Helmholtz-Smoluchowski Velocity Research Articles

Intelligent computing for the electro-osmotically modulated peristaltic pumping of blood-based nanofluid

The study delves into a novel application of artificial neural networks within the biomedical realm, specifically focusing on the peristaltic pumping of ionized blood-infused nanofluid using the Casson model. The investigation takes into account the impacts of electrokinetic forces, chemical reaction, thermal radiation and variable thermal conductivity. The endorsed nanofluid model encompasses both thermophoretic and Brownian diffusions. The Nernst-Planck and Poisson equations are used to characterize electroosmotic process. The mathematical model is then numerically solved using NDSolve in Mathematica. The variation in relevant hemodynamic characteristics concerning key flow parameters is explored through numerous graphical representations. Two distinct artificial neural networks have been developed to estimate values for rates of mass and heat transfer. The Levenberg-Marquardt algorithm is used as the training algorithm in network models with multi-layer perceptron architecture. Graphical inspection of the results demonstrates a decrease in blood flow with an elevated Helmholtz-Smoluchowski velocity. A lower pressure gradient is recorded with a higher electroosmotic parameter. Furthermore, an augmentation in the thermal conductivity parameter leads to a reduction in heat transfer rate at the wall. The concentration profile demonstrates an increase with a rise in the chemical reaction parameter. The results obtained from the neural network models exhibit an ideal harmony with the target values. The developed neural network models demonstrated the ability to predict rates of heat and mass transfer values with average deviations of −0.01% and 0.004%, respectively.

ELECTRO-OSMOTIC EFFECT ON PERISTALTIC FLOW OF PHAN–THIEN–TANNER FLUID IN A PLANAR CHANNEL

Abstract There are several factors that can cause the excessive accumulation of biofluid in human tissue, such as pregnancy, local traumas, allergic responses or the use of certain therapeutic medications. This study aims to further investigate the shear-dependent peristaltic flow of Phan–Thien–Tanner (PTT) fluid within a planar channel by incorporating the phenomenon of electro-osmosis. This research is driven by the potential biomedical applications of this knowledge. The non-Newtonian fluid features of the PTT fluid model are considered as physiological fluid in a symmetric planar channel. This study is significant, as it demonstrates that the chyme in the small intestine can be modelled as a PTT fluid. The governing equations for the flow of the ionic liquid, thermal radiation and heat transfer, along with the Poisson–Boltzmann equation within the electrical double layer, are discussed. The long-wavelength ( $\delta \ll 1$ ) and low-Reynolds-number approximations ( $Re \to 0$ ) are used to simplify the simultaneous equations. The solutions analyse the Debye electronic length parameter, Helmholtz–Smoluchowski velocity, Prandtl number and thermal radiation. Additionally, streamlines are used to examine the phenomenon of entrapment. Graphs are used to explain the influence of different parameters on the flow and temperature. The findings of the current model have practical implications in the design of microfluidic devices for different particle transport phenomena at the micro level. Additionally, the noteworthy results highlight the advantages of electro-osmosis in controlling both flow and heat transfer. Ultimately, our objective is to use these findings as a guide for the advancement of lab-on-a-chip systems.

Complex cilia-generated flow of hybrid nanofluid with electroosmosis, viscous dissipation and slippage

