Fluid Region Research Articles

Analysis of stability and internal flow mechanisms in spiral annular flow with different swirlers

Spiral annular flow within ducts is widely utilized in modern industry, with the swirler serving as a critical component in generating such flow patterns. The structure of the swirler significantly influences the generation and stability of the spiral annular flow. This study selected four different swirler structures with outstanding performance from previous research and analyzed their characteristics through visual image processing combined with numerical simulations. By analyzing the amplitude information of the wave fluctuations in the annular swirling flow liquid film under different operating conditions using probability density functions, it was found that the swirler A(Flat-vane swirler) and swirler B(Flat-vane swirler with hub) produced smaller fluctuations in the annular swirling flow liquid film, indicating better stability compared to the swirler C(Arc-vane swirler) and swirler D(Spiral-vane swirler), which exhibited poor performance. Combining the numerical simulation results with the analysis of the internal mechanism of the swirlers, it was discovered that within the swirler A and swirler B, the fluid between the swirler vanes experienced a larger pressure gradient, resulting in phenomena such as “jump” and “pull” under this pressure gradient. This, in turn, contributed to the generation of greater tangential velocity and radial pressure gradient after the fluid exited the swirler. Due to the influence of the swirler structure, the swirler A and swirler B did not completely separate the fluid region into four independent spaces. Instead, in the central connection area of the rear section of the swirler, the gas phase components aggregated earlier, greatly promoting the downstream generation of spiral annular flow. This study analyzed the two-phase flow process and mechanism inside the swirler, filling a gap in previous research and providing important references for the optimization and selection of swirlers.

Mechanism of the impact of sediment particles on energy loss in mixed-flow pumps

Numerical simulations were performed on the fluid domain of the mixed-flow pump with different solid-phase volume fractions to examine the influence of the sediment particles on internal energy dissipation. The energy properties of the mixed-flow pump were analyzed using the entropy production theory, considering the various flow rates and the solid particle conditions. The research examined the impact of the proportion of the solid particles in the flow on the performance and effectiveness, uncovering the complexities of the energy dissipation in the channel. The results showed that incorporating solid particle media resulted in the decrease in both the performance and effectiveness of the mixed-flow pump compared to water conditions. The mixed-flow pump's head decreased by 0.56 % and its efficiency declined by 2.74 % due to the change in particle volume fraction (Cv) from 5 % to 7.5 %. Upon transitioning from Cv = 7.5 % to Cv = 10 %, the head exhibited a 2.54 % decrease, coupled with a 7.22 % efficiency reduction, signifying pronounced energy loss. The findings highlight that the increase in the quantity of the solid particles enhances the pump's energy dissipation. Solid particles tend to be mainly concentrated in the impeller inlet, blade outer edge, guide vane inlet, and guide vane outer edge regions at varying solid-phase volume fractions. The main dissipation in the fluid region of the mixed flow pump mainly occurs in the impeller and the guide vane, the total energy loss in the guide vane is more than 500 W under the three volume fractions, the total energy loss in the impeller is also about 500 W, and the inlet and outlet losses are small. These research outcomes lay the groundwork for further enhancements in the energy characteristics of mixed-flow pumps.

Numerical study on temperature response of microheater and evolution characteristics of superheated zone under fast transient heating

The nucleate boiling process that occurs on the surface of a microheater immersed in a liquid pool under fast transient heating conditions can be regarded as homogeneous or near-homogeneous nucleation, exhibiting a significant difference when compared to boiling at conventional time scales on large and even micro spatial scales. This paper numerically investigates the boiling process at both small spatial and temporal scale by using a validated model. Results indicate a significant difference between the average microheater temperature and the maximum temperature at the boiling surface, which can reach up to 80 °C within the scope of present study. Consequently, the nucleation temperature, typically determined by the average temperature of the microheater in most references, may not precisely represent the homogeneous (or nearly homogeneous) nucleation temperature. At the initiation of nucleation, the profiles at the boundary of superheated zone are approximately circular in the z-plane and arched in the x-plane, respectively. Meanwhile, the profile of the superheated zone boundary at the onset of nucleation under direct heating mode (DHM) appears approximately trapezoidal, exhibiting a significant difference from that observed under indirect heating mode (IHM). It is also noted that the local temperature distribution in the fluid region can be considerably affected by natural convection, potentially exerting a substantial influence on the bubble dynamic behaviors during the subsequent bubble growing phase. These findings may provide valuable references for future experimental study on the mechanisms involving in microscale boiling heat transfer process under rapid heating conditions.

