Micropolar Parameter Research Articles

Mathematical model analysis for hydromagnetic flow of micropolar nanofluid with heat and mass transfer over inclined surface

In this study, a mathematical model analysis is made to figure out the impacts of relevant thermophysical effects on the rates of micropolar nanofluid transport phenomena near an inclined exponentially stretching surface. The flow phenomena are described mathematically using partial differential equations and simplified to dimensionless ordinary differential forms via suitable transformation variables. The resulting nonlinear coupled differential equations are then solved by using the optimal homotopy analysis method and the validity of the method is verified in convergence and comparative analysis. The rates of linear momentum, angular momentum, heat exchange and mass diffusion characteristics are investigated against continuous variations of pertinent parameters. Graphical elucidations are preferred to present the results of the study in detail. It was found that the rate of heat exchange is intensified with increasing values of micropolar parameter, Soret number and forces of buoyancy. Also, the rate of couple stress grows for higher estimation of micropolar parameter, surface shrinking, angle of inclination and heat sink parameter values. Further, the wall shear stress is strengthened for increasing values of the micropolar parameter, Dofour number, Soret number, buoyancy forces, heat release, chemical reaction and thermophoresis effects. On the other hand, the Sherwood number is enlarged with higher values of surface stretching parameter, medium porosity, Dufour number, chemical reaction, forces of buoyancy, heat release and Schmidt number.

Investigating the effect of structural changes of two stretching disks on the dynamics of the MHD model

The purpose of this theoretical study is to explore the behavior of an electrically conducting micropolar fluid when subjected to a uniform magnetic field along the vertical axis between two stretching disks as the structure of the problem changes. In this context, structural changes refer to alterations in the distance between the two discs or the stretching rate of the two discs. The governing equations of this problem are a set of nonlinear coupled partial differential equations, which are transformed into a nonlinear coupled ordinary differential equation set by a similarity transformation. The transformation results in four dimensionless quantities and their derivatives that appear in the equations. Nine dimensionless parameters are derived via similarity variables, including stretching Reynolds number, magnetic parameter, radiation parameter, Prandtl number, Eckert number, Schmidt number, and three micropolar parameters. Previous similarity solutions focused on analyzing the effect of changes in each parameter on the four dimensionless quantities. However, this type of analysis is mainly mathematical and does not provide practical results. This study’s primary novelty is to redefine the magnetic parameter, Eckert number, stretching Reynolds number, and two micropolar parameters to analyze physical parameters that depend on the stretching rate of the two discs or the distance between them. The semi-analytical hybrid analytical and numerical method (HAN-method) is used to solve the equations. The results demonstrate that structural changes affect all five quantities of radial velocity, axial velocity, microrotation, temperature, and concentration. The study’s most significant finding is that an increase in the stretching rate of the two disks causes a sharp increase in temperature and Nusselt number. Conversely, increasing the distance between the two disks causes a sharp decrease in micro-rotation and wall couple stress. They were compared to a previous study in a specific case to validate the results’ accuracy.

Effect of three types of magnetic field modulation on the instability of heat transfer in micropolar nanofluid filled within Hele-Shaw cell

This article investigates the impact of three different types of magnetic field modulation on the instability of micropolar nanofluid filled within Hele-Shaw cells applying both nonlinear and linear approaches. The truncated Fourier series approach is used to analyze nonlinear stability, while the analytical evaluation of linear stability is performed using the normal mode methodology. All the results are graphically demonstrated. Based on the outcomes, the micropolar parameter, magnetic Chandrasekhar number, Hele-Shaw number, and the coefficient of coupling between vorticity and spin effect have stabilized effects in the system. As opposed to that, nanoparticle Rayleigh number accelerate the start of convective motion inside the system. Some parameters play a significant influence in the transport of heat and mass in nonlinear analysis. The Hele-Shaw number, micropolar parameter, magnetic Prandtl number, and magnetic Chandrasekhar number perform a major contribution to the heat/mass transfer in the system. Using two different approaches, the system’s heat and mass transmission are investigated, the Runge–Kutta–Fehlberg method and Mathematica NDSolve, and It has been found that the rate of heat/mass transfer in both conditions is exactly the same. Moreover, It has been found that heat and mass transmission start earliest in the case of triangle waveforms as compared to other types of magnetic field modulations.

