Abstract
In this study, we investigated the dynamics of unsteady electroosmotic pulsatile flow involving a hybrid nanofluid within a curved artery, influenced by both stenosis and an embedded catheter. The hybrid nanofluid, a mixture of silver and aluminum oxide nanoparticles dispersed in blood, was modeled via the Carreau non-Newtonian framework to more accurately represent the intricate nature of blood flow. The electroosmotic forces introduced simulated the effect of an external electric field, while the catheter served as an additional structural constraint within the artery. To account for both the curvature of the vessel and the overlapping stenosis, we derived the governing equations for this model. Using numerical methods, particularly the finite-difference approach, we solved the nonlinear partial differential equations that govern the flow, temperature, and concentration distributions. Our findings suggest that the hybrid nanofluid demonstrates enhanced thermal and flow properties compared to standard fluids. The results showed significant influences from electroosmotic forces, curvature, and pulsatility on the velocity, temperature, and concentration profiles. Furthermore, an increase in the electroosmotic and Weissenberg parameters substantially accelerated fluid velocity by reducing viscous drag while improving mass transport. These results offer valuable insights into the behavior of blood flow in catheterized arteries and may inform future advancements in cardiovascular treatment technologies.
1 Introduction
Hybrid nanofluids, particularly those with non-Newtonian properties, have attracted significant interest lately due to their broad applications in biomedical engineering and fluid transportation. When combined with electroosmotic flow, these hybrid nanofluids exhibit additional complexities in behavior, making them well suited for use in microscale and nanoscale fluid manipulation scenarios (). Nanofluids and hybrid nanofluids are utilized in various disciplines, demonstrating their flexibility and potential impact. There are a variety of applications for nanofluids and hybrid nanofluids in fields such as biomedical applications, the energy sector, manufacturing, and engineering (; ; ). investigated the effects of bio-convection and activation energy on the Reiner–Rivlin nanofluid flow over a rotating disk with partial slips. By deriving a system of coupled nonlinear differential equations based on the Reiner–Rivlin fluid relationships, the study explores a variety of non-Newtonian fluid models and slip coefficients for numerical analysis. delved into the impact of volume fraction and Coriolis and Lorentz forces on the behavior of water-based silver (Ag) nanoparticle flow toward a continuously stretching sheet.
Electroosmotic flow, influenced by applied electric fields, offers precise control over fluid movement, which is highly desirable in medical contexts such as targeted drug delivery and microfluidic systems. demonstrated the ability of electroosmotic pumps to precisely regulate microflow in microfluidic applications. Hybrid nanofluids, typically composed of metal-based nanoparticles dispersed in base fluids, provide enhanced thermal and flow properties, making them ideal for improving the fluid efficiency in medical systems. ) reviewed hybrid nanofluids and their improved thermal properties, emphasizing their potential in various heat transfer applications. investigated third-grade fluid motion between vertical parallel walls utilizing an electromagnetic hydrodynamic approach. The walls, oriented vertically, contain a nanofluid with sodium alginate infused with gold and iron oxide nanoparticles in a porous structure. The Darcy–Brinkman–Forchheimer model is applied, particularly in scenarios with non-Darcy media. Numerical solutions are obtained using a shooting approach for the nonlinear differential equations. The results are analyzed through graphs and tables, revealing the favorable industrial application potential of the nanoparticle combination studied. Recent research has shown that these fluids exhibit superior heat transfer capabilities, which is crucial for biomedical use cases. demonstrated that hybrid nanofluids containing multiwalled carbon nanotubes (MWCNTs) and nanoparticles significantly improve heat transfer performance, indicating their potential in advanced thermal management systems.
The study of pulsatile flow in curved arteries with stenosis has gained importance in understanding cardiovascular health. conducted numerical investigations on physiologically realistic pulsatile flow through arterial stenosis, providing key insights into flow patterns and wall shear stress distributions essential for understanding atherosclerosis. Pulsatile flow, which mimics the heartbeat’s rhythm, is greatly influenced by arterial curvature and stenosis (). performed three-dimensional numerical analyses of pulsatile flow in carotid artery bifurcations, revealing that arterial geometry significantly affects flow patterns and wall shear stress, both critical factors in atherosclerosis.
Stenosis, or the narrowing of arteries, presents challenges to blood flow, increasing wall shear stress and pressure gradients, potentially leading to adverse cardiovascular events (). Curved arteries add to the complexity by introducing secondary flow patterns that further influence flow dynamics. Studying such systems is crucial for advancing treatments for vascular diseases (). reviewed the flow in curved pipes, showing how curvature induces secondary flows that alter the shear stress distribution, which is critical in understanding vascular pathologies. Recent research underscores the importance of considering realistic arterial geometries for accurate predictions of hemodynamic forces () (). discussed how computational fluid dynamics modeling using patient-specific geometries improves our understanding of cardiovascular hemodynamics, aiding in diagnosis and treatment. used in vivo MR angiography to quantify deformations of the superficial femoral artery. Numerical studies indicate that stenosed arteries under pulsatile flow behave differently from healthy arteries, highlighting the need for specialized treatments (). developed a theoretical and experimental model of pulsatile blood flow in the coronary arterial tree, demonstrating significant differences in hemodynamic parameters in stenosed arteries compared to healthy arteries, emphasizing the need for tailored therapeutic strategies.