In this study, we investigated how electroosmsis, viscous dissipation, and slippage affect the peristaltic flow of complex cilia-generated flow of hybrid nanofluid in a ciliated tube. The complex cilia-generated flow is characterized by a complex sinusoidal wave that transmits along the wall of the tube with a uniform speed having distinct amplitudes. The main objective of this work is to examine how this complex cilia on the wall drives the hybrid nanofluid flow under electroosmosis. The Helmholtz–Smoluchowski equation is used to model the electroosmosis, and the Poisson equation is solved analytically using the Debye-Huckel approximation. The lubrication approach is utilized to simplify the governing equations. The governing non-dimensional equations for hybrid nanofluid are solved exactly using the DSolve command of Mathematica. The results are presented graphically to accomplish the theoretical results from the complex-cilia wave evolution from the necessary flow parameters in an asymmetric tube. The study shows that increasing the electroosmotic parameter leads to an increase in the velocity profile at the boundary and a decrease in the middle of the tube. Conversely, the Helmholtz–Smoluchowski velocity parameter has the opposite effect. The Brinkman parameter increases the temperature of the hybrid nanofluid. The study also presents a graphical analysis of pressure rise and pressure gradient for various values of the parameters. The pressure rise against volumetric flow is rate and pressure gradient increases by increasing the electroosmotic parameter and Helmholtz-Smoluchowski parameter, while it decreases for increasing the velocity slip parameter. The streamlines are drawn to study the trapping phenomena of blood in the hybrid nanofluid flow in an asymmetric tube by the formation of bolus and the division of streamlines. It is observed that the size and number of bolus close to the artery walls increases for electroosmotic parameter while reverse behavior is observed for Helmholtz-Smoluchowski parameter. The tabular presentation of the heat transfer coefficient at the wall is presented. The current results can be used in bio mathematical models to control fluid flow through micro-channels and to investigate ways to cure artery blockages and cancer tumors in biomedicine. The study can also be used to design and optimize microfluidic devices for drug delivery, lab-on-a-chip devices, and other biomedical applications.

Numerical entropy analysis of MHD electro-osmotic flow of peristaltic movement in a nanofluid

The present study investigates the MHD electro-osmotic flow of entropy generation analysis for peristaltic movement in a nanofluid with temperature-dependent viscosity. Long wavelengths, i.e., The magnitude of a wave's energy corresponds directly to its frequency while being inversely related to its wavelength in terms of velocity, temperature, and concentration, govern and confine the flow stream in the laminar region. Ohmic heating and hall effects are also included. Graphs are used to obtain and examine numerical solutions for axial velocity, temperature, concentration, Bejan number, and entropy generation. The effects of this research can help to improve pumping and gastrointestinal movements in different engineering devices. Debye–Huckel and lubrication approximations are studied to access the Boltzmann distribution of electric potential across an electric double layer. The investigations of an existing model are important in illuminating the microfluidics machinery used at the micro level for various transport phenomena in which fluids as well as particles are transported together. The current study has many applications and can be further extended to a three-dimensional profile with appropriate modifications and assumptions. When studying entropy generation, it is essential to examine the irreversible factors, while also taking into account the velocity and thermal slip conditions at channel boundaries. Moreover, the concept of entropy generation holds significant importance in comprehending various biological phenomena. Hence, the current research holds promising implications for both industrial and medical fields. The entropy generation is minimum at left wall of the channel for negative values of Helmholtz-Smoluchowski velocity.

EDL Induced Electro-magnetized Modified Hybrid Nano-blood Circulation in an Endoscopic Fatty Charged Arterial Indented Tract.

The electrokinetic process for streaming fluids in magnetic environments is emerging due to its immense applications in medical and biochemical industrial domains. In this context, our proposed model seeks to inquire into the hemodynamic characteristics of electro-magnetized blood blended with trihybrid nanoparticles circulation induced by electro-osmotic forces in an endoscopic charged arterial annular indented tract. This steaming model also invokes the consequences of variable Lorentz attractive force, buoyancy force, heat source, viscous and Joule warming, arterial wall properties, and sliding phenomena for featuring more realistic problems in blood flows. Different shapes of suspended trihybrid nanoparticles, such as spheres, bricks, cylinders, and platelets, are included in the model formation. Electro-magnetized modified hybrid nano-blood is an electro-conductive solution comprising blood as base fluid and magnetized trihybrid nanoparticles (copper, gold, and alumina). Closed-form solution in terms of Bessel's functions is gotten for electro-osmotic potential due to the electric double layer (EDL). The homotopy perturbation methodology is implemented in order to track down the convergent series solutions of non-linear coupled flow equations being elicited. The physical attributes of distinct evolving parameters on the different dimensionless hemodynamic profiles and quantities of interest are elucidated evocatively via a sort of graphs and charts. The ancillary outcomes proved that the Debye-Hückel parameter and Helmholtz-Smoluchowski velocity have a dual impact on the ionized bloodstream. The bloodstream rapidity is alleviated/boosted for the assisting/opposing electroosmosis process. Cooling of ionized blood in the endoscopic arterial conduit is achieved with lower Hartmann numbers. Copper-gold-alumina/blood exhibits a superior heat transmission rate across the arterial wall than copper-gold-blood, copper-blood, and pure blood. Additionally, the contour topology for the bloodstream in the flow domain is briefly elaborated. The contour distribution is significantly amended due to the variant of the Debye-Hückel parameter. The model's new findings may be invaluable in electro-magneto-endoscopic operation, electro-magneto-treatment for cancer, surgical process, etc.

