15 research outputs found
Effect of an Inclined Magnetic Field on the Flow of Nanofluids in a Tapered Asymmetric Porous Channel with Heat Source/Sink and Chemical Reaction
This article deals with the effect of an inclined magnetic field with heat source/sink on the flow of nanofluids in a tapered asymmetric porous channel. Effect of chemical reaction has been taken into account. The blood is considered as an incompressible electrically conducting viscous fluid. The assumption of low Reynolds number and long wave length approximations has been adopted. Exact solutions for dimensionless axial velocity, concentration and temperature profile are obtained analytically. The obtained results are displayed and discussed in detail with the help of graphs for the variation of different emerging flow parameters
Peristaltic Transport of a Couple Stress Fluid: Some Applications to Hemodynamics
The present paper deals with a theoretical investigation of the peristaltic
transport of a couple stress fluid in a porous channel. The study is motivated
towards the physiological flow of blood in the micro-circulatory system, by
taking account of the particle size effect. The velocity, pressure gradient,
stream function and frictional force of blood are investigated, when the
Reynolds number is small and the wavelength is large, by using appropriate
analytical and numerical methods. Effects of different physical parameters
reflecting porosity, Darcy number, couple stress parameter as well as amplitude
ratio on velocity profiles, pumping action and frictional force, streamlines
pattern and trapping of blood are studied with particular emphasis. The
computational results are presented in graphical form. The results are found to
be in good agreement with those of Shapiro et. al \cite{r25} that was carried
out for a non-porous channel in the absence of couple stress effect. The
present study puts forward an important observation that for peristaltic
transport of a couple stress fluid during free pumping when the couple stress
effect of the fluid/Darcy permeability of the medium, flow reversal can be
controlled to a considerable extent. Also by reducing the permeability it is
possible to avoid the occurrence of trapping phenomenon
Micropolar pulsatile blood flow conveying nanoparticles in a stenotic tapered artery : non-Newtonian pharmacodynamic simulation
Two-dimensional rheological laminar hemodynamics through a diseased tapered artery with a
mild stenosis present is simulated theoretically and computationally. The effect of different
metallic nanoparticles homogeneously suspended in the blood is considered, motivated by drug
delivery (pharmacology) applications. The Eringen micropolar model has been deployed for
hemorheological characteristics in the whole arterial region. The conservation equations for
mass, linear momentum, angular momentum (micro-rotation), and energy and nanoparticle
species are normalized by employing suitable non-dimensional variables. The transformed
equations are solved numerically subject to physically appropriate boundary conditions using
the finite element method with the variational formulation scheme available in the FreeFEM++
code. A good correlation is achieved between the FreeFEM++ computations and existing
results. The effect of selected parameters (taper angle, Prandtl number, Womersley parameter,
pulsatile constants, and volumetric concentration) on velocity, temperature, and microrotational (Eringen angular) velocity has been calculated for a stenosed arterial segment. Wall
shear stress, volumetric flow rate, and hemodynamic impedance of blood flow are also
computed. Colour contours and graphs are employed to visualize the simulated blood flow
characteristics. It is observed that by increasing Prandtl number (Pr), the micro-rotational
velocity decreases i.e., microelement (blood cell) spin is suppressed. Wall shear stress
decreases with the increment in pulsatile parameters (B and e), whereas linear velocity
increases with a decrement in these parameters. Furthermore, the velocity decreases in the
tapered region with elevation in the Womersley parameter (α). The simulations are relevant to
transport phenomena in pharmacology and nano-drug targeted delivery in hematology
Generalized power-law model of magnetohydrodynamic blood flow in an inclined stenosed artery with body acceleration
This thesis focuses on the development of a mathematical model to investigate the effect of magnetic field and body acceleration on blood flow characteristics, heat and mass transfer from a stenosed artery, a condition due to the abnormal narrowing of a blood vessel. The arterial segment is assumed to be a cylindrical tube in an inclined position with oscillating boundary condition and the stenosis taking the shape of a cosine function. The momentum equation is based on the generalized power law model which is expected to handle the variations in blood rheology as blood flows through a different-sized vessel, with the index n 1 and n = 0 describing the shear-thinning, shear-thickening and Newtonian fluid respectively. The full governing equations comprising the generalized power-law equation, heat and mass equations are non-linear partial differential equations whose numerical procedure involves the discretization of the equations using the Marker and Cell (MAC) method, where pressure along the tube is calculated iteratively using the Successive-Over-Relaxation (SOR) technique. The results have been compared and validated