The finite-difference technique is widely used for numerically solving complex fluid flow problems, particularly in biomedical applications like cardiovascular treatments (). discussed computational methods in vascular fluid dynamics and how numerical techniques like the finite difference method solve fluid–structure interaction problems in blood flow simulations. This method is highly beneficial for solving nonlinear partial differential equations, which arise in blood flow modeling, especially in stenosed and catheterized arteries. used finite volume methods to study the behavior of gold and copper biomagnetic blood flow in an inclined stenosed artery with varying viscosities. numerically investigated pulsatile blood flow through a stenosed elastic artery. The finite-difference method provides a stable and efficient framework for understanding the intricate interactions between blood, vessel walls, and medical devices such as stents or catheters (). used computational models to predict the sites of neointimal hyperplasia after stent implantation, demonstrating the role of numerical methods in improving cardiovascular device design and patient outcomes. Studies have shown that the finite-difference method can efficiently model heat transfer and predict flow behavior in biomedical systems, leading to better clinical outcomes (). reviewed mathematical modeling of skin bioheat transfer, emphasizing the role of numerical methods like the finite-difference technique in predicting thermal responses in tissues.
Mathematical modeling and analysis are essential for understanding the complex behaviors of non-Newtonian hybrid nanofluids in biomedical applications. The Carreau non-Newtonian model is a foundational mathematical framework for characterizing shear-thinning fluids, like blood, especially under pulsatile flow in stenosed and curved arteries (). provided a detailed mathematical analysis of blood rheology using the Carreau model, advancing the understanding of non-Newtonian fluid dynamics under physiological conditions. Recent studies have also explored the impact of magnetic fields on the flow of non-Newtonian fluids in stenosed arteries. The mathematical analysis of pulsatile flow in curved arteries has advanced through the use of numerical methods like the finite-difference method (). developed a mathematical model to study the effects of magnetic fields on blood flow using finite-difference techniques. Additionally, studies on thermophoretic effects in non-Newtonian fluid flow have provided new perspectives on heat transfer in biological systems. analyzed thermophoresis and Brownian motion effects in non-Newtonian nanofluid flow over a stretching sheet, offering mathematical models that can be applied in biomedical engineering. discussed a viscoelastic three-element viscous model, comprising a spring in parallel with one dashpot and a second dashpot in series, and used it to analyze the heat and mass flow properties of the fluid across a variable-thickness sheet. Transport equations incorporating this model are solved using the numerical Runge–Kutta (RK) technique. The research highlights that viscosity exerts a more substantial influence on the outcomes than other parameters. Notably, a significant enhancement of 22 in the Nusselt number and 137 in the entropy generation rate was observed.
The main objective of this research is to analyze the unsteady electroosmotic pulsatile flow of a hybrid nanofluid through a stenosed, curved, catheterized artery using the Carreau non-Newtonian model. The study uses a numerical approach based on the finite-difference method to solve the governing equations of fluid motion, temperature, and concentration. This research is significant because it offers new insights into the behavior of hybrid nanofluids under electroosmotic forces in complex arterial geometries, which could help design more effective cardiovascular treatments and medical devices. The study results contribute to a broader understanding of hemodynamics in diseased arteries, providing valuable implications for improving patient outcomes in cardiovascular care.
2 Problem description and mathematical model
In our paper, we examine the unsteady laminar electroosmotic pulsatile flow of an incompressible Carreau non-Newtonian hybrid nanofluid (/blood) through a curved catheterized artery with stenosis. The blood is a base fluid containing suspended nanoparticles of both Ag and aluminum oxide . The artery segment with length has a mild constriction coiled in a circle with radius from the center . Another solid circular cylinder balloon catheter is inserted into this curved artery. We choose a coordinate system in which aligns with the radial direction and aligns with the artery axis. We also choose as the axis of symmetry for the two coaxial cylinders. The fluid is subjected to an axial electric field of strength and an imposed magnetic field in the radial direction. The temperature, concentration, and zeta potential near the arterial wall are given by , , and , respectively. The catheter wall is maintained at temperature , concentration , and zeta potential , where , , and . We assume that the nanoparticles are uniformly dispersed within the blood and that there is no agglomeration. The thermophysical properties of the hybrid nanofluid, such as thermal conductivity and viscosity, are considered to be functions of the nanoparticle volume fraction and temperature. Viscous dissipation is taken into account to understand the conversion of kinetic energy into thermal energy due to the fluid’s viscosity. Joule heating, resulting from the interaction of the electric field with the fluid, is also considered, which affects the temperature distribution within the artery. The arterial wall geometry with overlapping stenosis and the balloon model are defined as follows (see Equations 1, 2 and Figure 1) (; ):where is the stenotic position, is the length of the overlapping stenosis, and is the non-tapered artery’s radius in the non-stenotic portion. As a result, the proportion occurs in two different locations, namely, and . Here, represents the essential altitude of the stenosis. At , the elevation of the stenosis from the starting position is . For the annular inflated catheterization, it is presumed that is the catheter’s maximum height at , is the balloon’s axial displacement throughout catheterization, is the catheter’s inner radius, and seems extremely small. At any given value , the gradient of pressure can be written aswhere are the pressure gradient’s steady and pulsatile components, respectively, and , where is the pulse’s frequency.