Alteration in electroosmotic flow of couple stress fluids through membrane based microchannel

The fundamentals of electroosmosis are the most fascinating mechanism to induce flow of ionic solution under the effect of external electric field. The electroosmotic flow of the couple stress fluid in a microchannel with an active membrane pumping is analysed in the present model. The upper wall experiences membrane kinematics, generates the pressure to drive the fluid in the microchannel. Governing equations are formulated based on the mass and momentum conservation, and electric potential distribution of ions in diffuse layer. The suitable boundary conditions for the model have been considered. An analytical approach is employed to derive the solutions under the lubrication approximation, and the Debye–Hückel approximation. The effects of electric double layer thickness, couple stress parameter, and Helmholtz-Smoluchowski velocity on the velocity profile, pressure difference, net flow rate, induced streamline velocity, and local wall shear stress are computed for discussion of the physical significance of the model and its applications. Results reveal that electroosmosis mechanisms (axial electric field and electric double layer thickness) has remarkable role in modulating the fluids (Newtonian and non-Newtonian) flow driven by the rhythmic propulsion of membranes in microchannel. It is also worth mentioning that non-Newtonian fluids (couple stress fluids) need more external forces (electric force) to be pumped as compared to Newtonian fluids. Furthermore, it can be analysed that thinner electric double layers (EDLs) elevate wall shear stress, whereas stronger electric fields result in decreased wall shear stress. The results of the model help in designing smart membrane based electric pump for the use in various microscale transport phenomena of bio microfluidics systems.

Electroosmotically induced peristaltic flow of a hybrid nanofluid in asymmetric channel: Revolutionizing nanofluid engineering

The exploration of electroosmotic peristaltic flow in asymmetric channels using hybrid non-Newtonian nanofluids holds significant promise across multiple domains. From microfluidics and electronics cooling to energy systems and biomedical applications, its implications are vast. By leveraging the distinctive attributes of nanofluids and the precision offered by electroosmotic and peristaltic flow, this research has the potential to drive the development of more efficient and innovative designs in these diverse fields. The current investigation reveals an analysis of heat transfer concerning hybrid nano liquid based on water. This nano liquid is influenced by both electroosmosis and peristalsis, operating simultaneously. Within this water-based hybrid nanofluid, there are nanoparticles composed of copper and iron oxide (Fe2O3−Cu/H2O). The study investigates into characteristics of flow and heat transport processes, considering key factors such as the applied electric and magnetic fields, thermal conductivity, mixed convection, shape of nanoparticles, variable viscosity, and assumptions related to Ohmic heating. Thermal and velocity slip boundary conditions are considered. To handle the analysis, the Poisson-Boltzmann equation is approximated using the Debye-Hückel approximation. The governing equations are then simplified using lubrication approximation. To solve the resulting system of dimensionless differential equations, NDSolve build in command of computational package Mathematica is employed. The outcomes of study affirm that inclusion of nanomaterials plays a vital role in enhancing heat transfer processes. Specifically, an increase in Joule heating and electromagnetic parameters contributes to a higher heat transfer rate at the boundary. Additionally, the incorporation of nanomaterials leads to a decrease in the flow rate of the nanofluid due to an increase in Helmholtz-Smoluchowski velocity. Furthermore, the heat transfer rate at wall diminishes as the Hartman number and Helmholtz-Smoluchowski velocity are increased. Showcasing the potential to enhance heat transfer, microfluidic devices, and various systems by harnessing the distinctive characteristics of hybrid nanofluids and regulating flow through peristaltic and electroosmotic methods. Providing insights into potential applications and industries that could profit from these findings, including microfluidics, electronics cooling, biomedical devices, and energy systems.

