Jeffrey Fluid Model Research Articles

Simulation of blood flow in a tapered artery with ternary hybrid nanofluid and Jeffrey model

This research simulates flow of blood in a tapered peristaltic artery integrating ternary hybrid nanofluid using the Jeffrey fluid model. The simulation examines the effects of Au, Fe3O4, and Ag nanoparticles on the flow. The artery, modeled as a peristaltic channel, is subjected to nonlinear thermal radiation, magnetic forces, and heat source. The problem is formulated using non-linear Cartesian partial differential equations, which are then transformed into dimensionless form without approximations. Adomian Decomposition Method (ADM) is employed to solve these equations, revealing how normal and shear stress, normal and axial velocities, induced magnetic fields, and temperature profiles vary with changes in relevant parameters. Additionally, biological factors are considered to graph streamlines, providing a comprehensive analysis of the flow dynamics. Some notable results include that adding ternary nanoparticles increases the Nusselt number by 26.03% in Newtonian fluids and 158.69% in Jeffrey fluids, and increasing tapering parameters and wavenumber improves axial and normal velocities, heat transfer, and flow complexity.

Exploring the Dynamic Behavior of a Tapered Stenosed Artery: An Investigation into Its Unsteady Model

In this communication, blood flow is considered in a two-phase model of the tapered stenosed artery. Non-Newtonian and Newtonian models are considered in inner and outer regions, respectively. The transverse magnetic field is applied externally on the presumed pulsatile flow of blood to examine the nature of blood flow. It is anticipated that, in the inner region, blood follows the Jeffrey fluid model, and in the outer region, it follows the Bingham Plastic fluid model. The mathematical model of this system is formulated, a non-dimensionalization technique is used, and a numerical solution is obtained using the Finite difference method, one of the most suitable numerical methods for the formulated problem. The expressions for the primary/fundamental characteristics in determining the effect of blood flow are developed to explore the consequence of hematocrit, time component, tapering angle, and magnetic field. Scilab software is employed for mathematical simulations, revealing that flow characteristics within a stenosed artery undergo significant alterations, while the presence of a magnetic field aids in partially regulating the flow characteristics.

Thermal storage study and enhancement of heat transfer through hybrid Jeffrey nanofluid flow in ducts under peristaltic motion with entropy generation

This article examines the analysis of peristaltic transport within a vertical sinusoidal wavy duct using a hybrid nanofluid composed of deionized blood and nanoparticles such as Graphene Oxide (Go) and Molybdenum disulfide (MoS2). The study also investigates volumetric entropy generation, employing the Jeffrey fluid model known for its representation of both viscous and elastic fluid behaviors. The mathematical framework integrates Navier–Stokes equations and the energy equation. Simplifying the analysis, non-dimensional equations are derived for the hybrid nanofluid in a two-dimensional coordinate system, assuming a long wavelength (δ < 1) and low Reynolds number (Re). The Galerkin finite element method via MATLAB is employed for numerical solutions. The results, depicted graphically using MATLAB, offer insights into temperature variations and the two-dimensional peristaltic flow concerning different parameters. To the best of authors knowledge entropy generation analysis is still not carried out for blood base Go-MoS2 hybrid nanofluid in a vertical wavy channel. The aim of the present study is to explore the contribution of significant parameters on entropy generation. One of the key findings includes that flow rate and Brinkmann number contribute to enhance entropy generation in presence of hybrid nanofluid.

Influence of Suction and Injection on Peristaltic Mechanism of a Jeffrey Nanofluid in a Vertical Channel with Complete Slip Effects

The main goal of the current study is to understand how the peristaltic system of a Jeffrey nanofluid operating in a vertical tube with complete slip properties is influenced by suction and injection. The peristaltic flow was examined by several researchers using various biological fluid types. The majority of the authors used viscous (Newtonian) fluids to illustrate the peristaltic flow mechanism. Because of its uses in industry, non-Newtonian fluids have attracted a great deal of attention. There are numerous models for non-Newtonian liquids because of the complexity of fluids. The Jeffrey fluid model is the most straightforward linear model to depict the non-Newtonian fluid characteristics for which it is reasonable to expect that accurate or analytical solutions would eventually be discovered. Nanofluids are innovative substances that have endless applications in engineering, biology, medicine and other fields. This mathematical model can be used effectively to transport cervical cancer in the tiny blood channels of the cervix. The resulting flow model is then effectively simulated with the appropriate assumptions of a small Reynolds number and long wavelength. The governing conservation equations are then established. Analytical solutions have been found for, pressure rates per wavelength, temperature, velocity and concentrations of nanoparticles in the resultant flow problem. Using the software WOLFRAM MATHEMATICA, the effects of all physical parameters on streamline, velocity, temperature, concentration fields, pressure gradient, frictional force and pressure rate are graphically analyzed. We observed in both 2D-plot and 3D-plot that we increasing the slip parameters β1 and β2 lead to increase the velocity profile. By raising the Jeffrey nanofluid parameter, the pressure rise is decreased. With frictional force, the opposite behavior is observed. The effect of suction and injection parameter k on the trapping bolus, which gets greater as k is higher.

