoids allow energy to flow into any mode. The research employs numerical experiments to validate these findings and underscores the significance of angular momentum conservation in comprehending turbulence dynamics. Additionally, the study delves into the use of stereographic coordinates to analyze fluid flow dynamics on ellipsoids, highlighting the role of geometry in shaping turbulence. [Extracted from the article]

The article delves into the use of patterned heating to minimize pressure losses in sloping channels by creating separation bubbles that reduce friction and induce fluid rotation. Factors like Reynolds number, heating wavelength, and channel inclination impact the effectiveness of heating in reducing pressure losses. While judicious heating can significantly decrease pressure losses, excessive heating may lead to increased energy costs. The study suggests that heating can be a viable method for drag reduction in specific channel orientations, emphasizing the potential for energy efficiency and flow rate optimization through patterned heating. [Extracted from the article]

The article "Relative fluid stretching and rotation for sparse trajectory observations" in the Journal of Fluid Mechanics introduces a new method to quantify fluid stretching and rotation using relative Lagrangian velocities. The research focuses on identifying fluid structures in unsteady and sparsely sampled flows, like ocean buoy data and Lagrangian particle tracking, surpassing existing limits of sparse diagnostics. The study compares the proposed method with traditional metrics, demonstrating its advantages in various numerical and experimental flows. It also discusses the use of relative trajectory diagnostics to identify coherent flow features in sparse trajectory data, showcasing their effectiveness in identifying elliptic and hyperbolic Lagrangian coherent structures in different flow scenarios. [Extracted from the article]

The study of atmospheric Rossby waves could provide a theoretical basis for weather forecasting systems. In this paper, the barotropic quasi-geostrophic model is used to discuss the nonlinear Rossby waves induced by large-scale topography under the β -plane approximation. Starting from the potential vorticity equation, the atmospheric area is divided into internal region and external region, and the perturbation expansions of the two equations are carried out by using the separate multi-scale perturbation method. The Benjamin–Ono equation describing the wave amplitude is obtained by matching solutions of the internal and external equations at the boundaries. The distributions of the perturbation stream function, the total stream function, and the vorticity are obtained. It is found that the algebraic solitary waves induced by large-scale topography do exist. Moreover, the amplitude of the nonlinear Rossby waves is affected along with the changes of topography. [ABSTRACT FROM AUTHOR]

The importance of this investigation is to examine the heat and mass transportation of magneto nanofluid movement along a heated sheet with exponential temperature-dependent density, entropy optimization, thermal buoyancy, activation energy, and chemical reaction aspects. The influence of these factors in cutting tools by means of machining and nanofluid lubrication is a significant process in cutting zone, chip cleaning, lubricating, and cooling productivity in milling. The corresponding energy activation and chemical process are essential to understand the thermal behavior of nanofluid. The appropriate transformations are used to solve nonlinear partial differential equations within the framework of ordinary differential equations using stream functions and similarity variables. The Keller box method is employed to efficiently solve these equations computationally under the Newton–Raphson approach. Through tables and figures, the fluid velocity, temperature distribution, and concentration consequences are sketched using various controlling parameters. It is seen that the fluid temperature function increases with noticeable amplitude as the Eckert factor, variable density, chemical-reaction, and activation energy increase. It is found that the noticeable enhancement in heat and mass transportation is deduced for maximum Brownian motion and thermophoresis. This work is important in various applications such as cutting fluids, drilling, brake oil, engine oil, minimum quantity lubrication, enhanced oil recovery, and controlled friction between the tool-chip and tool-work during machining operations. [ABSTRACT FROM AUTHOR]

Background: Magnetoencephalography (MEG) and magnetic resonance imaging (MRI) are non‐invasive imaging techniques that offer effective means for disease diagnosis. A more straightforward and optimized method is presented for designing gradient coils which are pivotal parts of the above imaging systems. Purpose: A novel design method based on stream function combining an optimization algorithm is proposed to obtain highly linear gradient coil. Methods: Two‐dimensional Fourier expansion of the current field on the surface where the coil is located and the equipotential line of the expansion term superposition according to the number of turns of the coil are used to represent the coil shape. Particle swarm optimization is utilized to optimize the coil shape while linearity and field uniformity are used as parameters to evaluate the coil performance. Through this method, the main parameters such as input current distribution region, coil turns, desired magnetic field strength, expansion order and iteration times can be combined in a given solution space to optimize coil design. Results: Simulation results show that the maximum linearity spatial deviation of the designed bi‐planar x‐gradient coil compared with that of target field method is reduced from 14% to 0.54%, and that of the bi‐planar z‐gradient coil is reduced from 8.98% to 0.52%. Similarly, that of the cylindrical x‐gradient coil is reduced from 2% to 0.1%, and that of the cylindrical z‐gradient coil is reduced from 0.87% to 0.45%. The similar results are found in the index of inhomogeneity error. Moreover, it has also been verified experimentally that the result of measured magnetic field is consist with simulated result. Conclusions: The proposed method provides a straightforward way that simplifies the design process and improves the linearity of designed gradient coil, which could be beneficial to realize better magnetic field in engineering applications. [ABSTRACT FROM AUTHOR]