Numerical treatment and global error estimation for thermal electro-osmosis effect on non-Newtonian nanofluid flow with time periodic variations

The essential purpose of this study is to discuss the impact of time-periodic variations on mixed convection heat transfer for MHD Eyring-Powell nanofluid. The fluid flows through a non-Darcy porous medium over an infinite vertical plate. The effects of viscous dissipation, Ohmic dissipation, electro-osmosis force, heat source, thermal radiation, Dufour feature, and chemical reaction are presumed. The system of partial differential equations which governs the problem is transformed into a system of non-linear algebraic equations and then an explicit finite difference approach is espoused to solve these nonlinear algebraic equations. The numerical results for the velocity, temperature, and nanoparticles concentration distributions are computed and displayed through a set of graphs. Also, the skin friction coefficient, reduced Nusselt number, and Sherwood number are computed numerically for various values of the physical parameters. It is found that the velocity becomes greater with an elevation in the value of the Helmholtz–Smoluchowski velocity. Meanwhile, it enlarges with rising in the value of the electro-osmotic parameter. The rise in the value of the thermal radiation parameter causes a dwindling influence on both temperature and nanoparticles concentration. Investigations of these effects together are very useful due to their important vital applications in various scientific fields, especially in medicine and medical industries, such as endoscopes, respirators, and diverse medical implementations, as nanoparticles can be utilized in the remedy of cancer tumors. Additionally, electroosmotic flow is important due to its ability to control fluid movement and enhance mass transport, making it valuable in various application such as sample separation, drug delivery, and DNA analysis, offering enhanced efficiency and sensitivity.

Dynamics of blood conveying copper, gold, and titania nanoparticles through the diverging/converging ciliary micro-vessel: Further analysis of ternary-hybrid nanofluid

Following the relevance and significance of blood transporting copper, gold, and titania nanoparticles through the diverging/converging ciliary micro-vessel in biomedical and physiological applications, little is known about the dynamics using Jeffrey fluid model, with a focus on the influence of specific regulatory factors. This report presents the results of a mathematical simulation for evaluating the hemodynamic effects of a bloodstream infused with ternary hybrid nanoparticles through a diverging/converging ciliary micro-vessel while taking into account the combined effects of a heat source, buoyancy, viscoelastic, electro-osmotic, and Lorentz forces. The homotopic perturbing approach was used to address the re-scaled leading equations. The ternary-hybrid nano-blood velocity is elevated by electroosmosis and the aiding Helmholtz-Smoluchowski velocity parameters in the core domain of the diverging/converging tube, but the opposite tendency is seen in the tube's perimeter zone. The circulation of the ternary-hybrid nanofluid is reduced by lengthening the cilia. Diversely shaped ternary-hybrid nanoparticles are employed in surgical procedures to attain the required heat flow rate. Increased blood loadings of ternary-hybrid nanoparticles are associated with increased blood temperature. Additionally, ternary nanoparticles have more effective physio-thermal properties when injected into the circulation (117.6%) compared to binary (89%) or unitary (48.3%) nanoparticles. Additionally, the divergent micro-vessel wall has a faster heat transfer rate than the convergent one.

A multiphase ciliary flow of Casson fluid in a porous channel under the effects of electroosmosis and MHD: Exact solutions

The electro-osmosis effects on ciliary multiphase flow have broad applications in diverse fields, including microfluidics, biotechnology, chemical engineering, and environmental sciences. In the current analysis, the authors have elaborated the electro-osmosis effects on a ciliary two-phase channel flow of Casson fluid in the presence of solid particles and magnetic effects. The governing equations have been considered for the physical problem by applying the wave frame and dimensionless transformations. A lubrication approach has also been followed by the equations. Systems of differential equations have been solved on well-known software Mathematica by a built-in DSolve tool to acquire the exact solutions. From graphical evidences, it is observed that Helmholtz Smoluchowski velocity factor and solid particles contribution affects the electro-kinetic energy and reduces the flow speed.