A robust segmentation of retinal fluids from OCT images using MCFAR-net

This paper presents a novel architecture to detect Macular Edema (ME) in Optical Coherence Tomography (OCT) images that occurs due to high fluid accumulation between the retinal layers of the eye. These excessive fluids have swollen the macular region and may result in visual impairments. To alleviate this problem in its early stage, the proposed model, Multiscale Context Enhancive Aggregation & Refinement Network (MCFAR-Net) is implemented to detect these fluids enabling the prevention of visual loss. This MCFAR-Net is incorporated with two Context Feature Enhancive Modules (CFEM). The upper module is initially trained using contrastive loss for extracting the most pertinent multiscale feature maps allowing to segment thick fluid regions from OCT images. Further, the lower module elevates the feature maps to segment the minute fluid regions using the outputs of upper CFEM along with input image. Finally, the output fluid probabilistic feature maps of both paths of the two modules are stacked together and fed as input to Feature Synthesizer (FS) Module. This module improves the true positive rate of the proposed algorithm and segments the fluid region more accurately. The performance of the proposed model is trained and evaluated using publicly available datasets like RETOUCH, OPTIMA, and DUKE datasets. This model outperformed existing state-of the-art algorithms by attaining an average dice coefficient of 95.63 % when tested on the RETOUCH dataset. The performance of proposed MCFAR-Net reduced the misclassification errors enabling to identify ME more precisely in its early stage allowing the expert doctor to provide immediate treatment to the patients.

Topological optimization and fatigue life prediction of a single pad externally adjustable fluid film bearing

This work focuses on the prediction and comparison of the fatigue life of topologically optimized pads in an externally adjustable fluid film (EAFF) bearing. It integrates one-way/two-way fluid–structure interaction analysis, topological optimization (TO), and design modifications of the pad of an externally adjustable fluid film bearing. The major goal is to create an optimum pad design that minimizes weight and maintains structural integrity, and then to predict and compare the fatigue life of these alternative designs. The outcomes of the present study are as follows: (i) Two-way FSI results show a decrease of 65.64% in hydrodynamic fluid film pressure when compared to one-way FSI results because they take into account modifications in the fluid region's geometry caused by pad deformation; (ii) even though the maximum pad deformation in optimized pad geometry (Type-4) resulting from oil film pressure is relatively small (0.0036551 mm), the influence of pad deformation on the fluid domain due to hydrodynamic fluid film pressure cannot be understated; and (iii) when comparing the TO technique's results with fatigue life results, four elongated holes in the radial direction (Type-4) are most appropriate.

Two-interface and thin-filament approximation in Hele-Shaw channel flow

When a viscous fluid partially fills a Hele-Shaw channel, and is pushed by a pressure difference, the fluid interface is unstable due to the Saffman–Taylor instability. We consider the evolution of a fluid region of finite extent, bounded between two interfaces, in the limit that the interfaces are close, that is, when the fluid region is a thin liquid filament separating two gases of different pressure. In this limit, we derive a second-order ‘thin-filament’ model that describes the normal velocity of the filament centreline, and evolution of the filament thickness, as functions of the thickness, centreline curvature and their derivatives. We show that the second-order terms in this model, that include the effect of transverse flow along the filament, are necessary to regularise the instability. Numerical simulation of the thin-filament model is shown to be in accordance with level-set computations of the complete two-interface model. Solutions ultimately evolve to form a bubble of rapidly increasing radius and decreasing thickness.