FIGURE 1
The conservative continuity, momentum, energy, and concentration governing equations with thermophoresis and Brownian motion are as follows (; ; ; ; ):
Continuity equation:
Momentum equations:
Energy equation:
Concentration equation:where are the radial and axial velocities, respectively; is the density of the hybrid nanofluid; is the time; symbolizes the pressure of the fluid; is the electrical conductivity of the hybrid nanofluid; is the total ionic charge density; is gravitational acceleration; are coefficients of thermal and solutal expansions, respectively; is the fluid temperature; indicates specific heat at a constant pressure; indicates the heat conduction; is the Stefan–Boltzmann constant; is the fluid’s average temperature; is the Rosseland absorption coefficient; is the effective heat capacity ratio; is the Brownian diffusion coefficient; is the diffusion coefficient for thermophoresis; is the medium’s temperature; is the concentration of the fluid; and is the chemical term.
Considering that the electrolyte combination is homogeneous, the Poisson–Boltzmann equation provides the electrical potential disturbance for it by ()where is the potential electricity and is the dielectric permittivity.
Ionic energy density is described as . When an overlaid double electrical layer is ignored, the cation and anion densities are expressed asHere, represents the concentration of ions, stands for electrical charge, reflects the charge balance, indicates the Boltzmann constant, and denotes the electrolytic solution’s mean temperature.
By substituting and for their respective values in Equation 9, and by using the Debye–Hückel approach, the Poisson–Boltzmann equation for potential electricity can be expressed as
The extra stress tensor for the Carreau hybrid nanofluid according to the shear rate is formulated as (; ; ; )where is the extra stress tensor, is the viscosity at an infinite shear rate, is the viscosity of the hybrid nanofluid, is the constant of time, is the shear rate, is the power-law index, is the first Rivlin–Ericksen tensor, is the strain rate tensor’s second invariant, is the vector of velocity, and denotes the transpose.
Except for the fluid’s thermal conductivity and viscosity, all of its physical properties should remain constant. It is hypothesized that the viscosity varies with temperature in addition to shear rate dependence and presuming , . Consequently, the apparent viscosity is described as follows:
Here, the initial and boundary constraints are
Non-dimensional variables and parameters are defined as [() ()]where is the curvature parameter, is the Womersley frequency parameter, is the Reynolds number, is the parameter of amplitude fluctuation, represents the Hartmann number, is the Darcy number, symbolizes the electroosmotic parameter, is the Debye length, is the Helmholtz–Smoluchowski velocity, is the thermal Grashof number, is the solutal Grashof number, is the Weissenberg number, is the Prandtl number, is the radiation parameter, is the Joule heating parameter, is the Brickman number, is the heat source parameter, is the Brownian motion parameter, is the thermophoresis parameter, is the Schmidt number, and is the chemical parameter.
Based on the suppositions and simplifications outlined by for mild stenosis , . Applying Equation 16 and using the abovementioned presumption, the non-dimensional form of the Equations 3–15 is as follows:
The corresponding initial and boundary constraints arewhere Equations 23, 24 are the non-dimensional walls and , , and .
Comparing hybrid nanofluids to simple nanofluids, the former have shown better stability and thermal properties. In many facets of human endeavor, such as electronics, medical, power, and chemical engineering equipment, tiny concentrations of hybrid nanoparticles of metal or metal oxides are used. Tables 1, 2 list the thermal and physical characteristics of blood, silver nanoparticles, and aluminum oxide nanoparticles. In this case, the volume fraction for silver and aluminum oxide nanoparticles is denoted by and , respectively. The solid nanoparticles of Ag, solid nanoparticles of aluminum oxide , base fluid (blood), and nanoblood hybrid are denoted by the suffices , , , and , respectively. Specifically, if , the hybrid nanofluid is transformed into a nanofluid ().
TABLE 1
| Property | Hybrid nanoblood (Ag-Al2O3/blood) |
|---|---|
| Density | |
| Viscosity | |
| Thermal expansion coefficient | |
| ——- | |
| Heat capacity | |
| Electrical conductivity | where |
| Thermal conductivity | where |
Thermal physical features of the hybrid nanoparticles.