Analysis of two layered peristaltic-ciliary transport of Jeffrey fluid and in vitro preimplantation embryo development

The analysis of peristaltic-ciliary transport in the human female fallopian tube, specifically in relation to the growing embryo, is a matter of considerable physiological importance. This paper proposes a biomechanical model that incorporates a finite permeable tube consisting of two layers, where the Jeffrey fluid model characterizes the viscoelastic properties of the growing embryo and continuously secreting fluid. Jeffrey fluid entering with some negative pressure gradient forms the core fluid layer while continuously secreting Jeffrey fluid forms the peripheral fluid layer. The resulting partial differential equations are solved for closed-form solutions after employing the assumption of long wavelength. The analysis delineated that increasing the constant secretion velocity, Darcy number, and Reynolds number leads to a decrease in the appropriate residue time of the core fluid layer and a reduction in the size of the secreting fluid bolus in the peripheral fluid layer. Eventually, the boluses completely disappear when the constant secretion velocity exceeds 3.0 Progesterone (P4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_4$$\\end{document}) and estradiol (E2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_2$$\\end{document}) directly regulate the transportation of the growing embryo, while luteinizing hormone (LH) and follicle-stimulating hormone (FSH), prolactin, anti-mullerian hormone (AMH), and thyroid-stimulating hormone (TSH) have an indirect effects. Based on the number and size of blastomeres, the percentage of fragmentation, and the presence of multinucleated blastomeres two groups were formed in an in vitro experiment. Out of 50 patients, 26 (76.5%) were pregnant in a group of the good quality embryos, and only 8 (23.5%) were in a group of the bad quality embryos. The transport of growing embryo in the human fallopian tube and preimplantation development of human embryos in in vitro are constraint by baseline hormones FSH, LH, prolactin, E2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{2}$$\\end{document}, AMH, and TSH.

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 novel model for viscoelastic fluid flow and heat near a stretchable plate using variable fluid properties: A computational study

This article is concerned with the boundary layer formations over a deforming plane heated surface in a viscoelastic fluid having temperature-dependent physical properties. Viscoelastic fluid obeys a well-accepted Jeffrey fluid model that characterizes both relaxation and retardation times phenomena. Mathematical modeling is performed by considering exponential variations in viscosity, thermal conductivity, relaxation time, and retardation time with temperature. Transport equations are formulated under the aforesaid assumption and are solved for self-similar solutions using a numerical scheme. Solutions are utilized to generate streamlines and isotherms in both Newtonian and viscoelastic fluids. The momentum and thermal layers are specifically scrutinized for various controlling parameters. Illustrative results are included reflecting the consequences of variable physical properties on the induced viscoelastic fluid motion and accompanying heat transfer. In addition, skin friction factor for Jeffrey fluid with variable properties is evaluated and described.

Electro-osmotic effect on the heat and mass transfer of a viscoelastic nanofluid flow in a curved channel

For the past two decades, nanofluids have become the interest of researchers and engineers because of their thermo-physical features. The aim of the current investigation is to investigate the thermal behavior of peristaltically supporting viscoelastic tiny particles endorsed by electro-osmotic force. The Debye-Huckel linearization scheme and zero Reynolds assumptions are used to simplify the governing equations. The current formulation deals with the peristaltic motion of nanofluid in a two-dimensional curved channel. The complex arrangement of sinusoidal waves is used to enhance the pumping performance at the boundary walls. In the present analysis, the Buongiorno formulation is used for nanofluids. The Jeffrey fluid model is used in the current study as a viscoelastic fluid due to its both viscous and elastic features. The numerical solution is obtained using the NDsolve procedure. The graphs of flow features, such as stream function, axial velocity, temperature field, mass concentration, and electric potential function are plotted for various rheological parameters. Quantitative results related to the heat transfer coefficient and Sherwood number for different values of flow parameters are also provided. The asymmetry nature is observed in the diagram of axial velocity due to the curved shape of the flow regime. The mass concentration is enhanced (reduced) by aggregating thermal (Brownian) motion parameter. The temperature and mass concentration are enhanced by increasing Prandtl and Eckert numbers. Comparison between Newtonian and viscoelastic model is also argued in the current formulation. This study gives information of biological fluids flow relevance to micro-medical devices, nanoscale devices, electro-osmotic separation devices and complex pumps via peristaltic pumping.