Comparative Study of Convective Oldroyd-B Nanofluid and Hybrid Nanofluid Flow, Heat and Mass Transfer Analysis Over Stretching Sheet with Cattaneo-Christov Heat Flux Model

The current analysis appraises the flow, heat and mass transfer characteristics of Oldroyd-B nanofluids SWCNT-Water and hybrid nanofluids SWCNT/MWCNT-Water over the stretching sheet. Thermal radiation, modified Fourier heat flux and convective boundary conditions are also used to evaluate the flow. Graphs are used to compare the characteristics of nanofluid SWCNT-Water and hybrid nanofluid SWCNT/MWCNT-Water nanofluids in terms of concentration, temperature, and velocity. The flow mechanism is modelled in the form of nonlinear system of partial differential equation. These PDEs are converted into Ordinary differential equations by using the similarity variable techniques. The Finite Element Method is pre-owned to solve the obtained ODEs. Plots are used to show the results of temperature, concentration and velocity for both nanofluids for various values of the relevant parameters. The dimensionless skin friction coefficient, Nusselt number and Sherwood number values are scrutinized and revealed in tabular form. The important findings of this study reveal that the scattering of temperature and concentration of both SWCNT-Water nanofluid and SWCNT/MWCNT-Water hybrid OBF nanofluid elevates with amplifying values of thermal retardation parameter. With increasing values of the power low index number the sketches of temperature and velocity are both attenuate in the fluid region.

A water model study on mixing behaviour in a Kaldo furnace using acid–base neutralization decolourization method combined with RGB-based image analysis

Mixing time is usually used as an important parameter for quantifying the mixing performance of multiphase flow in a metallurgical bath. However, the topic of the mixing time of a Kaldo furnace for copper anode slime treatment has received little attention from scholars to date; this concept is important for guiding the optimization of high-efficiency smelting in the Kaldo furnace. In the present work, the mixing behaviour of gas-liquid two-phase flow in a Kaldo furnace was simulated using a scaled-down 1:4.5 water model fabricated from transparent acrylic plastic. A visualization technique and a quantitative characterization method for mixing performance in the Kaldo furnace—acid-base neutralization decolourization combined with RGB-based image analysis—were innovatively proposed. This approach can not only determine the global mixing level η¯(t) and track the frequency distribution of the local mixing performance ξk(t) of the fluid region during the mixing process but also quantify the mixing time. In addition, based on the proposed method and by using dimensional analysis, the effects of operating parameters (such as the gas flow rate Q, injection lance height h, rotation speed ω, liquid volume fraction φ, inclination angle θ, and liquid viscosity μl) on the mixing time of gas-liquid two-phase flow in the molten bath were discussed. On this basis, the empirical equation of the mixing time as a function of h, ω, φ, the modified Froude number (Fr'), μl and θ was established as the first quantitative relationship of the mixing time for the Kaldo furnace.

Bifurcation of solutions of Ornstein–Zernike equation in the gas–liquid coexistence region of simple fluids

One objective of this paper is to investigate bifurcation of solutions of Ornstein–Zernike equation in liquid state theory for the gas–liquid coexistence region of simple fluids. The analysis uses a discrete form of the Ornstein–Zernike equation in real space, together with a closure relation which provides nearly self consistent thermodynamic properties of fluids governed by interaction potentials like the Lennard-Jones potential. Accurate asymptotic forms of correlation functions are incorporated in the real space algorithm so as to mitigate the influence of cutoff length used in the discrete approximations. The global error reduction of this algorithm is similar to that of Simpson’s rule. It is found that there is no spinodal on the vapor side on a sub-critical isotherm. However, there is a density at which compressibility vanishes, but this lies on a nonphysical branch. There are fold bifurcation points on the vapor and liquid sides together with a ‘no-real-solution-region’ in between. This is followed by a region of negative compressibility extending up to the spinodal on the liquid side. Importantly, it is found that in regions where compressibility is non-positive, there are infinite number of solutions to OZE which violate an integral constraint that is needed for applications to thermodynamics. The emerging picture is somewhat similar to that in the case of the hypernetted-chain-closure. It is also found that complex solutions connect the physical solutions that exist outside the ‘no-real-solution-region’ as well as in region of negative compressibility. The second objective of the paper, in the light of bifurcation scenario, is to evolve an interpretation of the coupling-parameter expansion of correlation functions pertaining to the region of negative compressibility. It is shown that the expansion provides an accurate description of results of the restricted ensembles, implied in mean field theories and simulation methods. Bifurcation of singlet density to an in-homogeneous distribution at a spinodal is also established using a simple equation, which uses the direct correlation function. Thus the paper re-establishes the fact that restriction to a homogeneous singlet density is the root cause of all inconsistencies found in the gas–liquid coexistence region.