The Asian summer monsoon anticyclone (ASMA) plays a vital role in the transport and redistribution of the tracers in the upper troposphere and lower stratosphere during transient monsoon conditions. The ASMA can be identified using various diagnostics such as winds and divergence, potential vorticity, the Montgomery stream function or geopotential height. Its representation based on the commonly‐used existing method that takes a climatological range of the geopotential height (GPH) at a given pressure level is not robust and fails in several circumstances. In this study, we propose a new GPH method to define the ASMA for the active and break phases of the monsoon based on the GPH values at the tropical easterly jet (TEJ) and subtropical westerly jet (STJ) locations. The proposed method compares the GPH values at the locations corresponding to the wind speed maxima of TEJ and STJ at 100 hPa with the maximum GPH at 100 hPa and selects the one with the minimum difference to define the ASMA extent. The same procedures were applied to obtain the ASMA extent at 150 hPa. The ASMA extents are obtained using the method proposed here and the existing fixed GPH method for the 30 active and 27 break phases from 2005 to 2023. The fixed GPH method provides a larger ASMA extent for 24 active and 21 break phases, which appears to be an unrealistic estimation compared to the proposed method. Our proposed method identifies the ASMA extent that is larger and centred around the Iranian side during the active phases while it is smaller and centred around the Tibetan side during the break phases. Furthermore, the minimum concentration of ozone (O3), and maximum concentrations of carbon monoxide (CO) and water vapour (H2O) are also found to be centred near the Iranian side during the active phases and on the Tibetan side during the break phases. The tracer concentrations are generally higher for CO, H2O and O3 during the active phase than in the break phase. Tracer concentrations within the ASMA extent using the fixed GPH method are higher for O3 while lesser for CO and H2O when compared to the proposed method. [ABSTRACT FROM AUTHOR]

Nonlinear equations called the Stenflo equations are usually used for the analytical description of the propagation of internal gravity waves in the Earth's upper atmosphere. Solutions in the form of dipole vortices, tripole vortices, and vortex chains are previously obtained by these equations. The Stenflo equations also describe rogue waves, breathers, and dark solitons. If disturbances cease to be small, then their profiles are usually deformed, and, presumably, they cannot be considered plane waves. This study shows that this is not always the case for internal gravity waves and that these waves can propagate as plane waves even with large amplitudes. An exact solution of the system of nonlinear Stenflo equations for internal gravity waves that contain nonlinear terms in the form of Poisson brackets is given. The solution is obtained in the form of plane waves with arbitrary amplitude. To find a solution, the original system of equations is transformed. It is split into equations for the stream and vorticity functions as well as equations for the perturbed density. To solve the obtained equations, the procedure of the successive zeroing of Poisson brackets is applied. As a result, linear equations that allow one to find the accurate analytical solutions for internal gravity waves in the form of plane waves with arbitrary amplitude are obtained. By solving these linear equations in two different ways, we have analytically found expressions for the perturbed quantities and the dispersion equation. The nonlinear equations obtained for the current, vorticity, and perturbed density functions can be used to find other nonlinear solutions. The given solutions in the form of plane waves with arbitrary amplitude may be of interest for the analysis of the propagation of internal gravity waves in the Earth's atmosphere and the interpretation of experimental data. [ABSTRACT FROM AUTHOR]

Plastic pollution is an emergent global issue in freshwater and marine ecosystems. Microplastics enter waterways from a variety of sources, although the relative importance of point and nonpoint sources for a given watershed is not well understood. To determine whether medium-sized wastewater treatment plants are significant sources of microplastics to rivers draining into Lake Erie, we measured microplastic loads up- and downstream of two wastewater treatment plants in southeastern Michigan State (USA). We detected a significant increase in the microplastic load downstream from the wastewater treatment plant discharging into the Lower Rouge River, but not downstream from the one discharging into the Huron River. However, the background microplastic load was tenfold higher in the Huron River compared to the Lower Rouge River, likely obscuring our ability to detect the wastewater treatment plant as a point source. We found a positive relationship between river discharge and microplastic load in the Huron River, which drains a larger watershed area at the effluent discharge point than the Lower Rouge site, suggesting that watershed sources may be more important over larger spatial scales. We also performed experiments to test the effects of plastic on stream biofilm function to better understand how plastic pollution alters stream metabolism. Biofilms grown on high-density polyethylene and polypropylene had significantly lower metabolic diversity and metabolic response, respectively. Overall, our findings indicate that attention should be directed to both point and nonpoint sources to reduce microplastic pollution and that plastics may negatively affect the function of stream biofilm communities. [ABSTRACT FROM AUTHOR]