with existing results in certain limiting cases. New results in terms of pressure, streamlines, heat and mass distribution are obtained for various parameter values of each of the external body forces. Specifically, for a stenosis with 48% occlusion, separation is seen to occur for Newtonian fluids at Re = 1000 and this region can be seen to increase in the case of shear thickening fluids, while the shear-thinning fluid is shown to be free of separation region. Moreover, blood velocity, wall shear stress and pressure drop decrease with increase n, while heat and mass transfer increase. It is also demonstrated through the simulations that under the influence of magnetic field, the velocity in the centre of the artery and the separation region are reduced with a sufficient strength of magnetic field, depending on the severity of stenosis. For a 75% and 84% occlusion, the separation zones entirely disappear with magnetic strength 8 and 12 Tesla respectively, while the pressure drop, wall shear stress, heat and mass transfer increase. On the other hand, increasing periodic body acceleration leads to increase velocity and the pressure drop while reducing heat and mass transfer. Inclination angle increases the velocity and wall shear stress but decreases the pressure drop and heat and mass transfer. Based on the results, patients with blood vessel disease are advised not to do a high-intensity exercise; it can put extra strain on the heart leading to a risk in chest pain or even cardiac arrest. Regular exercise and suitable intensity of magnetic field could enhance vascular health
Computational fluid dynamic simulation of two-fluid non-newtonian nanohemodynamics through a diseased artery with a stenosis and aneurysm
This article presents a two-dimensional theoretical study of hemodynamics through a diseased
permeable artery with a mild stenosis and an aneurysm present. The effect of metallic nanoparticles
on the blood flow is considered, motivated by drug delivery (pharmacology) applications. Two
different models are adopted to mimic non-Newtonian characteristics of the blood flow; the Casson
(viscoplastic) fluid model is deployed in the core region and the Sisko (viscoelastic) fluid model
employed in the peripheral (porous) region. The revised Buongiorno two-component nanofluid
model is utilized for nanoscale effects. The blood is considered to contain a homogenous
suspension of nanoparticles. The governing equations are derived by extending the Navier-Stokes
equations with linear Boussinesq approximation (which simulates both heat and mass transfer).
Natural (free) double-diffusive convection is considered to simulate the dual influence of thermal
and solutal buoyancy forces. The conservation equations are normalized by employing appropriate
non-dimensional variables. The transformed equations are solved numerically using the finite
element method with the variational formulation scheme available in the FreeFEM++ code. A
comprehensive mesh-independence study is included. The effect of selected parameters
(thermophoresis, Brownian motion, Grashof number, thermo-solutal buoyancy ratio, Sisko
parameter ratio and permeability parameter) on velocity, temperature, nanoparticle concentration
2
and hemodynamic pressure have been calculated for two clinically important cases of arteries with
a stenosis and an aneurysm. Skin-friction coefficient, Nusselt number, volumetric flow rate and
resistance impedance of blood flow are also computed. Colour contours and graphs are employed
to visualize the simulated blood flow characteristics. It is observed that by increasing thermal
buoyancy parameter i.e. Grashof number (Gr), the nanoparticle concentration and temperature
decrease whereas velocity increases with an increment in Brownian motion parameter (Nb).
Furthermore, velocity decreases in the peripheral porous region with elevation in the Sisko
material ratio (m) and permeability parameter (k’). The simulations are relevant to transport
phenomena in pharmacology and nano-drug targeted delivery in haematology
Unsteady newtonian and non-newtonian fluid flows in the circular tube in the presence of magnetic field using caputo-fabrizio derivative
This thesis investigates analytically the magnetohydrodynamics (MHD) transport of
Newtonian and non-Newtonian fluids flows inside a circular channel. The flow
was subjected to an external electric field for the Newtonian model and a uniform
transverse magnetic field for all models. Pressure gradient or oscillating boundary
condition was employed to drive the flow. In the first model Newtonian fluid flow
without stenotic porous tube was considered and in the second model stenotic porous
tube was taken into account. The third model is concerned with the temperature
distribution and Nusselt number. The fourth model investigates the non-Newtonian
second grade fluid velocity affected by the heat distribution and oscillating walls. Last
model study the velocity, acceleration and flow rate of third grade non-Newtonian
fluid flow in the porous tube. The non-linear governing equations were solved
using the Caputo-Fabrizio time fractional order model without singular kernel. The
analytical solutions were obtained using Laplace transform, finite Hankel transforms
and Robotnov and Hartley’s functions. The velocity profiles obtained from various
physiological parameters were graphically analyzed using Mathematica. Results were
compared with those reported in the previous studies and good agreement were found.