Morphology of clean and surfactant-laden droplets in homogeneous isotropic turbulence

We perform direct numerical simulations of surfactant-laden droplets in homogeneous isotropic turbulence with Taylor Reynolds number $Re_\lambda \approx 180$ . The droplets are modelled using the volume-of-fluid method, and the soluble surfactant is transported using an advection–diffusion equation. Effects of surfactant on the droplet and local flow statistics are well approximated using a lower, averaged value of surface tension, thus allowing us to extend the framework developed by Hinze (AIChE J., vol. 1, no. 3, 1955, pp. 289–295) and Kolmogorov (Dokl. Akad. Navk. SSSR, vol. 66, 1949, pp. 825–828) for surfactant-free bubbles to surfactant-laden droplets. We find that surfactant-induced tangential stresses play a minor role in this set-up, thus allowing us to extend the Kolmogorov–Hinze framework to surfactant-laden droplets. The Kolmogorov–Hinze scale $d_H$ is indeed found to be a pivotal length scale in the droplets’ dynamics, separating the coalescence-dominated (droplets smaller than $d_H$ ) and the breakage-dominated (droplets larger than $d_H$ ) regimes in the droplet size distribution. We find that droplets smaller than $d_H$ have a rather compact, regular, spheroid-like shape, whereas droplets larger than $d_H$ have long, convoluted, filamentous shapes with a diameter equal to $d_H$ . This results in very different scaling laws for the interfacial area of the droplet. The normalized area, $A/d_H^2$ , of droplets smaller than $d_H$ is proportional to $(d/d_H)^2$ , while the area of droplets larger than $d_H$ is proportional to $(d/d_H)^3$ , where $d$ is the droplet characteristic size. We further characterize the large filamentous droplets by computing the number of handles (loops of the dispersed phase extending into the carrier phase) and voids (regions of the carrier fluid completely enclosed by the dispersed phase) for each droplet. The number of handles per unit length of filament scales inversely with surface tension. The number of voids is proportional to the droplet size and independent of surface tension. Handles are indeed an unstable feature of the interface and are destroyed by the restoring effect of surface tension, whereas voids can move freely in the interior of the droplets, unaffected by surface tension.

A Unified Thermo-Fluid–Solid Formulation for FSI and Phase Change Problems Based on the Particle Finite Element Method

The modeling of industrial processes that involve phase change (e.g., casting, welding or additive manufacturing) is challenging due to their multiscale and multiphysics nature. The coupling of the fluid and solid mechanics is difficult due to the unknown and evolving fluid–solid interface. To deal with the difficulty of the coupling, a unified approach has been developed where fluid and solid regions are represented in the same computational domain and solved by a single solver. The interaction of fluid and solid regions is therefore automatically captured and the material can locally undergo phase transition. This allows to capture the flow in the melt and the thermal stresses in the solid. The solid material model is currently limited to linear elasticity, but it opens the path to more complex material models with plasticity modeling, which already exist in the literature. The proposed method is based on the Particle Finite Element Method (PFEM), which has been shown to accurately handle both fluid and solid mechanics. In this work, we present the key aspects of this novel unified formulation and the treatment of the fluid–solid interface in the PFEM context. The methodology is presented and verified using a set of tests. A laser spot welding example test case demonstrates the potential of combining the unified formulation with the interface treatment and the phase change capabilities and is used for the validation of the present technique.

A Spatial Interpolation Approach to Assign Magnetic Resonance Imaging-Derived Material Properties for Finite Element Models of Adeno-Associated Virus Infusion Into a Recurrent Brain Tumor.