Ecosystem restoration initiatives present natures as intervention-requiring problems. However, not all stakeholders may be able to recognise and relate to the issues that motivate restoration. Instead, they may put forward alternative understandings of natures as problematic issues in need of management and collective action. Therefore, ecosystem restoration can turn generative into new forms of publics that are brought together – and drawn apart – by distinctive configurations of nature-issues. This paper analyses such a reorganisation by focusing on three restoration projects carried out in Finland. The projects sought to engage farmers in restoring agricultural streams while proposing the practice of stream restoration as an extensive ecosystem revitalisation. In the studied cases, farmers could become attentive to the potential of stream habitats to develop into viable and rich ecosystems, while their neighbours only showed interest in improving the drainage functions of streams. The restoration initiatives generated connectedness between farmers, streams habitats and the restoration projects, but also disconnectedness between natures and publics. The possibilities of the studied projects to carry out their restoration plans rested mostly on the specification of the restoration plans as a means to manage ontological differences. The findings indicate that instead of promoting ecosystem restoration as a tightly coupled practice, it can be useful to generate space for collective action that unfolds in terms of partially different natures and nature-issues. [ABSTRACT FROM AUTHOR]

Massive data shoving can reach the greatest throughput, which is necessary for distributed streaming storage to function at its best. The comparison of the distributed streaming storage systems Pulsar and Pravega for a given number of producers and data packet size is covered in detail in this study. This analysis' benchmark tool accommodates several producers and consumers. When connection pooling is enabled and 0.5 million records are thrust at a 10 Mbps data rate, both streaming storages are assessed for latency percentile comparison. A novel idea called sbk-charts is introduced in the current study, which can create practical charts from CSV files. Multiple CSV files can be joined by sbk-charts to construct a single combined xlsx file with helpful charts. The outcomes of the experiment are then evaluated for performance comparison in a number of dimensions. [ABSTRACT FROM AUTHOR]

The document delves into the linear stability analysis of generalized Couette-Poiseuille (GCP) flow between moving parallel plates under various conditions. It examines the neutral surface in (Re, α, β) space, the mapping to plane Couette-Poiseuille flow stability, and the global critical properties of GCP flow. The research articles included discuss the stability of different fluid flows, exploring topics like energy budget analysis, slip effects, and the impact of non-ideal fluids on flow stability. Researchers have explored modal and non-modal approaches to understanding the behavior of viscous and viscoelastic liquids in diverse flow scenarios. [Extracted from the article]

The investigation of blood flow into curved arteries is fascinating and essential to prevent the advancement of vascular disease. Motivated by electro-kinetic manipulation, gold nanoparticles, and their size applications, a mathematical model is developed to explain blood flow, entropy generation, and electro-kinetic energy conversion (EKEC) efficiency in curved arterial flow. To make this study more realistic, a patient-specific overlapped stenosis condition and non-Newtonian (power-law fluid) blood flow model have been considered. The effects of a magnetic field, external heating, and chemical reactions are also included. The Stone's strongly implicit scheme has been considered to solve the system of non-linear partial differential equations (PDE's) in the" MATLAB" software. In this numerical investigation, an error tolerance of 10 − 6 has been considered for every iteration step under Stone's scheme. The significance of various physical parameters, such as nanoparticle volume fraction (m), their size (dp), magnetic field intensity (M), inverse Debye length ( κ ¯ ), flow behavior index (Sc), heat source (H), and chemical reaction parameter (ξ) on the blood flow velocity, temperature, concentration, EKEC efficiency, and entropy generation have been explained graphically. This study also developed stream function contours to describe flow trapping patterns. The findings of this study conclude that the blood flow EKEC efficiency reduces with the presence of nanoparticles and stenosis in the artery. In addition, both flow velocity and entropy enhance by adopting large-size nanoparticles instead of small diametric nanoparticles. Clinical researchers and biologists may use the results of this computational study to forecast endothelial cell damage and plaque deposition in curved arteries with WSS profiles, by which the severity of these conditions can be reduced. [ABSTRACT FROM AUTHOR]

Environmental contamination by potentially toxic elements (PTEs) poses a significant challenge, particularly in the metropolitan regions of developing countries. This issue arises from the high levels of pollution driven by industrial growth and the increased traffic from fossil fuel-powered vehicles. Even after the wastewater treatment in treatment plants, PTEs often persist, posing risks to stream structure and function. This form of pollution is persistent, long-term, and irreversible, presenting a significant challenge in terms of freshwater conservation. This study aimed to assess the water quality and PTE concentrations in urban streams in Santo André, SP, Brazil, to identify the PTEs relevant to stream pollution. We analyzed the water quality in seven catchments in the Santo André municipality, in the metropolitan region of São Paulo, Brazil. The samples were collected during the dry (2021) and rainy periods (2022), and the concentrations of potentially toxic elements (PTEs) were analyzed via inductively coupled plasma–mass spectrometry (ICP-MS). The results showed elevated electrical conductivity (429 ± 211 μS·cm) and low dissolved oxygen concentrations in the streams (2.3 ± 0.95 μg·L), indicating potential problems such as eutrophication and toxicity to aquatic organisms. PTE concentrations, particularly those of Mn (30.8 ± 22.3 μg·L), Fe (91.1 ± 72.1 μg·L), and Zn (38.1 ± 28.7 μg·L), were among the highest concentrations. Seasonal variations affected the PTE concentrations, with Cr and Fe predominating during the dry season and Zn increasing during the rainy season. Associations were found between the PTE concentrations and the water pH, indicating the importance of continuous monitoring and remediation efforts. [ABSTRACT FROM AUTHOR]