Fractionalized Jeffrey fluid model for predicting magnetic nanoparticles trajectory: A physiological aspects of drug targeting

Fractionalized Jeffrey fluid model for predicting magnetic nanoparticles trajectory: A physiological aspects of drug targeting

Mathematical modelling on peristaltic motion and temperature distribution of dusty Jeffrey fluid under the influence of variable viscosity

ABSTRACT This study describes the behavior of peristaltic motion and temperature distribution of dusty Jeffrey fluid with variable viscosity. The flow-anchored equations are computed by assuming a low Reynolds number and long wavelength deliberations. The solution of the mathematical framework is heeded analytically by using Bernoulli’s rule of integration technique for velocity and temperature distribution, volume flow rate, and pressure rise. Pumping characteristics are studied based on different pressure ranges. The dynamics of various coherent parameters are deliberated through graphical elucidation. In fluid transmission, an interesting phenomenon is trapping in which a bolus is transported with the speed of the wave and this trapped bolus is pushed forward along the peristaltic wave. This trapping mechanism is visualized with the aid of contour plots and reveals that the size of the trapped bolus shows opposite behavior in both cases by increasing the viscosity parameter. The current inquiry is also designated for Newtonian fluid as a special case. The novelty of this work is to explain the Jeffrey fluid model which is capable of describing stress relaxation properties that normally lag in viscous fluids, thus this article clearly demonstrated the importance of choosing variable viscosity according to the requirement of the concerned fields. The outcome of this investigation can as well aid in understanding the transport phenomena in the human physiological system.

Electro-osmotically generalized bio-rheological fluid flowing through a ciliated passage

In this article, we have investigated a non-Newtonian Jeffrey fluid model, which shows the role of cilia generated metachronal waves in a vertical tube. Electroosmosis effects, a viscous dissipation term is also adopted in this current analysis. The partial differential equations that govern the flow are transformed into a non-dimensional form by considering a low wavelength and small Reynolds number approximations. The obtained set of coupled ordinary differential equations is further solved by using Mathematica solver to get the required flow properties. The current model's output has important heat transfer rate applications in the ciliated channel due to the enhanced viscous dissipation effects, which can be used for the analysis of various areas of biological transport processes such as to design artificial cilia and for the operation of some mechanical devices.

Impact of hydrodynamics and rheology of the ion partitioning effect on electrokinetic flow through a soft annulus with a retentive and absorptive wall.

The theoretical analysis for the mass transfer process of an oscillatory electroosmotic flow (EOF) in the fractional Jeffrey fluid model is studied through a polyelectrolyte layer (PEL) coated cylindrical annulus with reversible and irreversible wall reactions. The ion partitioning effect is observed due to the difference in permittivity of the PEL and the electrolyte solution, which is accounted for by the Born energy. Considering ion partitioning effects, analytical solutions for induced potential and axial velocity are presented, respectively in both the PEL and electrolyte region from the modified Poisson-Boltzmann equation and the Cauchy momentum equation with a proper constitutive equation, respectively. The Maxwell fluid and classical viscous Newtonian fluid models can be achieved separately by adjusting the relaxation and retardation time in the constitutive equation of this model. The analytical solution of the convection-diffusion equation for solute transport is established in the full domain. The separation of species is found to be dependent mainly on the Damköhler number, absorption parameter, phase partitioning coefficient, etc. It is observed that the osmotic pressure increases with the thickness and fixed charge density of the PEL. The velocity decreases with an increase in the permittivity difference of these layers. Our results suggest that the separation may be achieved through a difference in absorption kinetics.

Wall consequences for the peristaltic movement of non-Newtonian fluid in an inclined conduit

The ongoing work elaborates the development of non-Newtonian fluid utilizing Jeffrey fluid model through an inclined non-uniform peristaltic conduit considering under the lubrication approach. Axial and transverse mean velocities have been solved analytically and the effect of promising flow parameters on the velocity, trapping phenomenon has been analyzed through graphs. The current study has a wide range of applications in science and biomedical designing.