TABLE 2
| Property | Ag | Blood | |
|---|---|---|---|
| 8,933 | 6,320 | 1,063 | |
| 235 | 765 | 3,594 | |
| 16.7 | 18 | 0.18 | |
| 401 | 76.5 | 0.492 |
Thermal physical properties of silver (Ag) and aluminum oxide nanoparticles and blood fluid:
3 Numerical solution technique
The unsteady electroosmotic pulsatile flow-governing equations of the hybrid nanofluid are nonlinear partial differential equations governed by continuity, momentum, energy, and species concentration. To solve these equations, the finite-difference method was used due to its effectiveness in handling complex boundary conditions typically encountered in arterial geometries. More specifically, the Crank–Nicolson scheme was chosen as it provides a good balance between computational cost and accuracy. The solution domain was discretized using a uniform grid, and a semi-implicit formulation was used to ensure convergence. The resulting algebraic equations were solved iteratively until the desired level of accuracy was achieved, ensuring reliable simulations of the flow dynamics within the stenosed, curved, and catheterized artery. We used the finite-difference method to solve the coupled nonlinear partial differential Equations 17–21 with initial and boundary conditions given by Equation 22. To proceed, the physical domain is transformed into a regular uniform domain using the transformation:
Using Equation 25 in Equations 17–24, we obtain:
The associated initial and boundary conditions are
The finite-difference approach is used by the Crank–Nicolson semi-implicit discretization because it is unconditionally stable. Let us consider a uniform grid with spacing in the direction and time in the direction. Consider the discrete approximation of and at the grid point and . The discretization of the above equations (Equations 26–30) will be
The associated initial and boundary conditions are
The function FindRoot in Mathematica software is used to solve the produced system of nonlinear algebraic equations (Equations 31–35) and obtain the consecutive solutions. After several cycles of this procedure, a steady state is achieved. The steady-state solution is assumed to be obtained when the absolute differences between the values of and at two subsequent time steps are less than at all grid points.
4 Results and discussions
In this section, we discuss the effects of various physical parameters on the flow, heat transfer, and mass transfer characteristics of the hybrid nanofluid through a stenosed curved artery. Specifically, the influences of electroosmotic forces, pulsatility, curvature, and nanoparticle concentration on velocity, temperature, and concentration profiles are examined. The interaction of these parameters shows significant variations in hemodynamic parameters, which may hold relevance for medical applications involving catheters. The following sections present the results in relation to the figures provided, highlighting trends and comparing the effects of different governing parameters on velocity, temperature, and concentration.
4.1 Grid independence test
The grid independence test was carried out to ensure that the solution was not dependent on the mesh size used in the numerical solution, guaranteeing credible and ensuring computational efficiency for the velocity, temperature, and concentration profiles without sacrificing accuracy. The model was solved by using grids with dimensions of , , and . Figure 2 shows that the solutions found are always the same regardless of whether one uses a relatively small or large grid. We choose a grid size of for subsequent simulations.
FIGURE 2
4.2 Velocity
Figures 3, 4 show the behavior of the electric potential under different conditions. Figures 3A, B show the effects of the wall zeta potential and Debye–Hückel parameter on the electric potential distribution. As the wall zeta potential increases, the electric potential within the flow domain increases, increasing the electroosmotic effect. This results in a more uniform electric potential distribution along the artery, which enhances the electroosmotic flow and affects the velocity profile. The Debye–Hückel parameter, characterizing the thickness of the electrical double layer, also affects the electric potential distribution, with higher values causing a steeper potential gradient near the walls. Figure 4 highlights the impact of the curvature parameter on the electric potential. The results indicate that increasing the curvature enhances the asymmetry in the potential distribution, particularly near the outer wall of the curved artery segment, influencing the velocity distribution observed in subsequent figures.
FIGURE 3
FIGURE 4
The velocity profiles for the hybrid nanofluid are shown in Figures 5–9, illustrating the complex interaction of various physical parameters. Figure 5 shows the velocity distribution across the artery for different values of wall zeta potential and the Weissenberg number . As the wall zeta potential increases, the electroosmotic force strengthens, enhancing the overall velocity of the fluid. This is because the increased electrokinetic force reduces the resistance imposed by viscous forces. Additionally, the Weissenberg number, which characterizes the fluid’s elasticity, plays a key role. Higher values of increase the velocity peak near the artery’s central axis as the elastic properties of the Carreau fluid work to minimize viscous drag. The combined effect of the higher wall zeta potential and Weissenberg number produces a more favorable velocity distribution, enhancing mass transport, which is beneficial in medical applications involving catheterized arteries.
FIGURE 5
FIGURE 6
FIGURE 7
FIGURE 8
FIGURE 9
Figure 6 shows the velocity distributions over time for different values of the Hartmann number and the fluctuation parameter . The Hartmann number reflects the influence of the magnetic field on the flow, with higher values corresponding to a stronger magnetic field. As increases, the velocity decreases, indicating that the magnetic field exerts a damping effect on fluid motion, reducing the overall velocity. This magnetic damping effect is critical for controlling blood flow in biomedical applications where precise modulation is needed. In contrast, the fluctuation parameter , representing the amplitude of the pulsatile flow, causes more pronounced oscillations in the velocity profile with higher values, reflecting the increased impact of pulsatility on flow dynamics. The interplay between and reveals that although the magnetic field lowers the peak velocity, the pulsatile nature of the flow can counterbalance this effect, maintaining a dynamic and controlled flow environment.