Effect of Initial Stress and Mechanical Impedance Boundary on Scholte’s Wave at Micropolar Solid–Liquid Interface

In this paper, we study Scholte’s waves propagating along the interface of micropolar solid and liquid media, considering the effect of initial stress and impedance boundary surface. We obtained the phase velocities of basic elastic waves in both media and used them to derive the secular equation of Scholte’s wave. We found that the initial stress in the solid material does not affect the speed of basic longitudinal waves. After solving the secular equation, we obtained the speed of Scholte’s wave and the corresponding attenuation. We observed that Scholte’s surface wave obtained at the micropolar solid–liquid interface is inhomogeneous and dispersive. We investigated the effects of initial stress, Tiersten’s impedance boundary condition, and micropolar solid parameters on Scholte’s wave and basic shear waves. Numerically, these effects are computed for a particular model using the appropriate value of the parameters, and the results are illustrated graphically. This paper also contributes to not only understanding the behavior of Scholte’s waves in micropolar solid–liquid interfaces but also the factors that affect the propagation.

Flow and Heat Transfer of Micropolar Ferrofluid at Stagnation Point on a Horizontal Flat Plate in the Presence of Magnetic Field and Thermal Radiation

Ferrofluid demonstrates Newtonian or non-Newtonian fluid behaviour depending on the characteristics of ferrofluid. Generally, ferrofluid consists of a stable colloidal suspension of single-domain magnetic particles in a base fluid that can assume non-Newtonian fluid behaviour involving a spin vector and microinertia tensor in flow motion. These two properties possess the theory of micropolar fluid which exhibits microrotational motions and spin inertia in microscopic behaviour. Therefore, this theoretical study is focused to investigate the boundary layer of micropolar ferrofluid flow and heat transfer at the stagnation point on the horizontal flat plate. Magnetite (Fe3O4) nanoparticles and water (H2O) compose in ferrofluid exposed to the magnetic field and thermal radiation is considered. The influences of ferroparticles volume fraction and micropolar parameter on the ferrofluid flow and heat transfer are evaluated mathematically. The partial differential equations have been formulated based on purposed assumptions using Tiwari and Das model and are simplified into ordinary differential equations, which are then solved numerically by Runge-Kutta Fehlberg (RFK45) method. The numerical results of the velocity profile, temperature profile, angular velocity profile, reduced skin friction and reduced Nusselt number are scrutinised in different values of ferroparticles volume fraction and micropolar parameter to estimate the ferrofluid flow and heat transfer. It is found the velocity profile of micropolar ferrofluid flow increases when elevates the ferroparticles volume fraction but decreases when increasing the micropolar parameter. Meanwhile, enlarging ferroparticles volume fraction of micropolar ferrofluid also enhances the temperature profile, reduced skin friction and reduced Nusselt number in the presence of magnetic field and thermal radiation parameter.

Simulation of micropolar fluid flow with ternary nanoparticles over a permeable stretching surface involving nonlinear thermal radiation

ABSTRACT The primary goal of this research is to look into the rheological aspects of blood flow that contains ternary nanoparticles ( C u O + T i O 2 + A l 2 O 3 ). For this, the micropolar fluid model is adopted to simulate blood flow transport. Inclined magnetization and porosity characteristics are used to reveal the momentum attributes of flowing fluid, and nonlinearized radiating thermal flux is used to predict the thermal characteristics of the concerned flow. Further, the aspects of suction and injection of fluid over a permeable stretching sheet are also acknowledged. Governing system of partial differential equations are transformed into nonlinear ordinary differential equations by using similarity transformation. An effective built-in routine known as bvp4c, which is based on finite differencing, is used to acquire the solution. The results showed that the trihybrid nanofluid significantly boost fluid motion and temperature profiles more in the mass injection effect in comparison to suction phenomena. The increase in heat transfer rate is also noticed for augmented values of non-linear radiation parameter and micropolar parameter. There is a detailed discussion of the effects of the contributing parameters on the resulting dimensionless profiles. This research has significant implications for the delivery of magnetized blood, hyperthermia therapy, understanding of the bloodstream, transfer of complex bio-waste liquids, and capillary heat exchange.