To improve the quality and success of compensatory mitigation under Clean Water Act Section 404, the U.S. Army Corps of Engineers and the U.S. Environmental Protection Agency jointly promulgated regulations in 2008. These regulations promote the use of function assessments to determine appropriate compensatory mitigation to replace functions and services lost due to permitted impacts to aquatic resources and require a watershed approach to mitigation. The Oregon Removal‐Fill law, administered by the Department of State Lands, has similar requirements. Despite higher level policy, there is a paucity of scientific focus at the practical level needed to improve the tools and practices required for regulatory program implementation to achieve better mitigation outcomes, contributing to an implementation gap. By describing key challenges and specific solutions, we share lessons from a 15‐year interagency effort to develop and implement an integrated, function, and watershed‐based stream compensatory mitigation program in Oregon. We highlight the importance of an intentional process of engagement and change management and identify outstanding science and policy needs to improve stream compensatory mitigation programs and field‐scale outcomes. [ABSTRACT FROM AUTHOR]

The movement of bile inside ducts in a diseased state is investigated using a mathematical model that takes into account heat transport and chemical interactions. Bile is considered as a viscous fluid, geometry of ducts is assumed as finite length asymmetric channel and the flow is induced by peristaltic wave along the length of channel walls. Under the presumption of a long wave length and a low Reynolds number, the formulas for axial velocity, pressure gradient, volume flow rate, stream function, pressure increase, shear stress, and heat transfer coefficient are produced. In the end, a plot and discussion are made of how different emergent factors affect the relevant physical quantities. [ABSTRACT FROM AUTHOR]

This model consists of a porous spherical body rotating in an incompressible conducting fluid in the existence of a toroidal magnetic field. The toroidal field is generated by an electric dipole along the axis of symmetry. The model is split into two parts—the clear fluid region and the porous sphere. The clear fluid area is driven by the momentum equation and the permeable sphere region is driven by the Brinkman equation. The study is being done for the scenario where the impact of viscous force is much more than inertia force. The expression is found for fluid velocity and stream function by the superposition method. The results depict the impact of rotational parameters and the Darcy number on separation parameter. It is shown that the separation is low for the highly permeable sphere. [ABSTRACT FROM AUTHOR]

Data assimilation (DA) is a powerful technique for improving the forecast accuracy of dynamic systems by optimally integrating model forecasts with observations. Traditional DA approaches, however, encounter significant challenges when applied to complex, large-scale, highly nonlinear systems with sparse and noisy observations. To overcome these challenges, this study presents a new Neural Network-based Data Assimilation (DANet) model, specifically employing a Convolutional Long Short-Term Memory architecture. By leveraging the strengths of neural networks, DANet establishes the relationship among model forecasts, observations, and ground truth, facilitating efficient DA in large-scale spatiotemporal forecasting with sparse observations. The effectiveness of the DANet model is demonstrated through an initial case study of wind-driven oceanic flow forecasting, as described by a Quasi-Geostrophic (QG) model. Compared to the traditional Ensemble Kalman Filter (EnKF), DANet exhibits superior performance in cases involving both structured and unstructured sparse observations. This is evidenced by reduced Root Mean Square Errors (RMSEs) and improved correlation coefficients (R) and Structural Similarity Index. Moreover, DANet is seamlessly integrated with the QG model to operationally forecast vorticity and stream function in the long term, further confirming the accuracy and reliability of the DANet model. DANet achieves operational forecasting 60 times faster than EnKF, underscoring its efficiency and potential in DA advancement. [ABSTRACT FROM AUTHOR]

Rotationally symmetric bodies with longitudinal cross sections of parabolic shape are frequently used to model astrophysical objects, such as magnetospheres and other blunt objects, immersed in interplanetary or interstellar gas or plasma flows. We discuss a simple formula for the potential flow of an incompressible fluid around an elliptic paraboloid whose axis of symmetry coincides with the direction of incoming flow. Prescribing this flow, we derive an exact analytical solution to the induction equation of ideal magnetohydrodynamics for the case of an initially homogeneous magnetic field of arbitrary orientation being passively advected in this flow. Our solution procedure employs Euler potentials and Cauchy's integral formalism based on the flow's stream function and isochrones. Furthermore, we use a particular renormalization procedure that allows us to generate more general analytical expressions modeling the deformations experienced by arbitrary scalar or vector-valued fields embedded in the flow as they are advected first toward and then past the parabolic obstacle. Finally, both the velocity field and the magnetic field embedded therein are generalized from incompressible to mildly compressible flow, where the associated density distribution is found from Bernoulli's principle. [ABSTRACT FROM AUTHOR]