Electroosmotic flow of cobalt-ferrite nanoparticles in water and ethylene glycol through a ciliary annulus: A biomedical application.

Unique magnetic characteristics of cobalt-ferrite nanoparticles make them suitable for biological imaging and therapeutic applications. Understanding their activity in nanofluids via the ciliary annulus could lead to better contrast agents for magnetic resonance imaging and improved cancer therapy and other medical therapies. This article provides a comprehensive analysis of the theoretical conclusions regarding the transport of a nanofluid by electroosmosis across a ciliary annulus. The nanofluid consists of cobalt-ferrite nanoparticles (CoFe2 O4 ), water (H2 O), and ethylene glycol (C2 H6 O2 ). As part of the investigation into constructing a physical model, mathematical analysis is performed based on the conservation of mass, momentum, and energy. Dimension-free analysis and mathematical constraints are utilized to learn more about the system. By generating differential equations and including suitable boundary conditions, one can obtain exact solutions, which can then be visually inspected. Recent studies have demonstrated an inverse relationship between flow velocity and cilia length, zeta potential, and Helmholtz-Smoluchowski velocity. The streamlines show that the growth of the trapping boluses is affected by several factors, including the nanoparticles' volume fraction, the cilia's length, the amplitude ratio, the eccentricity, and the zeta potential. These results not only shed light on how nanofluids move, but they also have potential applications in microfluidics, heat transfer, and biomedical engineering.

Modified Darcy’s law and couple stress effects on electro-osmotic flow of non-Newtonian nanofluid with peristalsis

In this study, we focused on the heat transfer through a uniformly inclined rectangular duct caused by the electro-osmotic peristaltic flow of an unsteady non-Newtonian nanofluid. With couple stress, the fluid obeys the Papanastasiou model. The flow is through a porous medium that follows Darcy’s law in a modified form. In addition, Dufour and Soret effects, mixed convection, the impacts of a chemical reaction, and the effects of viscous couple stress dissipation are all considered. The governing equations that explain the velocity, temperature, and concentration of nanoparticles are simplified when wave transformation is used. The homotopy perturbation method was used to solve these equations analytically. Additionally, a collection of figures is used to discuss and visually illustrate the consequences of the physical characteristics. In fact, the modified Darcy’s law makes the velocity gradient appear in the momentum equation, which increases the contribution of the velocity gradient to the velocity profile. In addition, the electro-osmotic parameter and Helmholtz-Smoluchowski velocity have a significant impact on the velocity gradient’s direction, as well as the velocity gradient’s ability to be either positive or negative, depending on their values. In addition, in the case of forced convection, the values of the Nusselt number and the Sherwood number are highly affected by the value of Helmholtz–Smoluchowski velocity. The current findings have applications in biology and medicine, particularly in cancer therapy, which involves peristaltic blood pumps(arteries) and suspended gold nanoparticles (nanofluid). According to our knowledge, no prior studies have merged the couple stress Papanastasiou model and the modified Darcy’s law.

An electroosmotic peristaltic flow of graphene-lubrication oil nanofluid through a symmetric channel

The purpose of this manuscript is to analyze the electroosmotic peristaltic motion of graphene-lubrication oil nanofluid. Rheological characteristics of such fluids are predicted by using the Carreau’s model. Effects of magnetic field, electric field, viscous dissipation, Joule heating, Brownian motion and thermophoresis are also reckoned. Debye-Hückel linearization and lubrication approach are employed in mathematical modeling. Obtained non-linear system of equations are analytically solved by using the builtin command NdSolve and parametric study is carried out to visualize the variation in temperature, velocity, heat transfer rate, concentration profiles, pressure gradient and pressure rise per wavelength. Results unveil that strong electroosmotic parameter enhances both velocity and temperature. Temperature and velocity decline on the enlargement of the Helmholtz-Smoluchowski velocity. Variation in electroosmotic parameter decreases and Helmholtz-Smoluchowski velocity increases mass transfer rate. Pumping region can also be maintained by thickening and thinning the Electric Double Layer (EDL). Present study has useful applications in industries, defect sensor, energy saving, domestic air conditioning, cooling power electronic components and heat extraction and heat transportation.