Figure 7 shows the velocity distributions for different values of the Grashof number and volume concentrations . The Grashof number represents the ratio of buoyancy to viscous forces, and as increases, the velocity profile exhibits a notable enhancement due to the increased buoyant force acting on the fluid. This buoyant force helps overcome the resistance of the arterial walls, thus increasing the flow rate. The volume concentrations of hybrid nanoparticles also significantly influence the velocity. Higher concentrations lead to improved thermal conductivity and reduced effective viscosity, resulting in a more pronounced velocity peak. The combined effect of an increased Grashof number and higher nanoparticle concentration significantly enhances the overall velocity, which can help improve blood flow in stenosed arteries.
Figure 8 shows the velocity distributions for different values of the electroosmotic parameter and solutal Grashof number . The electroosmotic parameter influences the electrokinetic flow within the artery, and as its value increases, the overall fluid velocity increases due to the enhanced electroosmotic force, providing additional driving support for the flow. The solutal Grashof number , which represents the ratio of solutal buoyancy forces to viscous forces, also significantly affects the velocity profile. Higher values increase the buoyant force, enhancing fluid velocity, particularly in the core region of the artery. The combined effects of and contribute to a more efficient flow, crucial for optimizing mass transport in biomedical applications involving stenosed arteries.
Figure 9 presents the velocity distributions over time for different values of the curvature parameter . The curvature parameter strongly influences the velocity profile due to the centrifugal forces generated by the artery’s curved geometry. As increases, the velocity near the outer wall of the artery increases, leading to an asymmetric velocity distribution. This effect is due to centrifugal forces pushing the fluid toward the outer curvature, increasing the velocity in that region while reducing it near the inner wall. The pulsatile nature of the flow further modulates these effects, with peak velocity occurring during the systolic phase, especially in regions affected by a higher curvature. This interaction between the curvature and pulsatility is critical for understanding hemodynamics in curved arterial segments, particularly in the presence of stenosis or catheterization.
4.3 Heat and concentration distribution
Figure 10 shows the distribution of temperature and concentration for different values of the curvature parameter and radiation parameter . Panel (a) shows the temperature distribution, which is significantly influenced by the artery’s curvature. As increases, the temperature distribution becomes more asymmetric, with higher temperatures near the artery’s outer curvature. This asymmetry is attributed to enhanced convective heat transfer driven by centrifugal forces that push the fluid carrying thermal energy toward the outer wall. The radiation parameter also plays an important role; higher values increase radiative heat flux, leading to a more uniform temperature profile across the artery, which is crucial for maintaining stable thermal conditions. Panel (b) shows the concentration distribution for various values of and . Similar to the temperature distribution, the concentration profile is influenced by curvature and radiation effects. Higher values result in an asymmetric concentration profile, with more concentration near the artery’s outer wall. enhances mass diffusion, leading to a more uniform concentration distribution. The combination of curvature and radiation parameters is crucial in optimizing both heat and mass transfer, making it valuable for biomedical applications like targeted drug delivery and thermal therapies.
FIGURE 10
Figure 11 shows the heat and concentration distributions for different values of the thermophoresis parameter . Panel (a) shows how the temperature distribution is significantly affected by the thermophoresis effect. As increases, the temperature gradient becomes steeper, enhancing heat transfer from regions of higher temperature to lower temperature. This effect is particularly important in applications where maintaining a controlled temperature gradient is essential, such as in hyperthermia treatments. Panel (b) shows the concentration distribution for different values. The thermophoresis effect causes particles to move from hot to cold regions, leading to a decrease in the concentration in the hotter areas and an increase in the cooler areas. As increases, the concentration distribution becomes more uniform, reflecting enhanced mass transfer and more effective diffusion of nanoparticles within the fluid. Generally, a decrease in the concentration in hotter regions and an increase in the concentration in cooler areas align with thermophoresis, which drives movement from hot to cold. However, achieving a more consistent concentration across the entire domain or a uniform reduction suggests a balanced distribution, which is beneficial in biomedical applications like targeted drug delivery, where a homogeneous distribution is often desired for optimal therapeutic outcomes.
FIGURE 11
Figure 12 shows the heat and concentration distributions for different values of the Brownian motion parameter at a fixed thermophoresis parameter value. Panel (a) illustrates that the Brownian motion parameter significantly affects the temperature distribution. Panel (b) shows the concentration distribution for different values of the Brownian motion parameter . The concentration distribution is highly sensitive to the Brownian motion at the beginning of the time interval; this sensitivity decreases as time increases, and the concentration goes to its steady state.