Adeno-associated virus (AAV) is a clinically useful gene delivery vehicle for treating neurological diseases. To deliver AAV to focal targets, direct infusion into brain tissue by convection-enhanced delivery (CED) is often needed due to AAV's limited penetration across the blood-brain-barrier and its low diffusivity in tissue. In this study, computational models that predict the spatial distribution of AAV in brain tissue during CED were developed to guide future placement of infusion catheters in recurrent brain tumors following primary tumor resection. The brain was modeled as a porous medium, and material property fields that account for magnetic resonance imaging (MRI)-derived anatomical regions were interpolated and directly assigned to an unstructured finite element mesh. By eliminating the need to mesh complex surfaces between fluid regions and tissue, mesh preparation was expedited, increasing the model's clinical feasibility. The infusion model predicted preferential fluid diversion into open fluid regions such as the ventricles and subarachnoid space (SAS). Additionally, a sensitivity analysis of AAV delivery demonstrated that improved AAV distribution in the tumor was achieved at higher tumor hydraulic conductivity or lower tumor porosity. Depending on the tumor infusion site, the AAV distribution covered 3.67-70.25% of the tumor volume (using a 10% AAV concentration threshold), demonstrating the model's potential to inform the selection of infusion sites for maximal tumor coverage.

Influence of porosity properties on natural convection heat transfer in porous square cavity

A numerical investigation was conducted to examine free convection heat transfer within a square cavity containing a fluid-saturated porous layer at the bottom under laminar flow conditions. The enclosure's left and right walls experienced heating and cooling, while the top and bottom walls remained adiabatic. The study explored the influence of the Darcy number, porosity number, and dimensionless thickness of the porous layer on heat transmission. This investigation utilized a FORTRAN computation program alongside the finite volume method, effectively solving the equations governing flow and heat exchange within porous materials through natural convection. The flow pattern is determined by the Navier–Stokes equations in the fluid region and the Darcy–Brinkman–Forchheimer formula in the porous region. The energy equation was employed to compute the thermal field. The increase in the Darcy number results in both an increase in heat transfer rate due to enhanced fluid flow through pores and an intensification of fluid flow patterns. Higher porosity leads to higher heat transfer rates due to greater fluid penetration and an increased surface area for heat exchange. The thicker porous layer reduces heat transfer rate due to increased resistance to fluid flow and decreased contact area.

Viscous flow and collapse of macroscopic cavities in a granular material

The viscous flow in a granular material containing macroscopic cavities (or clear fluid regions) is determined on the basis of the generalized Darcy equation (outside the cavity region) and the Stokes equation (inside the cavity region). A three-dimensional singularity termed a “Darcylet”, which is a fundamental solution in the granular material, is distributed over the surface of a spherical cavity of unit size that surrounds the isolated singularity. The latter is calibrated with the exact solution and applied to describe the interaction between two cavities, which successfully reproduces previous analytic results. The proposed method is applicable to two cavities until they come into contact, thus providing a theoretical explanation of the fundamental collapse-and-merger process of two cavities. Furthermore, we extend this method to the interaction among multiple cavities, which reveals the effect on the flow field of an arbitrary number of cavities in an arbitrary configuration. To demonstrate the potential of the proposed method, we first apply it to a one-dimensional array of cavities of arbitrary orientation and curvature and estimate the convective diffusion of fluid volume, before considering a two-dimensional slightly disordered array of cavities. The results indicate the development and creation of new fluid passages, which may provide clues for predicting the anomalously fast spread of contaminants in inhomogeneous granular material; the formation of waterways, collapse of river banks, and landslides in civil engineering; and fluidization in chemical engineering. Our results may also provide insights into medical engineering techniques for creating new blood veins for micro-circulation (angiogenesis).