An efficient mathematical model of electroosmotic blood flow in a non-uniform wavy microvessel is investigated. In the present study, the microvessel is considered as an impermeable microchannel in which the Herschel–Bulkley (H–B) model of shear-thinning character is chosen to represent the complex flow of blood. An external electric field is applied along the channel length. Due to the negative charge of the glycocalyx layer located at the inner surface of the microchannel, an electric double layer is formed. As a result, an electric potential developed, which is described by the Poisson–Boltzmann equation. Eventually, the study analytically solves a boundary value problem to determine the axial velocity of H–B fluid flow by employing a long wavelength and low Reynolds number. Additionally, the analysis derives the volumetric flow rate in the microchannel across a single wavelength and stream function for the flow field. Using Mathematica symbolic software, graphs are plotted to visualize the impact of rheological features on the axial velocity, streamlines, and volumetric flow rate concerning various physical parameters such as H–B shear-thinning flow index, plug radius, Debye length, and Helmholtz–Smoluchowski velocity. It is found that the flow of blood becomes smoother as blood behaves more shear-thinning in nature, which is the key innovation of this work. Also, an increment in Debye length helps in increasing the size of fluid bolus remarkably, which adds the novelty of physics to this study. Such a model can have applications in canalicular flow, transport in human skin, fluid dialysis, and separation methods. [ABSTRACT FROM AUTHOR]

In this Letter, we develop an analytical theory to study the transport of active liquids, which contain active and self-propelling particles (with vortex defects), inside a long and thin permeable capillary tube. This transport is triggered by a pressure gradient induced by an imposed gradient in the activity (or the particle concentration). Our results show a clear distinction in the radial and axial velocity profiles between the pressure-driven transport of active (with either extensile or contractile activity) and non-active liquids inside such permeable capillaries. We also identify the stream function characterizing the active liquid velocity field inside such permeable tubes. [ABSTRACT FROM AUTHOR]

The current of a free mode included in a zonally elongated basin is zonal almost everywhere, with the exception of the westernmost and easternmost areas of the fluid domain. The main difference between different circulation fields basically concerns the latitudinal localisation of the maximum and minimum flow. This aspect is investigated by determining how total vorticity selects above localisations. The result is that the latter only depends on the value taken by the total vorticity at the points where the stream function is zero. A set of examples illustrates the results. [ABSTRACT FROM AUTHOR]

We show the existence and the regularity properties of (a class of) weak solutions to the two-dimensional stationary incompressible inhomogeneous Navier–Stokes equations with density-dependent viscosity coefficients, by analyzing a fourth-order nonlinear elliptic equation for the stream function. For some stationary symmetric flows, we reformulate the Navier–Stokes equations as ordinary differential equations and give explicit examples of weak solutions. We present some further (ir-)regularity results in the case of piecewise-constant viscosity coefficients. [ABSTRACT FROM AUTHOR]

Rivers of tropical islands formed by volcanic eruptions experience unpredictable and heavy rainfall and are characterised by irregular topography. During the 2019 and 2020 low-water season, we investigated the responses of benthic macroinvertebrate assemblages to variations in local environmental conditions in four rivers located in areas of different rainfall intensity. We found that changes in local environmental conditions associated with lower rainfall intensity reduced abundance and taxonomic richness and modified taxonomic composition but did not impact the balance of functional feeding groups of macroinvertebrate communities amongst streams, except for piercer herbivores. Heterotrophy associated with substrate instability and autotrophy with a more stable substrate co-occurred in semi-arid climate rivers. In contrast, a change from heterotrophy upstream to autotrophy and substrate stability downstream was apparent in the two humid rivers studied. Surrogates of stream ecosystem function revealed a very low ratio of coarse to fine particulate organic matter related to the quasi-absence of shredders in these streams and suggested a low allochthonous input contribution, which could be the result of the 5% decline in forest cover over the two past decades. [ABSTRACT FROM AUTHOR]

The present study investigates electro-osmotically modulated peristaltic transport of third-grade fluid through a microtube taking into consideration the intricate coupling of zeta potential and hydrodynamic slippage. The analytical results encompass the mathematical expressions for dimensionless electrical potential distribution as well as series solutions for stream function and axial pressure gradient up to first order utilizing the perturbation technique for small Deborah number coupled with the Cauchy product for infinite series. Critical values and ranges of wavelength have been obtained where the axial pressure gradient vanishes. Moreover, pivotal values and ranges of wavelength have also been noted for the invariance of pressure gradient with respect to Deborah number as well as Debye-Hückel parameter. Trapping phenomenon has also been investigated by contours of streamlines wherein the zones of recirculation or trapped boluses are formed predominantly near the microtube walls. Additionally, the relative enhancement in hydrodynamic slippage amplifies the trapped bolus size, whereas a diminishing behavior on bolus size is observed by the electro-osmotic parameter. [ABSTRACT FROM AUTHOR]