Two different micro-polar phase-field models for brittle fracture and their open-source finite element implementation

Realizing the limitations of classical phase-field fracture models and the need for the development of non-local phase-field models that can capture the experimentally observed size effects in brittle and quasi-brittle materials, we propose thermodynamically consistent volumetric-deviatoric and spectral decomposition-based phase-field models (PFMs) for brittle fracture in micro-polar continua. For developing the proposed models, we have considered the micro-rotation as an additional kinematic descriptor, and have derived the balance equations by invoking the virtual power principle. On satisfying the thermodynamic laws, we have determined the constitutive relations for the thermodynamic fluxes and demonstrated that any dissipative effect can easily be incorporated into the proposed models. We have provided an open-source finite element (FE) implementation of the micro-polar PFMs using Gridap in Julia. The implementation includes various benchmark problems to illustrate how the responses in a specimen change with the variations in micro-polar material parameters. Through a series of numerical examples with different values of micro-polar material parameters, we have showcased both the capabilities and limitations of the proposed volumetric-deviatoric and spectral decomposition-based micro-polar PFMs.

Axisymmetric motion of a solid particle embedded in a Brinkman micropolar fluid in the presence of a plane wall

The axisymmetric motion of a solid spherical particle embedded in a hydrogel medium in the presence of a planar wall surface is investigated semi-analytically. The hydrogel medium is modeled as a porous medium saturated with a microstructure fluid of micropolar type. The no-slip velocity and no-slip spin boundary conditions are considered at both the particle surface and the plane wall surface. The sixth-order differential equation describing the stream function of the micropolar fluid flow through the voids of the porous medium is constructed under the assumption of low Reynolds numbers. The general solution of the equation satisfied by the stream function in the porous region is obtained from the superposition of basic solutions in both cylindrical and spherical coordinates. To satisfy first the boundary condition at the planar surface, we apply the Fourier–Bessel transforms and then at the surface of the particle by a boundary collocation technique. The collocation scheme for the normalized drag force acting on the particle is calculated with good convergence for various values of the relevant parameter. Our results are in good agreement with the available data in the literature. The findings of the present investigation demonstrate that the presence of the planar surface, micropolarity, and permeability parameters has significant effects on the drag force. This study is motivated by its potential application on micro- and ultra-filtration.

A novel approach to micropolar fluid flow between a non-porous disk and a porous disk with slip

This paper considers the problem of steady, laminar, incompressible, and two-dimensional micropolar fluid flow between two disks. The top disk is considered porous, while the lower one is not. The body forces and body couples were neglected, and the flow was assumed to be fully developed. The governing equations of the problem were reduced to a set of ordinary differential equations (ODEs) by Von-Karman's similarity transformations. Since the obtained governing ODEs have not been solved analytically according to the previous studies, in this article, the Modified Akbari-Ganji method (Modified AGM) and the hybrid analytical and numerical method (HAN-method) have been chosen to solve these equations analytically, which is one of the novelties of this study. However, most of this article's novelty is related to the physical results obtained from the analytical solution of these equations. The effects of various slip coefficients, Reynolds number, and micropolar parameters of vortex viscosity, spin gradient viscosity, and microinertia density on profiles of normal velocity, streamwise velocity, and microrotation. The validity of these two analytical solutions was proved by comparison with previously published results. The results of the two methods are almost the same in all cases, which can be seen as an indirect sign of the validity of the results of this study.

Arrhenius activation energy effect in thermally viscous dissipative flow of micropolar material with gyrotactic microorganisms

The rheology of micropolar material with heat energy transport features is fully progressive, which allows considerable industrial and engineering applications. In this study, numerical analysis is presented to examine the micro-rotation characteristics of magnetized micropolar fluid flow towards the stagnation point region on a porous shrinking surface with gyrotactic microorganisms. To describe the convective energy transport features, Arrehenius activation energy, thermal radiation, Ohmic, and viscous dissipation effects are taken into consideration. The governing equations are converted into ordinary differential equations using appropriate similarity variables. The physical features of flow constraints are displayed and explained for velocity, thermal and solutal distributions, microorganism profile, as well as friction drag, couple stress, and energy transport rate. The results revealed that suction strength contributes to the increment of friction drag, couple stress, and energy transport rate, but the boosted values of the micropolar parameter lower the values of these physical quantities. For a specific range of the shrinking parameter, analysis confirmed the persistence of non-uniqueness solutions. Further, the microorganism profile declines as the bioconvection Lewis number and the bioconvection Peclet number increases. Additionally, according to time-dependent stability analysis, only the upper branch of solutions is physically stable, while the lower branch is not physically.

