scholarly journals Fractional model of MHD blood flow in a cylindrical tube containing magnetic particles

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Samina Majeed ◽  
Farhad Ali ◽  
Anees Imtiaz ◽  
Ilyas Khan ◽  
Mulugeta Andualem
Keyword(s):  
Blood Flow ◽  
Magnetic Particles ◽  
Flow Direction ◽  
Mass Parameter ◽  
Cylindrical Tube ◽  
Hankel Transform ◽  
Minimal Invasive ◽  
Diagnostic Tools ◽  
Physical Parameters ◽  
Finite Hankel Transform

AbstractIn recent years, the use of magnetic particles for biomedicine and clinical therapies has gained considerable attention. Unique features of magnetic particles have made it possible to apply them in medical techniques. These techniques not only provide minimal invasive diagnostic tools but also transport medicine within the cell. In recent years, MRI, drug supply to infected tissue, Hyperthermia are more enhanced by the use of magnetic particles. The present study aims to observe heat and mass transport through blood flow containing magnetic particles in a cylindrical tube. Furthermore, the magnetic field is applied vertically to blood flow direction. The Caputo time fractional derivative is used to model the problem. The obtained partial fractional derivatives are solved using Laplace transform and finite Hankel transform. Furthermore, the effect of various physical parameters of our interest has also been observed through various graphs. It has been noticed that the motion of blood and magnetic particles is decelerated when the particle mass parameter and the magnetic parameter are increased. These findings are important for medicine delivery and blood pressure regulation.

scholarly journals Magnetohydrodynamic Blood Flow in a Cylindrical Tube with Magnetic Particles: A Time Fractional Model

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Farhad Ali ◽  
Samina Majeed ◽  
Anees Imtiaz
Keyword(s):  
Blood Flow ◽  
Magnetic Particles ◽  
Mass Parameter ◽  
Classical Model ◽  
Cylindrical Tube ◽  
Definition Of ◽  
Circular Cylindrical Tube ◽  
Short Time ◽  
Applied External Magnetic Field ◽  
Fractional Parameter

The present work theoretically investigates the natural convection blood flow as a Brinkman-type fluid with uniformly distributed magnetic particles in a circular cylindrical tube with the applied external magnetic field. The classical model for the blood flow is generalized by using the definition of Caputo time-fractional derivative. The exact solutions are obtained by using the Laplace and Henkel transforms. Unlike the classical model, the obtained general results are expressed in the form of “Lorenzo and Hartley’s” and “Robotnov and Hartley’s” functions. Graphs are plotted to show the effects of different parameters on the blood flow. Furthermore, the velocity and temperature distributions are discussed in terms of memory. The effect of fractional parameter α for a long and short time has also been observed. It is noticed that blood velocity can be controlled using the fractional parameter. It is also found that, for τ > 0 , fluid and particles motion increased, and reverse behavior is observed for τ < 0 . It has been noticed that increasing values of particle mass parameter P m and magnetic parameter M slow down the motion of blood and magnetic particles. These results are helpful for effective drug delivery and regulating blood flow.

Generalized Brinkman Type Dusty Fluid Model for Blood Flow

2020 ◽  
pp. 154-170
Author(s):  
Muhammad Saqib ◽  
Sharidan Shafie ◽  
Ilyas Khan
Keyword(s):  
Blood Flow ◽  
Magnetic Parameter ◽  
Fluid Model ◽  
Cylindrical Tube ◽  
Hankel Transform ◽  
Governing Equations ◽  
Two Phase ◽  
Cylindrical Coordinate ◽  
Long Time ◽  
Fractional Parameter

This chapter is dedicated to studying the magnetic blood flow with uniformly distributed magnetite dusty particles (MDP) in a cylindrical tube. For this purpose, the two-phase fractional Brinkman type fluid model is considered. The fractional governing equations are modeled in the cylindrical coordinate system taking into consideration the magnetization of the fluid due to the applied magnetic field. The fractional governing equations are subjected to physical initial and boundary conditions. The joint Laplace and Hankel transform is employed to develop exact analytical solutions. The obtained solutions are computed numerically and plotted in different graphs. It is noticed that for a long time the blood and MDP velocities increase with increasing values of the fractional parameter. In contrast, this effect reverses for a shorter time. In the case of the magnetic parameter, both velocities are decreased with increasing values of the magnetic parameter.

Spatial Variability of Physical Parameters and Processes in Two Field Soils

1991 ◽  
Vol 22 (5) ◽  
pp. 327-340 ◽  
Author(s):  
K. Høgh Jensen ◽  
J. C. Refsgaard
Keyword(s):  
Transport Model ◽  
Flow Direction ◽  
Measurement Data ◽  
Flow Simulation ◽  
Solute Concentration ◽  
Conclusive Evidence ◽  
Physical Parameters ◽  
Effective Parameters ◽  
The Mean ◽  
Tracer Experiments

A numerical analysis of solute transport in two spatially heterogeneous fields is carried out assuming that the fields are composed of ensembles of one-dimensional non-interacting soil columns, each column representing a possible soil profile in statistical terms. The basis for the analysis is the flow simulation described in Part II (Jensen and Refsgaard, this issue), which serves as input to a transport model based on the convection-dispersion equation. The simulations of the average and variation in solute concentration in planes perpendicular to the flow direction are compared to measurements obtained from tracer experiments carried out at the two fields. Due to the limited amount of measurement data, it is difficult to draw conclusive evidence of the simulations, but reliable simulations are obtained of the mean behaviour within the two fields. The concept of equivalent soil properties is also tested for the transport problem in heterogeneous soils. Based on effective parameters for the retention and hydraulic conductivity functions it is possible to predict the mean transport in the two experimental fields.