Clay-based cementitious nanofluid flow subjected to Newtonian heating

In recent years, a novel technique for producing robust cementitious materials, called nanocomposites, has emerged. These materials are comprised of clay minerals and polymers. As a result, a vertical flat plate has been used to evaluate a clay-based cementitious nanofluid in this research. The impacts of first-order chemical reactions, heat generation/heat absorption, and the Jeffrey fluid model are taken into account for the study of flow. Newtonian heating and the conditions for slippage velocity have also been considered. The mathematical problem for the flow analysis has been established in relations of partially coupled partial differential equations and the model has been generalized using constant proportional Caputo (CPC) fractional derivative. The problem is solved using the Laplace transform technique to provide precise analytical solutions. On the concentration, temperature, and velocity fields, the physics of a number of crucial flow parameters have been examined graphically. The acquired results have been condensed to a very well-known published work to verify the validity of the current work. It is important to note here that the rate of heat transfer in the fluid decreases by 10.17% by adding clay nanoparticles, while the rate of mass transfer decrease by 1.31% when the value of [Formula: see text] reaches 0.04.

EDL aspect in cilia-regulated bloodstream infused with hybridized nanoparticles via a microtube under a strong field of magnetic attraction

Cilia-regulated micro-scale transit via assorted micro and nanofluidic devices that employ EDL phenomena dictates drugs and physiological constituent delivery. Stirred by these implications, the present mathematical simulation intends to unravel the electric double layer (EDL) aspect in a cilia-attenuated peristaltic transport of viscoelastic ionized blood diffused with hybridized nanoparticles inside a microtube due to its impressive nanomedicine functionalities. A magnetic field extraordinarily durable is usually enforced to the blood transit via a cilia-layered microtube to unfold the electromagnetic (Hall and ion-slip currents) facts. An electric field aligned axially is imputed to the bloodstream. In this modelling, the collective effects of buoyancy force, viscous dissipation, and heat source are also evoked. Gold (Au) and copper (Cu) nanoparticles are selected in the hybridizing process to prepare the requisite hybrid nano-blood. Four unlike geometrical shapes (sphere, brick, cylinder and platelet) of nanoparticles are considered. The Jeffrey fluid model is favoured to emulate the rheological functionality of viscoelastic hybrid nano-blood. The homotopy perturbation method (HPM) is assigned to evaluate the analytical series solution upon simplifying the normalized model equations employing lubrication and Debye-Hückel linearization postulates. The changes in pertinent factors lead to an amendment in hemodynamical attributes, which are elucidated via graphs. The contribution of electro-osmotic force and electromagnetic events (Hall and ion-slip currents) are acknowledged to boost up the bloodstream in the core part of the microtube while impeding it close to the tube wall. The growth in the heat exchange rate for hybrid nano blood (201.5% for Au-Cu/blood) is higher than for nano blood (86.27% for Cu-blood and 148.4% for Au-blood). The captivated boluses expand for Hall and ion-slip, EDL and cilia length factors. This search could benefit the medical domain, such as haematology, haemato-oncology, radiology, pulmonology, electrobiology, etc. • Electric double layer (EDL) aspect in a cilia-attenuated peristaltic transit of viscoelastic blood diffused with hybridized nanoparticles inside a microtube in attendance of stronger magnetic influence is presented. • In this modelling, the cumulative effects of buoyancy force, viscous dissipation, and heat source are also evoked. • The electro-osmotic body force assists the blood flow in the core area of the micro-vessel and resists it in the peripheral region of the micro-vessel. • The augmentation in heat exchange rate for hybridized nanoblood (201.5% for Au-Cu/blood) is greater than nanoblood (86.27% for Cu-blood, and 148.4% for Au-blood). • The captivated boluses notably expanded due to thinner EDL, stronger Hall and ion-slip currents or longer cilia length.

Theoretical analysis of electrical double layer effects on the multiphase flow of Jeffrey fluid through a divergent channel with lubricated walls

A theoretical study of two-phase non-Newtonian fluid with heat transfer is presented in this article. Jeffrey fluid model is used as the base liquid to form a multiphase suspension with the help of gold particles. Heating effects have also been applied on an electro-osmotic two-phase flow through a divergent channel. The lubrication effects have been applied to dampen the skin friction of the opposite walls. An analytical solution is obtained for the nonlinear multiphase fluid flow with heat transfer. Separate expressions for the volumetric flow rate of two-phase flow and pressure gradient are determined via a complex mathematical manipulation. A concise parametric study reveals that slippery walls of the channel have a prominent influence on the momentum of both phases.