Analysis of bidirectional flow of Williamson micropolar fluid in porous medium with activation energy and thermal radiation

The prime objective of the proposed model is to explore the impacts of viscous dissipation and Ohmic heating on the bidirectional flow of micropolar and Williamson fluids in porous medium over a stretching surface. The velocity slips and heat convection are assessed at the surface as well. The concernment of chemical reaction, thermophoresis, and Brownian motion repercussions is also considered. More complex nonlinear ordinary differential equations arise when the variables are combined in a suitable manner to represent the mathematical model of the problem. The Galerkin weighted residual approach is used to solve non - linear differential equations’ system that has been developed. Flow patterns are presented by utilizing multiple plots and assessing the influence of various emerging factors. Tables are frequently utilized to characterize the rates of mass and heat transfer. The current findings have yielded several important crucial findings, including the fact that skin friction improves with improvements in the porosity, Williamson fluid, and micropolar fluid parameters. The Nusselt number decays with increments in Eckert numbers and heat source parameters. The velocity field speeds up in the x-direction as the slip parameter enhances, but it lessens in both directions with rise in the porosity parameter and the Williamson fluid parameter. The microrotation velocity profiles in both directions experience a significant reduction as the microrotation slip parameter increases. Also, it has been noted that the nano-liquid concentration profile becomes lesser while the temperature distribution becomes higher for higher values of the Eckert numbers. The thermal profile accelerates as the heat source parameter increases.

Uncovering the mystery of the vortex dynamics in a micropolar fluid with multiple magnetic field strips: A novel case study

From transportation to energy production, environmental protection, and medical advancements, vortices are known to influence everything. Therefore, a remarkable aspect of engineering and scientific research in these areas is the prediction, control, and optimization of such vortices. Motivated by these potential applications, we numerically study ‘how confined magnetic fields may give rise to new vortices in the micropolar flow inside a square cavity, by employing the Alternating Direction Implicit approach. Unlike most of the previous studies, we do not assume a uniform magnetic field throughout the flow domain, which is more realistic. Instead, we introduce several confined magnetic fields in the form of multiple horizontal and vertical strips. Further, we have applied the theory of micropolar fluids proposed by Eringen to model the micropolar fluid and visualize the flow patterns around the magnetic strips in the flow regime. Using our self-developed MATLAB codes, we examine how various parameters, such as the magnetic field strength, the number and position of the strips, and the micropolar parameter affect the flow and thermal properties of the micropolar fluid. The findings of this study will contribute to a better understanding of the vortex generation and heat transfer enhancement of micropolar fluids in lid-driven cavities under localized magnetic fields. The study reveals that both the Nusselt number (Nu) and skin friction (CfRe) coefficient decrease by 45% and 1% respectively with a magnetic number (Mn) for a fixed Reynolds number (Re). However, increasing the Reynolds number at a fixed magnetic number increases the Nusselt number (909%) and skin friction coefficient (7%). This means that the higher flow velocity translates into increased wall shear stress and heat transfer, which destabilizes the flow and may cause turbulence. This knowledge can be used to develop new and improved micropolar fluid-based technologies for a variety of applications, such as energy production, medical devices, and microfluidics.

Effect of thermal instability on heat transfer of micropolar nanofluid saturated in porous medium with rotation

This article investigate the impact of thermal instability on heat transfer of micropolar nanofluid saturated in porous medium with rotation in linear and nonlinear ways. The truncated Fourier series approach is used to analyze nonlinear stability, while analytical evaluation of linear stability is performed with normal mode methodology. Based on outcomes, the micropolar and rotation parameter has stabilizing effect in the system. As opposed to that, nanoparticle Rayleigh number, porosity parameter and Lewis number accelerate the start of convective motion inside the system. Some parameters play a significant influence in transport of heat and mass in non-linear analysis. The rotation parameter, micropolar parameter, perform a major contribution in heat/mass transfer in the system. Mass/heat transfer in the system is analyzed by two different approaches, Mathematica NDSolve and Runge-Kutta-Fehlberg method(RKF-45), and it is found that the rate of mass/heat transfer is exactly the same in both cases.