Fractional derivative and electric field are in direct relation whereas magnetic field and
porosity are in inverse relation with respect to the velocity profile in Newtonian flow
case. Meanwhile, fractional derivative and Womersely number are in direct relation
whereas magnetic field, third grade parameter, frequency ratio and porosity are in
inverse relation in third grade non-Newtonian flow case. In the case of second grade
fluid, Prandtl number, fractional derivative and Grashof number are in direct relation
whereas second grade parameter and magnetic field are in inverse relation. The fluid
flow model can be regulated by applying a sufficiently strong magnetic field
Finite element analysis of non-Newtonian magnetohemodynamic flow conveying nanoparticles through a stenosed coronary artery
The present study considers two-dimensional mathematical modelling of non-Newtonian nanofluid hemodynamics with heat and mass transfer in a stenosed coronary artery in the presence of a radial magnetic field. The second-grade differential viscoelastic constitutive model is adopted for blood to mimic non-Newtonian characteristics and blood is considered to contain a homogenous suspension of nanoparticles. Vogel’s model is employed to simulate the variation of blood viscosity as a function of temperature. The governing equations are an extension of the Navier-Stokes equations with linear Boussinesq’s approximation and Buongiorno’s nanoscale model (which simulates both heat and mass transfer). The conservation equations are normalized by employing appropriate non-dimensional variables. It is assumed that the maximum height of the stenosis is small in comparison with the radius of the artery and furthermore that the radius of the artery and length of the stenotic region are of comparable magnitude. To study the influence of vessel geometry on blood flow and nano-particle transport, variation in the design and size of the stenosis is considered in the domain. The transformed equations are solved numerically by means of the finite element method based on the variational approach and simulated using the FreeFEM++ code. A detailed grid-independence study is included. Blood flow, heat and mass transfer characteristics are examined for the effects of selected geometric, nanoscale, rheological, viscosity and magnetic parameters i.e. stenotic diameter (d), viscoelastic parameter (), thermophoresis parameter (Ni), Brownian motion parameter (Nb) and magnetic body force parameter (M) at the throat of the stenosis and throughout the arterial domain. The velocity, temperature and nanoparticle concentration fields are also visualized through instantaneous patterns of contours. An increase in magnetic and thermophoresis parameters is found to enhance the temperature, nanoparticle concentration and skin-friction coefficient. Increasing Brownian motion parameter is observed to accelerate the blood flow. Narrower stenosis significantly alters the temperature and nano-particle distributions and magnitudes. The novelty of the study relates to the combination of geometric complexity, multi-physical nanoscale and thermomagnetic behaviour and also the simultaneous presence of bio-rheological behaviour (all of which arise in actual cardiovascular heat transfer phenomena) in a single work with extensive visualization of the flow, heat and mass transfer characteristics. The simulations are relevant to diffusion of nanodrugs in magnetic targeted treatment of stenosed arterial disease
Cilia-assisted hydromagnetic pumping of biorheological couple stress fluids
A theoretical study is conducted for magnetohydrodynamic pumping of electro-conductive couple stress physiological liquids (e.g. blood) through a two-dimensional ciliated channel. A geometric model is employed for the cilia which are distributed at equal intervals and produce a whip-like motion under fluid interaction which obeys an elliptic trajectory. A metachronal wave is mobilized by the synchronous beating of cilia and the direction of wave propagation is parallel to the direction of fluid flow. A transverse static magnetic field is imposed transverse to the channel length. The Stokes’ couple stress (polar) rheological model is utilized to characterize the liquid. The normalized two-dimensional conservation equations for mass, longitudinal and transverse momentum are reduced with lubrication approximations (long wavelength and low Reynolds number assumptions) and feature a fourth order linear derivative in axial velocity representing couple stress contribution. A coordinate transformation is employed to map the unsteady problem from the wave laboratory frame to a steady problem in the wave frame. No slip conditions are imposed at the channel walls. The emerging linearized boundary value problem is solved analytically, and expressions presented for axial (longitudinal) velocity, volumetric flow rate, shear stress function and pressure rise. The flow is effectively controlled by three geometric parameters, viz cilia eccentricity parameter, wave number and cilia length and two physical parameters, namely