FIGURE 12
Figure 13 shows the impact of the Schmidt number and chemical parameter on the concentration distribution. Panel (a) and Panel (b) illustrate that the Schmidt number and chemical parameter significantly affect the concentration distribution. Furthermore, the concentration distribution is reduced by increasing Schmidt number and chemical parameter . Physically, a thicker hydrodynamic layer compared to the mass transfer layer is indicated by a greater Schmidt number, which causes the concentration to diffuse more slowly. In processes like chemical reactors or environmental engineering, where regulated mass transfer is sought, this is essential.
FIGURE 13
5 Conclusion
The flow of hybrid nanofluid through a stenosed, curved, and catheterized artery was treated as unsteady electroosmotic pulsatile flow using the Carreau non-Newtonian model. The characteristics of the velocity, temperature, and concentration distributions were analyzed for various representative physical parameters. The main findings are as follows.
• The results of the dimensionless potential distribution shown in Figure 2B match the results obtained by .
• Numerical analysis of the hybrid nanofluid flow within a stenosed, curved, and catheterized artery showed significant influences of electroosmotic forces, curvature, and pulsatility on velocity, temperature, and concentration profiles.
• Increases in the electroosmotic and Weissenberg parameters substantially accelerated fluid velocity by reducing viscous drag while improving mass transport.
• The curvature parameter and radiation effects played a crucial role in creating asymmetric heat and concentration distributions, optimizing thermal and mass transport.
• The thermophoresis parameter influenced temperature and concentration distributions by promoting uniformity, which is beneficial in biomedical applications for efficient mass diffusion.
• The fluctuating patterns imply that the concentration distribution is extremely responsive to the parameter of Brownian motion. In procedures requiring exact concentration control, such as chemical reactions or material creation, this might be extremely important.
Statements
Data availability statement
The original contributions presented in the study are included in the article/Supplementary Material; further inquiries can be directed to the corresponding author.
Author contributions
ME: conceptualization, formal analysis, investigation, methodology, project administration, resources, software, supervision, validation, visualization, writing–original draft, and writing–review and editing. AA: conceptualization, formal analysis, investigation, methodology, project administration, resources, software, supervision, validation, visualization, writing–original draft, and writing–review and editing. YA: conceptualization, formal analysis, investigation, methodology, project administration, resources, software, supervision, validation, visualization, writing–original draft, and writing–review and editing. SA: conceptualization, formal analysis, investigation, methodology, project administration, resources, software, supervision, validation, visualization, writing–original draft, and writing–review and editing.
Funding
The author(s) declare that financial support was received for the research, authorship, and/or publication of this article.
Acknowledgments
Abdullah Alsharif acknowledges Taif University, Saudi Arabia, for supporting this work through the project number TU-DSPP-2024-185. Sara I. Abdelsalam acknowledges Fundación Mujeres por África for supporting this work through the fellowship awarded to her.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declare that no Generative AI was used in the creation of this manuscript.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
References
1
AbdalS.MariamA.AliB.YounasS.AliL.HabibD. (2021). Implications of bioconvection and activation energy on Reiner-Rivlin nanofluid transportation over a disk in rotation with partial slip. Chin. J. Phys.73, 672–683. 10.1016/j.cjph.2021.07.022
2
AkbarN. S.NadeemS. (2014). Carreau fluid model for blood flow through atapered artery with a stenosis. Ain Shams Eng. J.5, 1307–1316. 10.1016/j.asej.2014.05.010
3
AkhtarS.McCashL. B.NadeemS.SaleemS.IssakhovA. (2021). Mechanics of non-Newtonian blood flow in an artery having multiple stenosis and electroosmotic effects. Sci. Prog.104 (3), 368504211031693–15. 10.1177/00368504211031693
4