Analysis of magnetized micropolar fluid subjected to generalized heat-mass transfer theories

Abstract In this study, the steady 2D flow of micropolar fluid via a vertical surface is taken into account. The magnetohydrodynamics applied normally to the flow direction at a vertical surface in the presence of temperature-dependent attributes. The effect of the chemical reaction under the generalized Fourier–Fick law is considered to investigate the heat transference rate at the vertical sheet. Under the flow assumptions, the boundary layer approximations were applied to the nonlinear differential equations and partial differential equations were obtained. The use of similarity modifications allows for a reduction in the number of partial differential equations. The resulting ordinary differential equations are then resolved numerically using a technique known as the homotopy analysis method. The results reveal that microparticle suspensions have a significant impact on the flowing domain when varied fluid characteristics are utilized. The effect of potential factors on flow, micro-rotation velocities, temperature, drag force factor, and heat transport rate is investigated. The obtained results show that the velocity profile and micropolar function increase for larger values of micropolar parameters. Drag force effects are also seen, and required outcomes are observed to be in outstanding accord with the available literature. Significant results of this work were toward the velocity function, which gets reduced with increasing magnetic field parameter values, but the velocity function enhances for higher values of β \beta and λ \lambda . On temperature distribution, it decreased for higher values of ϵ 1 {{\epsilon }}_{1} and temperature profile declines due to higher values of Pr \text{Pr} , γ 2 {\gamma }_{2} and γ 1 {\gamma }_{1} or both cases of δ > 0 \delta \gt 0 and δ < 0 \delta \lt 0 . The higher values of Sc \text{Sc} resist declining the temperature function at the surface.

Analytical solution for nonlinear ODEs arising in flow and heat transfer of MHD Micropolar fluid caused by stretching sheet

Present study examines the MHD flow of a micropolar fluid and heat transfer over a linear stretching sheet. By utilizing a set of dimensionless variables, the system of PDE’s that represents the problem can be converted into dimensionless equations. The dimensionless equations obtained are subsequently solved by using power series method. The impacts of Chandrashekhar number, Micropolar parameter S and Prandtl number Pr on flow, velocity and temperature are examined through graphical representation.

Thermal features of Darcy-Forchheimer on a micropolar fluid flow over a curved stretching surface with homogenous-heterogeneous reactions

The main focus of contemporary study is to explore the Darcy magnetized flow of a micropolar second-grade fluid by consideration of homogeneous-heterogeneous reactions over a curved stretching surface. The thermal aspects of the fluid flow are analyzed with the inclusion of joule heating and thermal radiation effects. Moreover, magnetic field is imposed normal to the surface and thermal stratification condition is considered on the boundary of surface. An appropriate transformation is used to convert the flow model into a set of ordinary differential equations, which are nonlinear in the nature. The numerical solutions of this nonlinear system of equations are obtained using the bvp4c technique on MATLAB. The velocity, temperature, concentration, and micro-rotation distribution variation for various parameter is shown graphically and with numerical data. The main finding in the current problem to see that that greater estimation of micropolar parameter improves the angular velocity of the fluid, whereas linear velocity of fluid declines for larger values of magnetic parameter because of the resistance effect take place due to magnetized flow. Furthermore, it seems that curvature parameter produces the improvement in the linear and angular velocity of the fluid.

Micropolar Hydromagnetic Fluid Over a Vertical Surface in Darcian Regime: An Analytical Approach

In the present paper, the researcher investigates the mutual impact of radiative heat and mass exchange on hydromagnetic micropolar fluid moving along an infinite vertical surface in a porous regime. The goal of the research is to investigate the impact of convective temperature and mass flow on hydromagnetic motion of micropolar fluid across a vertical plate ingrained in a porous regime. The conservation equations with appropriate boundary conditions are resolved analytically by assuming a convergent series solution and thus obtained the analytical solutions for velocity, angular velocity (microrotation), temperature and molar-concentration. The novelty of the current work is that it takes heat transfer into account while considering for the impacts of chemical reaction in a micropolar fluid flow of reactive diffusing species. The influence of different physical variables on temperature, molar-concentration, velocity and angular velocity of the fluid molecules have been presented graphically for dual solutions. It is seen that the micropolar parameter and porosity of the medium play a significant behaviour over the momentum and thermal boundary layers. This investigation may involve with various disciplines of chemical engineering, bio-mechanics and medical sciences. The outcomes of the present study have significant applications in MHD generators and geothermal resource extraction.