magnetohydrodynamic body force parameter and couple stress non-Newtonian parameter. Analytical solutions are numerically evaluated with MATLAB software. Axial velocity is observed to be enhanced in the core region with greater wave number whereas it is suppressed markedly with increasing cilia length, couple stress and magnetic parameters, with significant flattening of profiles with the latter two parameters. Axial pressure gradient is decreased with eccentricity parameter whereas it is elevated with cilia length, in the channel core region. Increasing couple stress and magnetic field parameter respectively enhance and suppress pressure gradient across the entire channel width. The pressure-flow rate relationship is confirmed to be inversely linear and pumping, free pumping and augmented pumping zones are all examined. Bolus trapping is also analyzed. The study is relevant to MHD biomimetic blood pumps
Computational Assessment of Fluid Flow in Stenotic Arteries: Application in Targeted Drug Therapy
Blood flow dynamics are crucial in the development and progression of cardiovascular diseases. Computational modeling of blood circulation in arteries is vital for understanding disease symptoms and enhancing treatments. Aneurysms, stenoses, and atherosclerosis can change blood flow characteristics, leading to serious healthcomplications due to abnormal blood flow patterns and high wall shear stresses (WWS). Simulating these changes can help in detecting cardiovascular diseases early and managing them effectively. The commencement of the dissertation involves an effort to create a model of the 2D shape of a non-uniform artery wall that has a restricted segment, using a segmented function, which includes an obstruction of approximately 40%. The blood flow in the body follows a rhythmic pressure gradient that imitates the heart’s systolic and diastolic phases. Because blood behaves like a non-Newtonian fluid in certain situations, the Casson model for non-Newtonian fluids is used to account for the yield stress resulting from the formation of red blood cell aggregates at low shear rates. The Navier-Stokes equations, which describe incompressible and unsteady fluid flow, are expanded to include the non-Newtonian behavior of blood flow in radial coordinates. This is accomplished by including a temperature equation. To analyze the impact of stenosis over the flow, drug delivery agents such as copper (Cu) and alumina (Al2O3) nanoparticles with a concentration of about 0.03% are used. The concept of magnetohydrodynamics (MHD) involves applying a magnetic field to blood flow in an artery, taking into account the Hall current, to deliver magnetic drug carriers to a specific location within the bloodstream. The simulation of blood flow begins from a state of rest with zero velocity and temperature, using initial conditions to simplify the mathematical modeling process. On the symmetry axis, a zero radial gradient condition is applied to both velocity and temperature, while no-slip conditions are applied to the arterial wall. The complexity of the governing partial differential equations is removed by nondimensionalizing them. There are two cases to consider: the first case involves disregarding the long wavelength approach, which remains open issue for future consideration. The alternative scenario involves presenting the acquired dimensionless PDEs through the long-wavelength approximation and then applying a radial coordinate transformation to simplify them even further. Afterward, MATLAB software is utilized to execute the 2D explicit forward time central space (FTCS) differentiation method. Momentum and thermal analysis were done for blood, Cublood nanofluid, and Cu-Al2O3-blood hybrid nanofluid, along with wall shear stress (WWS) and local Nusselt number (Nulocal) evaluation.We proceed to revise the last batch of dimensional partial differential equations (PDEs) describing the behavior of non-Newtonian Cu-Al2O3-blood by incorporating magnetohydrodynamic (MHD) effects. Our approach involves converting the PDEs into a Reynolds-averaged Navier Stokes equation (RANS), which employs Reynolds averaging to account for turbulence in the mean flow. This is achieved by decomposing the flow variables into average and perturbed components. The equations for fluid dynamics include turbulent forces caused by eddy shear and molecular turbulence. These forces are accounted for using Boussinesq’s eddy-viscosity hypothesis, which is based on the average flow of the fluid. Additionally, the Zero-equation turbulence model, which is also called the algebraic turbulence model, is utilized by combining the principles of Prandtl mixing length and Boussinesq approximation. Turbulent flow is considered unsteady and fully developed, and flow properties are also modified using the Prandtl mixing length model with the laminar and turbulent effect contribution. The subsequent step involves making these equations nondimensional and then utilizing radial coordinate transformations. The resulting set of dimensionless partial differential equations that consists