AliB.SiddiqueI.AhmadianA.SenuN.AliL.HaiderA. (2022). Significance of Lorentz and Coriolis forces on dynamics of water based silver tiny particles via finite element simulation. Ain Shams Eng. J.13 (2), 101572. 10.1016/j.asej.2021.08.014
5
AliL.LiuX.AliB. (2020). Finite element analysis of variable viscosity impact on MHD flow and heat transfer of nanofluid using the cattaneo-christov model. Coatings10 (4), 395. 10.3390/coatings10040395
6
ApostolidisA. J.BerisA. N. (2014). Modeling of the blood rheology in steady-state shear flows. J. Rheology58 (3), 607–633. 10.1122/1.4866296
7
BashaH. T.RajagopalK.AhammadN. A.SathishS.GunakalaS. R. (2022). Finite difference computation of Au-Cu/Magneto-bio-hybrid nanofluid flow in an inclined uneven stenosis artery. Complexity2022 (1), 2078372–18. 10.1155/2022/2078372
8
BergerS. A.TalbotL.YaoL. S. (1983). Flow in curved pipes. Annu. Rev. Fluid Mech.15 (1), 461–512. 10.1146/annurev.fl.15.010183.002333
9
BhattiM. M.AbbasM. A.MuhammadS. (2024). “Optimizing fluid flow efficiency: third-grade hybrid nanofluid flow with electro-magneto-hydrodynamics in confined vertical spaces,” in Nanofluids (Elsevier), 243–275. 10.1016/b978-0-443-13625-2.00012-7
10
ChakravartyS.MandalP. (1996). A nonlinear two dimensional model of blood flow in an overlapping arterial stenosis subjected to body acceleration. Math. Comput. Model.24 (1), 43–58. 10.1016/0895-7177(96)00079-9
11
ChengC. P.WilsonN. M.HallettR. L.HerfkensR. J.TaylorC. A. (2006). In vivo MR angiographic quantification of axial and twisting deformations of the superficial femoral artery resulting from maximum hip and knee flexion. J. Vasc. Interventional Radiology17 (6), 979–987. 10.1097/01.rvi.0000220367.62137.e8
12
DasS.BarmanB.JanaR. N.MakindeO. D. (2021). Hall and ion slip currents impact on electromagnetic blood flow conveying hybrid nanoparticles through an endoscope with peristaltic waves. Bio Nanosci.11, 770–792. 10.1007/s12668-021-00873-y
13
El-DabeN. T. M.MostaphaD. R. (2020). Hall current and Joule heating effects on peristaltic flow of a Sisko fluid with mild stenosis through a porous medium in a tapered artery with slip and convective boundary conditions. Sains Malays.49 (5), 1175–1190. 10.17576/jsm-2020-4905-23
14
El KotM. A.Abd ElmaboudY. (2021). Hybrid nanofluid flows through a vertical diseased coronary artery with heat transfer. J. Mech. Med. Biol.21 (02), 2150012. 10.1142/s0219519421500123
15
El KotM. A.Abd ElmaboudY. (2023). Model of LDL-C concentration of blood flow through a vertical porous microchannel with multiple stenoses: computational simulation. J. Taibah Univ. Sci.17 (1), 2176194. 10.1080/16583655.2023.2176194
16
El KotM. A.Abd ElmaboudY. (2024). Numerical simulation of electroosmotic sutterby hybrid nanofluid flowing through an irregularly mild stenotic artery with an aneurysm. Arabian J. Sci. Eng.49, 2483–2498. 10.1007/s13369-023-08257-y
17
El-MasryY. A. S.Abd ElmaboudY.Abdel-SattarM. A. (2020). Direct current/alternating current magnetohydrodynamic micropump of a hybrid nanofluid through a vertical annulus with heat transfer. J. Therm. Sci. Eng. Appl.12 (4). 10.1115/1.4046058
18
GijsenF. J. H.van de VosseF. N.JanssenJ. D. (1999). The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model. J. Biomechanics32 (6), 601–608. 10.1016/S0021-9290(99)00015-9
19
HaghighiA. R.KabdoolA. A.AslM. S.KiyatsatfarM. C. (2006). Numerical investigation of pulsatile blood flow in stenosed artery. Int. J. Appl. Comput. Math.2, 649–662. 10.1007/s40819-015-0084-0
20
HassanM.ChunweiZ.FirdousA.BhattiM. M. (2024). Viscoelastic fluid flow on variable thickness sheets using a three-element viscous model. Int. J. Model. Simul., 1–12. 10.1080/02286203.2024.2338583
21
HuminicG.HuminicA. (2018). Hybrid nanofluids for heat transfer applications - a state-of-the-art review. Int. J. Heat Mass Transf.125, 82–103. 10.1016/j.ijheatmasstransfer.2018.04.059
22
HuoY.KassabG. S. (2006). Pulsatile blood flow in the entire coronary arterial tree: theory and experiment. Am. J. Physiology-Heart Circulatory Physiology302 (6), H1074–H1087. 10.1152/ajpheart.00200.2006
23
JohnstonB. M.JohnstonP. R.CorneyS.KilpatrickD. (2004). Non-Newtonian blood flow in human right coronary arteries: steady state simulations. J. Biomechanics37 (5), 709–720. 10.1016/j.jbiomech.2003.09.016
24
LaDisaJ. F.Jr.OlsonL. E.MolthenR. C.HettrickD. A.PrattP. F.HardelM. D.et al (2005). Alterations in wall shear stress predict sites of neointimal hyperplasia after stent implantation in rabbit iliac arteries. Am. J. Physiology-Heart Circulatory Physiology288 (5), H2465–H2475. 10.1152/ajpheart.01107.2004
25