In this paper, the effect of the rotation variable and other variables on the peristaltic flow of Sutterby fluid in an Inclined asymmetric channel containing a porous medium with heat transfer is examined. In the presence of rotation, mathematical modeling is developed using constitutive equations based on the model of Sutterby fluid. In flow analysis, assumptions such as long wavelength approximation and low Reynolds number are used. The resulting nonlinear ordinary differential equation was analytically solved using the perturbation method. The effects of the Grashof number, the Hartmann number, the Reynold number, the Froude number, the Hall parameter, the Darcy number, the magnetic field, the Sutterby fluid parameter, and heat transfer analysis on the stream function, and the pressure gradient are analyzed graphically. Utilizing MATHEMATICA software, numerical results were computed. It is discovered that the size of boluses decreases as some parameters increase, whereas the pressure gradient is directly proportional to the majority of parameters. [ABSTRACT FROM AUTHOR]

We consider non-isentropic Euler-Maxwell equations with relaxation times (small physical parameters) arising in the models of magnetized plasma and semiconductors. For smooth periodic initial data sufficiently close to constant steady-states, we prove the uniformly global existence of smooth solutions with respect to the parameter, and the solutions converge global-in-time to the solutions of the energy-transport equations in a slow time scaling as the relaxation time goes to zero. We also establish error estimates between the smooth periodic solutions of the non-isentropic Euler-Maxwell equations and those of energy-transport equations. The proof is based on stream function techniques and the classical energy method but with some new developments. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying structural stability of steady subsonic Euler flows in 2D finitely long nozzles. The reference flow is subsonic shear flows with general size of vorticity. The problem is described by the steady compressible Euler system. With admissible physical conditions and prescribed pressures at the entrances and the exits of the nozzles respectively, we establish unique existence and structural stability of this kind of subsonic shear flows. Due to the hyperbolic-elliptic coupled form of the Euler system in subsonic regions, the problem is reformulated via Lagrange transformation and then decoupled into an elliptic mode and two hyperbolic modes. The elliptic mode is a mixed type boundary value problem of second order quasilinear elliptic equation for the stream function. The hyperbolic modes are transport types to control the total energy and the entropy. Mathematically, the iteration scheme is executed in a weight Hölder space with low regularity. • 2-D subsonic Euler flow with physical boundary conditions. • Weighted Hölder space with optimally low regularity. • Reformulating 2-D compressible Euler system via Lagrange transformation. [ABSTRACT FROM AUTHOR]

This paper concerns the steady Euler-Poisson system with self-gravitation in a two dimensional annulus of finite radius, which can be used to describe the expansion of disk-like stars and ring galaxies. Via the stream function, the Euler-Poisson system in the subsonic region is reformulated into a second order nonlinear elliptic system. One of the crucial ingredients of the analysis is to obtain the well-posedness of the boundary value problem for the associated linearized elliptic system, which is achieved through a special structure of the elliptic system to gain an energy estimate. By combining the iteration method with a priori estimates of solutions to the elliptic system, we establish the existence, uniqueness and nonlinear structural stability of subsonic flows. [ABSTRACT FROM AUTHOR]

This paper aims to study the nanofluids with peristaltic flow motion in a confined length of non-uniform horizontal tube with an endoscope. In addition to wall properties and velocity slip effect, three geometries (i.e., sphere, cylinders, and blades) of Gold – blood MHD nanoparticles are also considered. To peruse the realistic study of the model, equations and boundary conditions are modeled and formed in dimensionless control equations. Expressions for the exact solutions of velocity, nanoparticle shape effects for temperature, heat transfer, and stream function are obtained. Visual depiction of these solutions is also demonstrated by carrying out various parameters. After analyzing, a few observations illustrate that platelet-shaped nanoparticles attain the highest thermal conductivity. The maximum temperature is experienced for sphere-shaped nanoparticles and the increasing behavior is also observed for higher values of thermal slip parameter. The conduct of velocity profile increases for greater values of the slip parameter. Sphere-shaped nanoparticles also show dominance compared to brick- and platelet- shaped particles. A trapping phenomenon is also discussed in the current study. The presented model can useful for applications associated with the metabolic structures that play a vital role in heat sources inside the human body. [ABSTRACT FROM AUTHOR]

Entropy generation is an imperative feature of every thermal transportation processes. It helps to decrease irreversibility factor in a system. Therefore, present study investigates entropy generation analysis for a peristaltic motion of fourth-grade fluid in a symmetric channel in the presence of an induced magnetic field. Effects of thermal radiation, viscous dissipation, and thermal absorption/generation are considered. Slip condition is also imposed at the upper wall of the channel. Furthermore, the liquid is pondered to possess variable viscosity which displays exponential alteration over the width of the channel. Lubrication approximation theory is used to simplify partial differential equations that are strongly nonlinear. The perturbation technique has been used to yield the solution for momentum and stream function. However, the energy equation is solved numerically. The impacts of numerous embedded dimensionless substantial parameters on liquid flow are exhibited through graphs. Outcomes divulge that entropy generation enhances with an escalation of thermal conductivity parameter, however it diminutions with an enhancement of magnetic parameter. Such outcomes benefits in biomedical sciences. [ABSTRACT FROM AUTHOR]