Dynamic patterns of electroosmosis peristaltic flow of a Bingham fluid model in a complex wavy microchannel

The purpose of this paper is to present a rigorous analysis of streamline patterns and their bifurcation to a viscoplastic Bingham fluid model that involves heat and mass transfer in an electroosmotic flow through a complex wavy microchannel. The Bingham fluid act as a solid medium in the core layer, which divides the channel into three distinct sections utilized to model the problem as a switched dynamical system between these zones. To track multiple steady states (stagnation points) and related trapping phenomena, we perform both analytical and numerical bifurcation analysis of each subsystem with respect to different physical effects such as electrical double layer thickness and Helmholtz-Smoluchowski velocity. The key feature of the technique presented here is its ability to reveal the peristaltic transport characteristics of the Bingham fluid model in the presence or absence of symmetric flow properties. The primary novelty here is the ability to regulate the location and stability of the equilibrium points in the domain of interest. This leads to the detection of global bifurcations that reflect important dynamic elements of the model. Our results highlighted a new category of complex behavior that controls transitions between qualitatively different transport mechanisms, as well as a class of non-classical trapping phenomena.

Heat and mass transfer analysis of non-Newtonian radiative nanofluid flow driven by the combined action of peristalsis and electroosmosis

The present numerical investigation uncovers the flow, heat, and mass transfer of ethylene glycol-based nanofluid (BN-EG) led by the combined impacts of peristaltic pumping and electroosmosis. The thermal conductivity of carrier liquid is deemed to change with temperature. Further, the features of electric field, Ohmic heating, radiative heat flux, mixed convection, and magnetic field are taken. Mathematical modeling is conducted under the assumption of lubrication theory. The nonlinear-coupled equations are addressed numerically by implementing Shooting method. The effective results of all physical constraints linked with the flow model are vigilantly studied and highlighted through various curves. The observations obtained from current analysis reveal that temperature augments with higher electroosmotic parameter. However, the Joule heating parameter increases the rate of heat transmission, while a lower rate of heat transfer is perceived for the radiation parameter. An increment in Helmholtz–Smoluchowski velocity increases the velocity profile. Pressure gradient rises in a forward way when electrical field favors peristaltic flow. Concentration of nanomaterial considerably declines when concentration Grashoff number is assigned higher values.

Electroosmosis oriented flow of Jeffrey viscoelastic model through scraped surface heat exchanger

Scraped surface heat exchanger (SSHE) is vibrantly utilized in various industries. The heat exchanger devices play pivotal role in the energy transfer phenomenon between the fluids, and it improves the efficient use of energy. The steady isothermal flow of a rheological aqueous ionic solution in a narrow gap scraped surface heat exchanger is explored. The mathematical model is established with the aid of lubrication approximation theory and extracted analytical solution. Exact analytical expressions are gathered for velocities, volume fluxes, pressure gradients, pressure at the edges of the blades and stream functions in the various stations of SSHE. Strength of significant flow parameters on the velocities, volume fluxes, pressure gradients, pressure at the edges of the blades and stream functions is revealed with aid of various plots. Significant enhancement in the velocity profile is observed in main domain of the flow with increasing ratio of relaxation to retardation time parameter and Helmholtz Smoluchowski velocity. While, it is observed that electro-osmotic parameter creates impediments to the flow.