of Reynold and turbulent Prandtl numbers are then simulated using FTCS methodology. Additionally, the effect of various emerging parameters is analyzed through a graphical representation of the momentum equation for high Reynold numbers (Re = 42000, 46000). The last analysis involved flow momentum and pressure for the laminar flow scenario by considering blood as a Newtonian fluid. Using AutoCAD software, a 3D constricted artery with a 70% elliptical shaped stenosis was created. To proceed further, an ideal mesh was created using OpenFOAM’s blockMesh and snappyHexMesh tools. The simulation for laminar and incompressible flow has been conducted using the coFoam solver, which guarantees the convergence of the simulation at Courant number ≈ 0.2 < 1. Two different scenarios have been taken into account for the velocity inlet. Firstly, a parabolic velocity profile was used with a maximum inlet velocity of 0.003m/s. The outlet velocity was set to zero gradient and the inlet pressure was also set to zero. Secondly, we used a constant inlet velocity of 0.0137m/s for laminar flow with a Reynolds number of 200. We graphically analyzed the momentum and pressure of the fluid both at the center of the stricture and throughout the constriction arterial segment for both inlet velocity conditions
Blood flow mediated hybrid nanoparticles in human arterial system : recent research, development and applications
Blood flow dynamics contributes an elemental part in the formation and expansion of cardiovascular
diseases in human body. Computational simulation of blood flow in the human arterial system has been widely
used in recent decades for better understanding the symptomatic spectrum of various diseases, in order to improve
already existing or develop new therapeutic techniques. The characteristics of the blood flow in an artery can be
changed significantly by arterial diseases, such as aneurysms and stenoses. The progress of atherosclerosis or
stenosis in a blood vessel is quite common which may be caused due to the addition of lipids in the arterial wall.
Nanofluid is a colloidal mixture of nanometer sized (which ranges from 10-100m) metallic and non-metallic
particles in conventional fluid (such as water, oil). The delivery of nanoparticles is an interesting and growing
field in the development of diagnostics and remedies for blood flow complications. An enhancement of nano-drug
delivery performance in biological systems, nanoparticles properties such as size, shape and surface characteristics
can be regulated. Nanoparticle offers remarkably advantages over the traditional drug delivery in terms of high
specificity, high stability, high drug carrying capacity, ability for controlled release. Highly dependency has been
found for their behavior under blood flow while checking for their ability to target and penetrate tissues from the
blood. In the field of nano-medicine, organic (including polymeric micelles and vesicles, liposomes) and inorganic
(gold and mesoporous silica, copper) nanoparticles have been broadly studied as particular carriers because as
drug delivery systems they delivered a surprising achievement as a result of their biocompatibility with tissue and
cells, their subcellular size, decreased toxicity and sustained release properties. For the extension of nanofluids
research, the researchers have also tried to use hybrid nanofluid recently, which is synthesized by suspending
dissimilar nanoparticles either in mixture or composite form. The main idea behind using the hybrid nanofluid is
to further improve the heat transfer and pressure drop characteristics. Nanoparticles are helpful as drug carriers to
minimize the effects of resistance impedance to blood flow or coagulation factors due to stenosis. Discussed
various robust approaches have been employed for the nanoparticle transport through blood in arterial system.
The main objective of the paper is to provide a comprehensive review of computational simulations of blood flow
containing hybrid-nanoparticles as drug carriers in the arterial system of the human body. The recent developments
and analysis of convective flow of particle-fluid suspension models for the axi-symmetric arterial bodies in
hemodynamics are summarized. Detailed existing mathematical models for simulating blood flow with
nanoparticles in stenotic regions are reviewed. The review focuses on selected numerical simulations of
physiological convective flows under various stenosis approximations and computation of the temperature, velocity, resistance impedance to flow, wall shear stress and the pressure gradient with the corresponding boundary
conditions. The current review also highlights that the drug carrier nanoparticles are efficient mechanisms for
reducing hemodynamics of stenosis and could be helpful for other biomedical applications. The review considers
flows through various stenoses and the significances of numerical fluid mechanics in clinical medicine. The review
examines nano-drug delivery systems, nanoparticles and describes recent computational simulations of nanopharmacodynamics