In this paper, a high‐order compact finite difference method in general curvilinear coordinates is proposed for solving unsteady incompressible Navier‐Stokes equations. By constructing the fourth‐order spatial discretization schemes for all partial derivative terms of the pure streamfunction formulation in general curvilinear coordinates, especially for the fourth‐order mixed derivative terms, and applying a Crank‐Nicolson scheme for the second‐order temporal discretization, we extend the unsteady high‐order pure streamfunction algorithm to flow problems with more general non‐conformal grids. Furthermore, the stability of the newly proposed method for the linear model is validated by von‐Neumann linear stability analysis. Five numerical experiments are conducted to verify the accuracy and robustness of the proposed method. The results show that our method not only effectively solves problems with non‐conformal grids, but also allows grid generation and local refinement using commercial software. The solutions are in good agreement with the established numerical and experimental results. [ABSTRACT FROM AUTHOR]

A theoretical method is described to analytically calculate a pair of surface current densities, which produce a desired static magnetic field in one region of the space and zero magnetic field in another. The analysis is based on the known relationship between a surface current density and a stream function, the equivalence of stream functions and surface magnetic dipole density, and the scalar potential representation of the associated magnetic field in free space. From these relations, we formulate the magnetostatic problem, which is often treated as a vector field problem, as a scalar field problem in which a two-dimensional scalar field (stream function) is related to a three-dimensional one (magnetic scalar potential) via the differentiation of the electrostatic Green's function 1/|r–rs|. It is shown that, in a coordinate system in which a separated form of the Green's function exists (separable coordinate system), there exists a simple relationship between a harmonic component of a stream function and a harmonic component of the magnetic scalar potential. The method is applied to calculate idealized surface current patterns for actively shielded, linear gradient field coils in the Cartesian, cylindrical, and spherical coordinates. [ABSTRACT FROM AUTHOR]

The focus of present study is to incorporate the variable viscosity and temperature slip impact on heating rate and induced magnetic gradient along the moving non-conducting wedge under magnetic field. In industrial and engineering procedures, the impact of induced magnetization improves the efficiency of thermal systems to main the heating rates. The similarity transformations and stream functions are applied to reduce the governing equations into ordinary form. During this transformation, the pertinent parameters such as wedge parameter, moving parameter, Prandtl factor, viscosity parameter and temperature-slip parameter is obtained. These parameters play a prominent role on the physical values of fluid velocity, induced magnetic field and temperature distributions. The skin friction, Nusselt coefficient and induced magnetic gradient are incorporated through these parameters. The numerical values are executed by using the Keller box analysis with Newton–Raphson technique. It is depicted that the maximum slip in fluid velocity and temperature distribution is obtained for each values of thermal-slip parameter. It is noticed that maximum magnitude in induced magnetic field is reported for each wedge factor. The maximum velocity slip and temperature slip is observed for each choice of moving parameter. It is reported that the maximum variation in heating rate and induced magnetic gradient is obtained for magnetic force and viscosity parameter. The enhancing behavior of skin friction is observed for maximum values of Prandtl number. [ABSTRACT FROM AUTHOR]

Motile cilia are hair-like, tiny structures that originate in different types of biological processes. Yeleswarapu fluid model is approximated as non-Newtonian mucus, which is viscous and slippery fluid with key roles in lubrication, protection, and particle trapping in the respiratory and digestive systems. The properties of Yeleswarapu fluid with heat transfer in ciliated channels are investigated in this study. The fluid flow is characterized as laminar (low Reynold number) and incompressible (constant density) in a two-dimensional complex wavy channel generated via metachronal waves of cilia. A static frame of reference is first transformed into a dynamic frame of reference. Afterward, the system of governing equations is transformed into a non-dimensional form by using scaling factors. The half-width of the channel is substantially smaller than the wavelength of metachronal waves. Hence, the constitutive equations are simplified by the long wavelength hypothesis. The perturbation approach is employed to solve the simplified system of differential equations. This research investigates how different boundary walls and rheology affect fluid flow. Additionally, graphs of the streamlines, velocity field, temperature, heat transfer coefficient, and pressure rise are included. [ABSTRACT FROM AUTHOR]