A hybrid approach using CNN and active contour model for automated segmentation of macular edema

Macula is the part of retina responsible for sharp and clear vision. Macular edema is caused by the accumulation of intraretinal fluid (IRF) in the macula, which is further distinguished by the compromised integrity of the blood-retinal barrier, particularly evident in the retinal vasculature. This results in swelling, that may lead to vision impairment and is the dominant sign of several ocular diseases, including age-related macular degeneration, diabetic retinopathy, etc. Quantitative analysis of the fluid regions in macular edema helps in ascertaining the severity as well as the response to treatment of the diseases. Optical coherence tomography (OCT) is a major tool used by ophthalmologists for visualizing edema. The prevalent practice for diagnosing and treating macular edema involves measuring Central Retinal Thickness (CRT). Segmenting the IRF in OCT images offers the potential for a more accurate and better quantification of macular edema. This paper proposes a novel method combining convolutional neural network (CNN) and active contour model for segmenting the IRF to ascertain the severity of macular edema. The IRF region is initially segmented using an encoder-decoder architecture. Contour evolution is then performed on this segmented image to demarcate the IRF boundaries. The advantage of the method is that it does not require precisely labeled images for training the CNN. A comparison of the experimental results with models employing CNN alone and with other state-of-the art methods demonstrates the superior performance and consistency of the proposed method.

A New Non-Extensive Equation of State for the Fluid Phases of Argon, Including the Metastable States, from the Melting Line to 2300 K and 50 GPa

A new equation of state for argon was developed with the view of extending the range of validity of the equation of state previously proposed by Tegeler et al. and obtaining a better physical description of the experimental thermodynamic data for the whole fluid region (single-phase, metastable, and saturation states). As proposed by Tegeler et al., this equation is also based on a functional form of the residual part of the reduced Helmholtz free energy. However, in this work, the fundamental equation for Helmholtz free energy was derived from the measured quantities CV(ρ, T) and P(ρ, T). The empirical description of the isochoric heat capacity CV(ρ, T) was based on an original empirical description explicitly containing the metastable states. The thermodynamic properties (internal energy, entropy, and free energy) were then obtained by combining the integration of CV(ρ, T). The arbitrary functions introduced by the integration process were deduced from a comparison between calculated and experimental pressure P(ρ, T) data. The new formulation is valid for the whole fluid region from the melting line to 2300 K and for pressures up to 50 GPa. It also predicts the existence of a maximum of the isochoric heat capacity CV along isochors, as experimentally observed in several other fluids. For many applications, an approximate form of the equation of state for the liquid phase may be sufficient. A Tait–Tammann equation is therefore proposed between the triple-point temperature and 148 K.

Thermophysical dynamics of magnetohydrodynamic electroosmotic two phase mixed convective flow in vertical annulus: neuro computation

ABSTRACT The thermophysical dynamics of electro – magnetohydrodynamic mixed convective electrically conducting fluid flow in the vertical cylindrical annulus are explored with electric and magnetic fields. The flow and heat transfer properties are explicitly examined in viscous fluid and electroosmotic flow regions. The coupling between an external pressure gradient, electroosmosis, and an extended electromagnetic field can control fluid flow and heat transfer. The governing equations associated with the physical phenomenon are addressed with the Galerkin finite element method. Eloquently, the analysis revealed that, in the absence of a lateral electric field, the flow velocity decelerates as the Hartmann number increases, which in turn ultimately, causes the Nusselt number to rise. Since a lateral electric field is involved, the flow field, temperature field, and Nusselt number profiles are presented in two regions. The artificial neural network model discusses the thermal transport phenomenon in both regions. The artificial neural network models regression, performance plots, weights, and bias are presented. The research outcome can be utilized to design exquisite and efficacious electromagnetic devices, particularly within a particular range of thermal physical properties.

Enhancing point annotations with superpixel and confident learning guided for improving semi-supervised OCT fluid segmentation