Numerical simulation of 3D Darcy–Forchheimer fluid flow with the energy and mass transfer over an irregular permeable surface

The Jeffrey fluid model is capable of accurately characterizing the stress relaxation behavior of non-Newtonian fluids, which a normal viscous fluid model is unable to perform. The primary objective of this paper is to provide a comprehensive investigation into the effects of MHD and thermal radiation on the 3D Jeffery fluid flow over a permeable irregular stretching surface. The consequences of the Darcy effect, variable thickness and chemical reaction are also considered. The phenomena have been modeled as a nonlinear system of PDEs. Using similarity substitution, the modeled equations are reduced to a dimensionless system of ODEs. The parametric continuation method (PCM) is used to determine the numerical solution to the obtained sets of nonlinear differential equations. The impact of physical parameters on temperature, velocity and mass profiles are presented through Figures and Tables. It has been noticed that the energy profile magnifies with the increment of porosity term, thermal radiation and heat source term, while diminishing with the flourishing upshot of power index and Deborah number. Furthermore, the porosity term and wall thickness parameter enhance the skin friction.

Impact of slip boundary conditions, magnetic force, and porous medium on blood flow of Jeffrey fluid

AbstractIn this study, the comparative study of the peristaltic flow of Newtonian and non‐Newtonian fluids under the consideration of the magnetic field in the porous inclined channel is investigated. The effects of velocity slip and convective boundary conditions are also considered. Moreover, the variable liquid properties are also taken. The mathematical model is developed with the help of the Jeffrey fluid model in the form of partial differential equations. After that, convert them into dimensional form by using the dimensionless quantities. The resultant system of equations is solved through the perturbation method and presented the solution of velocity, temperature, and concentration in analytical form. The impact of physical parameters on the velocity, temperature, and concentration profiles are highlighted with the help of the graphs. The outcomes revealed that the magnetic parameter slows down the velocity of the fluid while the Darcy number enhanced the velocity and temperature distribution and suppressed the concentration profile.

Propagation of H1N1 virus through saliva movement in oesophagus: a mathematical model.

H1N1 (Swine flu) is caused by the influenza A virus which belongs to the Orthomyxoviridae family. Influenza A is very harmful to the elderly, and people with chronic respiratory disease and cardiovascular disease. Therefore, it is essential to analyse the behaviour of virus transmission through the saliva movement in oesophagus. A mathematical paradigm is developed to study the saliva movement under the applications of transverse magnetic field. Jeffrey fluid model is considered for saliva to show the viscoelastic nature. The flow nature is considered creeping and assumptions of long wavelength and low Reynolds number are adopted for analytical solutions. The Basset–Boussinesq–Oseen equation is employed to understand the propagation of H1N1 virus through saliva under the effect of applicable forces such as gravity, virtual mass, basset force, and drag forces. The suitable data for saliva, oesophagus and H1N1 virus are taken from the existing literature for simulation of the results using MATLAB software. From the graphical results, it is observed that the susceptibility to viral infections is less because the magnetic field reduces the motion of the virus particle. Further, the chances of infections in males are more as compared to females and children due to variation in viscosity of saliva. Such findings provide an understanding of the mechanics of the virus floating through the saliva (viscoelastic fluids) in the oesophagus.

Flow of two immiscible non-Newtonian fluids in an elastic tube

PurposeThis paper aims to investigate the flow of two-layered non-Newtonian fluids with different viscosities in an axisymmetric elastic tube.Design/methodology/approachA mathematical model was considered for this study to describe the flow characteristics of two-layered non- Newtonian Jeffrey fluids in an elastic tube. Because Jeffrey fluid model is a better model for the description of physiological fluid motion. Further, this model is a significant generalization of Newtonian fluid model. Analytical expressions for flux, stream functions, velocities and interface velocity have been derived in terms of elastic parameters, inlet, outlet and external pressures. The effects of various pertinent parameters on the flow behavior have been studied.FindingsThe volumetric flow rate was calculated by different models of Mazumdar (1992) and Rubinow and Keller (1972); from this it was found that the flux of Jeffrey fluid is more in the case of Rubinow and Keller model than Mazumdar. A comparative study is made between single-fluid and two-fluid models of Jeffrey fluid flows and it was observed that more flux and higher velocities were observed in the case of two-fluid model rather than single-fluid model. Furthermore, when both the Jeffrey parameter tends to zero and ratios of viscosities and radii are unity, the results in this study agree with those of Rubinow and Keller (1972).Originality/valueTo describe the fluid flow in an elastic tube with two-layered systems, the models and solutions developed here are very important. These results will be highly suitable in analyzing the rheological characteristics of blood flow in a small blood vessel because of their elastic nature.