A new analytical model for the generation of axisymmetric tornado-type vortices has been developed. A solution to the nonlinear equation for the stream function in an unstable stratified atmosphere is obtained and analyzed within the framework of ideal hydrodynamics. The solution is sought by smooth connecting continuous solutions for the internal region (eye), the central region ("wall" with maximum velocities), and the external region of the tornado. Expressions describing radial dependences for the radial and vertical velocity components include combinations of Bessel functions. The vortex is spatially localized by radius and height. Convective instability of a stratified atmosphere leads to an increase in the radial and vertical components of velocities according to the hyperbolic sine law. A downward flow is observed near the tornado axis. The maximum speed of the upward flow is achieved at a certain radial distance at a certain height. Below this height, radial flows converge toward the central part of the tornado, and above this height, there is an outflow from the wall to the axis and to the periphery. The radial structure of the azimuthal velocity is determined by the structure of the initial disturbance and can change with height. Maximum rotation is achieved in the tornado wall at a certain height. The increase in azimuthal velocity can occur according to a superexponential law. Possible structures of movements, scenarios for the development of a tornado, and its dynamics are discussed. [ABSTRACT FROM AUTHOR]

The present study aims to investigate the steady state mixed convection flow for a viscous incompressible fluid along a cantilever shape. The study has analyzed the impact of mixed convection boundary layer flow behavior and heat transfer characteristic of the cantilever shape. The leading equations for the said problem are the Navier-Stokes and energy equations. These leading equations are converted into ordinary differential equations using the stream function formulation, and the numerical solution is obtained using the shooting technique with BVP4C and built in MATLAB program. The impact of dimensionless parameters such as n , Pr, and λ on the velocity and temperature profile within the boundary layer of the cantilever cylinder is presented graphically. The results for velocity slope and temperature gradient under the effects of various emerging parameters are presented in tables. The study has concluded that mixed convection parameter has a significant impact on the velocity and temperature distribution, as well as on the velocity slope and temperature gradient rates along a cantilever shape geometry. The outcomes of the current study can be utilized for the design and optimization of various engineering devices involving cantilever shapes. Further, research regarding the impact of other parameters on the cantilever shape including heat transfer characteristics can be conducted using the approach presented in this study. The novelty of the current work can be claimed by saying that for reduced gravity, other forces involved in the flow model induced the fluid motion and temperature gradient. [ABSTRACT FROM AUTHOR]

AbstractThis study investigates the impact of convective boundary conditions, thermal radiation, and viscous dissipation on the flow of fluid–particle mixture in a ciliated walled horizontal tube filled with Rabinowitsch fluid. A mathematical model is developed using partial differential equations of continuity, motion, and energy, which are solved using the symbolic software MATHEMATICA 12.0 with convective boundary conditions. Exact solutions for velocity, temperature distribution, pressure gradient, pressure rise, stream function, and heat transfer rate are obtained and analyzed for dilatant, Newtonian, and pseudoplastic fluids. Computational results reveal that the velocity and temperature profiles are highest at the center of the tube for pseudoplastic and Newtonian fluids compared to dilatant fluid. Additionally, pressure gradient fluctuates near the tube walls. The study also explores special cases where the Rabinowitsch fluid model is reduced to dilatant, Newtonian, and pseudoplastic fluids. The findings have potential applications in medical treatments for respiratory system tumors, airway cleaning, physiological fluids, and manufacturing processes involving peristaltic flow. This original research contributes to the understanding of fluid dynamics in complex systems and has implications for various practical applications. [ABSTRACT FROM AUTHOR]

In this paper, we have analyzed the bifurcation of stagnation points in the non-Newtonian flow of the FENE-P fluid through a channel induced by peristalsis. The stream function for the flow under consideration is developed under negligible inertia and streamline curvature effects. A nonlinear autonomous system is developed for scrutiny of the critical points. A dynamical system approach is used to examine the stability of bifurcation points. Streamline patterns, and local and global bifurcation diagrams are plotted for analysis of the backward flow, trapping, and augmented flow regions. The impacts of important embedded parameters, i.e., extensibility parameter and Deborah number on local and global bifurcation diagrams, are also examined. The whole analysis reveals that two critical conditions appear in the flow field that are actually responsible for the conversion of backward flow to trapping and trapping to augmented flow. It is further seen that bifurcations occur at lower flow rates for increasing Deborah's number while an opposite trend prevails for increasing the extensibility parameter. A comparison of bifurcations between planar and axisymmetric flows is also performed. It is observed that a greater area of the trapping region is encountered for axisymmetric flow than that for planar flow. [ABSTRACT FROM AUTHOR]

AbstractThis research is conducted to investigate the heat transfer analysis in a two-phase fluid model under the impact of an electric double layer and magnetic field through two types of geometries with porous media. The Darcy model is used to capture the effect of porous medium. The perturbation technique is employed to produce the analytical solution of fluid and particulate velocities, temperature distribution, volumetric flow rate, and stream function. The computational revealed that the two-phase model produces 32 and 36% greater heat transfer as compared to the single-phase model by considering convergent and divergent channels, respectively. It is observed that the divergent channel provides 4% more heat transfer as compared to the convergent channel. The present study will offer valuable insights into the electric double-layer dynamics of two-phase fluid through complex configurations, such as biomedical engineering. The current two-phase model is also very important and applicable in electrofluidic dynamic and biomedical engineering where biomedical electronic devices such as two-phase lab-on-chip may be engineered. [ABSTRACT FROM AUTHOR]