Automatic segmentation of fluid in Optical Coherence Tomography (OCT) images is beneficial for ophthalmologists to make an accurate diagnosis. Although semi-supervised OCT fluid segmentation networks enhance their performance by introducing additional unlabeled data, the performance enhancement is limited. To address this, we propose Superpixel and Confident Learning Guide Point Annotations Network (SCLGPA-Net) based on the teacher-student architecture, which can learn OCT fluid segmentation from limited fully-annotated data and abundant point-annotated data. Specifically, we use points to annotate fluid regions in unlabeled OCT images and the Superpixel-Guided Pseudo-Label Generation (SGPLG) module generates pseudo-labels and pixel-level label trust maps from the point annotations. The label trust maps provide an indication of the reliability of the pseudo-labels. Furthermore, we propose the Confident Learning Guided Label Refinement (CLGLR) module identifies error information in the pseudo-labels and leads to further refinement. Experiments on the RETOUCH dataset show that we are able to reduce the need for fully-annotated data by 94.22%, closing the gap with the best fully supervised baselines to a mean IoU of only 2%. Furthermore, we constructed a private 2D OCT fluid segmentation dataset for evaluation. Compared with other methods, comprehensive experimental results demonstrate that the proposed method can achieve excellent performance in OCT fluid segmentation.

Asymptotic analysis of electrohydrodynamic flow through a swarm of porous cylindrical particles

The present article reveals the study of an electrohydrodynamic flow through a membrane composed of a swarm of porous layered cylindrical particles adopting a heat transfer approach. The configuration of the proposed theoretical model is segregated into two regions in which the region proximate to the solid core of the cylindrical particle is a porous region. However, a region surrounded by a porous region is a non-porous (clear fluid) region. The thermal equations are employed under steady-state conditions to establish the temperature distribution when heat conduction prevails over heat convection. The Brinkman and Stokes equations regulate fluid flow through a swarm of porous layered cylindrical particles in porous and non-porous regions, respectively. With the purpose of addressing an electric field in the fluid flow process through a swarm of porous layered cylindrical particles to understand the role of a Hartmann electric number, the momentum equation and the charge density are coupled and nonlinear. The nonlinear second-order differential equation governs the momentum equation and regulates fluid flow through a swarm of porous cylindrical particles. The solutions of the energy equations for both regions are analytically obtained. The asymptotic expansions of velocities for porous and non-porous regions have been derived using the perturbation technique for the small and large values of the nonlinearity parameter α. The effects of various parameters like Hartmann electric number, Grashof number, radiation parameter, viscosity ratio parameter, and porosity of the porous material on the hydrodynamical permeability, Kozeny constant of the membrane, and temperature are analyzed graphically. A noteworthy observation is that a rising Hartmann electric number, the ratio of electric force to the viscous force, enhances the velocity, which is relatively more significant for higher permeability and hence enhances the membrane permeability; however, decay in Kozeny constant is reported with a rising Hartmann electric number. Significant velocity and membrane permeability growth are described with a rising Grashof number, a ratio of thermal buoyancy and viscous forces. The observations from the present study hold promise for advancing our understanding of critical physical and biological applications, including wastewater treatment filtration processes, petroleum reservoir rocks, and blood flow through smooth muscle cells.

TOPOGRAPHICAL EFFECTS ON WAVE SCATTERING BY AN ELASTIC PLATE FLOATING ON TWO-LAYER FLUID

This article illustrates the hydroelastic interactions between surface gravity waves and a floating elastic plate in a two-layer liquid with variable bottom topography under the assumptions of small amplitude waves and potential flow theory. In this study, semi-infinite and finite-length plates are considered. The eigenfunction expansion method is applied in the fluid region with uniform bottom topography. A system of differential equations (mild-slope equations) is solved in the fluid region with variable bottom topography. From the matching and jump conditions, the solution is expressed as a linear algebraic system from which all the unknown constants are computed. We explored the effects of density ratio, depth ratio, and bottom topography on the bending moment, shear force, and the deflection of the elastic plate. Results show that when the density ratio becomes closer to one, the occurred bending moment and shear forces to the elastic plates tend to diminish. The bending moment and shear forces to the pates are higher and lower at a smaller depth ratiofor the incident surface wave and interfacial waves, respectively. The variations in the bending moment, shear force, and plate deflection, caused by surface and interfacial waves, are observed to be in opposite trends, respectively. Bottom profiles similarly affect semi-infinite and finite-length plates when they undergo free-edge conditions. These effects, however, are substantial when the plate is simply supported at the edges. Elastic plate with free edges experiences lower deflection for concave-up and plane-sloping bottoms for incident surface and interfacial waves, respectively.