Heat and mass transfer analysis for MHD non‐miscible micropolar and Newtonian fluid flow in a rectangular porous channel

AbstractThe aim of the present work is to examine the entropy production characteristics, thermal profile, and flow behaviour of two non‐miscible natures of Newtonian and micropolar fluids, which take place through a rectangular porous enclosure channel. The flow region is divided into two distinct porous zones of the channel and is subjected to a constant oriented magnetic field. The Eringen's micropolar fluid is taking place in the upper porous zone, whereas in the lower porous zone, the Newtonian fluid is flowing. The wall surface of a rectangular porous channel is isothermal, and the flow of immiscible fluid through a porous channel takes place because of a constant pressure gradient. No slip condition is imposed on the static walls and continuity of vorticity, velocity, shear stress component, thermal distribution, and thermal flux are prescribed at the interface. Here, the production of entropy due to fluid friction and thermal exchange for non‐miscible Newtonian and micropolar fluids is evaluated. The characteristics of various estimated parameters on thermal and flow properties, such as Bejan number distribution, flow velocity, entropy production, and thermal profile, are discussed. The obtained results show that entropy production is directly proportional to viscous dissipation and Reynolds number, whereas it has a reverse nature with micropolarity parameter, inclination angle parameter, and Hartman number. Our results corroborate with previous published results.

Computation of micropolar nanofluid from a wedge with heterogeneous carbon/metallic nanoparticles, viscous dissipation and heat sink/source: rheological nanocoating flow simulation

ABSTRACT Motivated by nanotechnological coating applications, a theoretical study is presented for the laminar, steady-state, incompressible nonlinear boundary layer flow of a non-Newtonian nanofluid external to a wedge-shaped configuration. The wedge surface is assumed to be isothermal. The Eringen micropolar model is deployed for rheological properties of the nanofluid. The dimensionless thermal perimeter layer equations are solved with the efficient MATLAB bvp4c numerical scheme. Validation with earlier studies is conducted. Aqueous-based nano-polymers are examined with either metallic/metallic oxide or carbon-based nanoparticles. The influence of Hartree pressure gradient parameter, Eringen vortex viscosity parameter, nanoparticle volume fraction, heat absorption parameter, Prandtl number and nanoparticle type on velocity, angular velocity, temperature, skin friction function and Nusselt number function are visualized graphically and in tables. Temperature is strongly elevated with increasing micropolar parameter and nanoparticle volume fraction. Velocity is boosted with increasing nanoparticle volume fraction. Temperatures are elevated with heat source but suppressed with heat sink. Temperatures are a maximum for silver and progressively lower for copper, diamond and with a minimum for titania. Skin friction is boosted with pressure gradient parameter whereas Nusselt number is depleted. Nusselt number is observed to be a maximum for diamond whereas it is a minimum for silver.

Bayesian regularization networks for micropolar ternary hybrid nanofluid flow of blood with homogeneous and heterogeneous reactions: Entropy generation optimization

This study aims to analyze a Bayesian regularization backpropagation algorithm for micropolar ternary hybrid nanofluid flow over curved surfaces with homogeneous and heterogeneous reactions, Joule heating and viscous dissipation. The ternary hybrid nanofluid consists of nanoparticles of titanium oxide (TiO2), copper oxide (CuO), and silicon oxide (SiO2), with blood as the base fluid. The governing partial differential equations for the fluid flow are converted into ordinary differential equations using a group of self-similar transformations. The ordinary differential equations are solved using an appropriate shooting algorithm in MATLAB. The effects of physical parameters including curvature, micro-polar, radiation, magnetic, Prandtl, Eckert, Schmidt, and homogeneous and heterogeneous chemical reaction parameters are analyzed for velocity, micro rotational, temperature, and concentration profile. Physical quantities of engineering interest like heat transfer rate, mass transfer rate, skin friction coefficient, couple stress coefficient, and entropy generation are also discussed in this study. A Bayesian regularization backpropagation algorithm is also designed for the solution of the ordinary differential equations. The obtained network is analyzed using training state, performance, error histograms, model response, Error autocorrelation, and input-error correlation plots. It is observed that the entropy generation and the Bejan number increase for enhancing Brinkman and radiation parameter. Clinical researchers and biologists may use the results of this computational study to forecast endothelial cell damage and plaque deposition in curved arteries, by which the severity of these conditions can be reduced.