LongQ.XuX. Y.RamnarineK. V.HoskinsP. (2001). Numerical investigation of physiologically realistic pulsatile flow through arterial stenosis. J. Biomechanics34 (10), 1229–1242. 10.1016/s0021-9290(01)00100-2
26
MorrisP. D.NarracottA.von Tengg-KobligkH.Silva SotoD. A.HsiaoS.LunguA.et al (2016). Computational fluid dynamics modelling in cardiovascular medicine. Heart102 (1), 18–28. 10.1136/heartjnl-2015-308044
27
PalD.MondalH. (2011). Effects of Soret, Dufour, chemical reaction, and thermal radiation on MHD non-Darcy unsteady mixed convective heat and mass transfer over a stretching sheet. Commun. Nonlinear Sci. Numer. Simul.16 (4), 1942–1958. 10.1016/j.cnsns.2010.08.033
28
PerktoldK.ReschM.PeterR. O. (1991). Three-dimensional numerical analysis of pulsatile flow and wall shear stress in the carotid artery bifurcation. J. Biomechanics24 (6), 409–420. 10.1016/0021-9290(91)90029-M
29
PincombeB.MazumdarJ. (1977). The effects of post-stenotic dilatations on the flow of a blood analogue through stenosed coronary arteries. Math. Comput. Model.25 (6), 57–70. 10.1016/S0895-7177(97)00039-3
30
QuarteroniA.TuveriM.VenezianiA. (2000). Computational vascular fluid dynamics: problems, models and methods. Comput. Vis. Sci.2 (4), 163–197. 10.1007/s007910050039
31
RamanamurthyJ. V.PrasadK. M.NarlaV. K. (2013). Unsteady peristaltic transport in curved channels. Phys. Fluids25, 1903–1909. 10.1063/1.4821355
32
RanaJ.LiaoS. (2019). A general analytical approach to study solute dispersion in non-Newtonian fluid flow. Eur. J. Mech. - B/Fluids77, 183–200. 10.1016/j.euromechflu.2019.04.013
33
SarkarJ.GhoshP.AdilA. (2015). A review on hybrid nanofluids: recent research, development and applications. Renew. Sustain. Energy Rev.43, 164–177. 10.1016/j.rser.2014.11.023
34
SundarL. S.FarookyMd. H.SaradaS. N.SinghM. K. (2013). Experimental thermal conductivity of ethylene glycol and water mixture based low volume concentration of Al2O3 and CuO nanofluids. Int. Commun. Heat Mass Transf.41, 41–46. 10.1016/j.icheatmasstransfer.2012.11.004
35
SundarL. S.SinghM. K.SousaA. C. M. (2014). Enhanced heat transfer and friction factor of MWCNTF e3O4/water hybrid nanofluids. Int. Commun. Heat Mass Transf.52, 73–83. 10.1016/j.icheatmasstransfer.2014.01.012
36
TawadeJ. V.GuledC. N.NoeiaghdamS.Fernandez-GamizU.GovindanV.BalamuralitharanS. (2022). Effects of thermophoresis and Brownian motion for thermal and chemically reacting Casson nanofluid flow over a linearly stretching sheet. Results Eng.15, 100448. 10.1016/j.rineng.2022.100448
37
TzirtzilakisE. E. (2005). A mathematical model for blood flow in magnetic field. Phys. Fluids17 (7), 077103. 10.1063/1.1978807
38
WajihahS. A.SankarD. S. (2021). Effects of porosity in four-layered non-linear blood rheology in constricted narrow arteries with clinical applications. Comput. Methods Programs Biomed.199, 105907. 10.1016/j.cmpb.2020.105907
39
WangX.ChengC.WangS.LiuS. (2009). Electroosmotic pumps and their applications in microfluidic systems. Microfluid. Nanofluidics6 (2), 145–162. 10.1007/s10404-008-0399-9
40
WangX.JiangY.QiaoY.XuH.QiH. (2020). Numerical study of electroosmotic slip flow of fractional Oldroyd-B fluids at high zeta potentials. ELECTROPHORESIS41 (10-11), 769–777. 10.1002/elps.201900370
41
XuF.LuT. J.SeffenK. A.NgE. (2009). Mathematical modeling of skin bioheat transfer. Appl. Mech. Rev.62 (5). 10.1115/1.3124646
42
YoungD. F. (1968). Effect of a time-dependent stenosis on flow through a tube. J. Eng. Industrial Trans. ASME90 (2), 248–254. 10.1115/1.3604621
43
ZamanA.KhanA. A. (2021). Time dependent non-Newtonian nano-fluid (blood) flow in w-shape stenosed channel; with curvature effects. Math. Comput. Simul.181, 82–97. 10.1016/j.matcom.2020.09.017
Summary
Keywords
hybrid non-Newtonian nanofluid, electroosmotic flow, pulsatile flow, curved stenosed artery, finite-difference technique, cardiovascular treatment
Citation
El Kot MA, Alsharif AM, Abd Elmaboud Y and Abdelsalam SI (2024) Harnessing electroosmotic hybrid nanofluid dynamics in curved arteries: insights into biomedical flow enhancement. Front. Nanotechnol. 6:1520183. doi: 10.3389/fnano.2024.1520183
Received
31 October 2024
Accepted
29 November 2024
Published
23 December 2024
Volume
6 - 2024
Edited by
Anwar Shahid, Quanzhou Institute of Information Engineering, China
Reviewed by
M. M. Bhatti, North West University, South Africa
Bagh Ali, Harbin Institute of Technology, China
Updates
Copyright
© 2024 El Kot, Alsharif, Abd Elmaboud and Abdelsalam.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Sara I. Abdelsalam, sara.abdelsalam@bue.edu.eg
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.