Mathematical model for numerical simulations of thermal energy of nano-fluid in a complex peristaltic transport within a curved passage:Pharmacological and engineering biomedical application

The proposed scientific model is based on peristaltic movement of nanofluid within a curved channel of an electrically conducting material. To obtain a numerical solution for the electric potential function, the Debye-Hückel and Lubrication theory approximations are used. Stream function, electroosmotic, axial velocity, and curvature are all estimated using low zeta potentials. The behaviour of electroosmotic flow governs two dimensionless parameters: the Debye-Hückel parameter and the Helmholtz-Smoluchowski velocity. It is also investigated how curvature influences blood flow caused by electroosmosis. It was also investigated how the curvature parameter affects the nano-fluid flow induced by electroosmosis. Nano-biofluid evaluation with varied particle shapes such as cylinder, platelet, brick, and blade flowing in complex travelling wave. It can be stated that the velocity component of nanofluid is decreasing due to magnetic force, particle size, and wall compliance. It is also stated that nanoparticles considerably improve the thermal conductivity of the fluid.

Hall currents and EDL effects on multiphase wavy flow of Carreau fluid in a microchannel having oscillating walls: A numerical study

In this analysis, the authors reveal the effects of electro-osmosis on the multiphase flow of Carreau fluid in a microchannel in the presence of Hall currents and solid particles. Moreover, the compliant channel walls are subject to oscillation occurring at the surface. To investigate the problem quantitatively, mathematical models for fluid phase and particulate phase have been structured. A lubrication approach is adopted due to laminar flow and the small dimensions of the channel. To produce the data, a system of differential equations is produced with the help of a numerical process performed on Mathematica through a built-in NDSolve tool. The results are presented graphically to examine the effects of various physical factors on the flow quantities. From pictorial discussion, it is gathered that the Helmholtz–Smoluchowski velocity parameter and the presence of an increasing amount of solid particles increasing the heat exchange while producing electro-kinetic energy. It is also found that velocity is a direct function of solid particles and compliant walls, but an inverse link is seen in the presence of electro-kinetic energy. Such studies can be employed with microfluidic devices and \may also be productive in medical and mechanical research.

Electroosmosis Augmented MHD Third-Grade Fluid with Slip and Variable Properties: An Application for Blood Flow in Arteries

The electroosmotic force effect on the peristaltic motion of the third-grade fluid is considered in a uniform channel. The governing equations that supplement the flow are designed for long wavelengths and low Reynolds numbers. Solutions are obtained for velocity, temperature, concentration, and trapping by considering the variable liquid properties for analyzing the various parameter effects. These effects are depicted through graphs and the relevance is discussed. The variable fluid properties have a declining impact on the velocity and temperature fields. Increasing the Helmholtz–Smoluchowski velocity values decreases the velocity field. Temperature decreases as the Deborah number increases. The velocity slip characteristics rise, and the trapping bolus’s size shrinks. The results of this paper may be beneficial in understanding the control of microvascular transport in the time of fractionation of blood into plasma and erythrocytes.

EMHD ciliated pumping of viscoelastic liquid in a complex convergent/divergent channel

Because of the diverse applications of cilia propulsions and viscoelastic fluids in biochemical engineering, we consider the flow of a non-Newtonian fluid through both convergent and divergent channels. The transportation of fluid through the flow geometry takes place due to metachronal waves that exist at both walls. Expressions of the Jeffrey fluid in the presence of magnetic and electric fields are used in the development of rheological equations. The mathematical analysis is carried out under the valid physiological assumption of creeping phenomena and long-wavelength approximation in the wave frames. The solutions of rheological equations are obtained analytically with an integration scheme. The transport features are discussed for numerous sundry variables via the Mathematica Software 11.0. Comparative studies among viscous and viscoelastic liquids also argued for both complex convergent and divergent channels. The special nature of metachronal waves (i.e. wavy pattern) is used in both boundary walls. The viscoelastic and magnetic parameters have played an important role to boost of the velocity profile magnitude. The impacts of the cilia length and Helmholtz–Smoluchowski velocity parameters have a significant act in the augmentation of pressure gradient and flow rate under the influence of magnetic and electric fields (EMHD phenomena) for the divergent channel. The current mathematical formulation gives information to the medical students about how to handle the transportation of viscoelastic fluids in both convergent and divergent channels via ciliated walls and electro-magnetic devices. The consequences of the present analysis have remarkable applications in micro-ciliated pumps, blood pumping in uniform and non-uniform arteries, and the rheology of viscoelastic liquids in different chemical processes.