scholarly journals Advanced Constitutive Modeling of the Thixotropic Elasto-Visco-Plastic Behavior of Blood: Steady-State Blood Flow in Microtubes

Materials ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 367
Author(s):  
Konstantinos Giannokostas ◽  
Yannis Dimakopoulos ◽  
Andreas Anayiotos ◽  
John Tsamopoulos
Keyword(s):  
Blood Flow ◽  
Steady State ◽  
Constitutive Model ◽  
Blood Plasma ◽  
Constitutive Modeling ◽  
Flow Direction ◽  
Momentum Balance ◽  
Plastic Behavior ◽  
Flow Investigation ◽  
The Impact

The present work focuses on the in-silico investigation of the steady-state blood flow in straight microtubes, incorporating advanced constitutive modeling for human blood and blood plasma. The blood constitutive model accounts for the interplay between thixotropy and elasto-visco-plasticity via a scalar variable that describes the level of the local blood structure at any instance. The constitutive model is enhanced by the non-Newtonian modeling of the plasma phase, which features bulk viscoelasticity. Incorporating microcirculation phenomena such as the cell-free layer (CFL) formation or the Fåhraeus and the Fåhraeus-Lindqvist effects is an indispensable part of the blood flow investigation. The coupling between them and the momentum balance is achieved through correlations based on experimental observations. Notably, we propose a new simplified form for the dependence of the apparent viscosity on the hematocrit that predicts the CFL thickness correctly. Our investigation focuses on the impact of the microtube diameter and the pressure-gradient on velocity profiles, normal and shear viscoelastic stresses, and thixotropic properties. We demonstrate the microstructural configuration of blood in steady-state conditions, revealing that blood is highly aggregated in narrow tubes, promoting a flat velocity profile. Additionally, the proper accounting of the CFL thickness shows that for narrow microtubes, the reduction of discharged hematocrit is significant, which in some cases is up to 70%. At high pressure-gradients, the plasmatic proteins in both regions are extended in the flow direction, developing large axial normal stresses, which are more significant in the core region. We also provide normal stress predictions at both the blood/plasma interface (INS) and the tube wall (WNS), which are difficult to measure experimentally. Both decrease with the tube radius; however, they exhibit significant differences in magnitude and type of variation. INS varies linearly from 4.5 to 2 Pa, while WNS exhibits an exponential decrease taking values from 50 mPa to zero.

scholarly journals Significance of Slippage and Electric Field in Mucociliary Transport of Biomagnetic Fluid

Lubricants ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 48
Author(s):  
Sufian Munawar
Keyword(s):  
Shear Stress ◽  
Flow Direction ◽  
Pressure Rise ◽  
Physical Parameters ◽  
Slippage Effect ◽  
Channel Surface ◽  
Electro Osmosis ◽  
Biomagnetic Fluid ◽  
Velocity Pressure ◽  
Metachronal Waves

Shear stress at the cilia wall is considered as an imperative factor that affects the efficiency of cilia beatings as it describes the momentum transfer between the fluid and the cilia. We consider a visco-inelastic Prandtl fluid in a ciliated channel under electro-osmotic pumping and the slippage effect at cilia surface. Cilia beating is responsible for the stimulation of the flow in the channel. Evenly distributed cilia tend to move in a coordinated rhythm to mobilize propulsive metachronal waves along the channel surface by achieving elliptic trajectory movements in the flow direction. After using lubrication approximations, the governing equations are solved by the perturbation method. The pressure rise per metachronal wavelength is obtained by numerically integrating the expression. The effects of the physical parameters of interest on various flow quantities, such as velocity, pressure gradient, pressure rise, stream function, and shear stress at the ciliated wall, are discussed through graphs. The analysis reveals that the axial velocity is enhanced by escalating the Helmholtz–Smoluchowski velocity and the electro-osmosis effects near the elastic wall. The shear stress at the ciliated boundary elevates with an increase in the cilia length and the eccentricity of the cilia structure.

scholarly journals Altered biventricular hemodynamic forces in patients with repaired tetralogy of Fallot and right ventricular volume overload because of pulmonary regurgitation

2018 ◽  
Vol 315 (6) ◽  
pp. H1691-H1702 ◽  
Author(s):  
Pia Sjöberg ◽  
Johannes Töger ◽  
Erik Hedström ◽  
Per Arvidsson ◽  
Einar Heiberg ◽  
...  
Keyword(s):  
Blood Flow ◽  
Right Ventricular ◽  
Tetralogy Of Fallot ◽  
Flow Direction ◽  
Pulmonary Regurgitation ◽  
Ventricular Volume ◽  
Left Ventricular ◽  
Hemodynamic Forces ◽  
Control Subjects ◽  
Repaired Tetralogy Of Fallot

Intracardiac hemodynamic forces have been proposed to influence remodeling and be a marker of ventricular dysfunction. We aimed to quantify the hemodynamic forces in patients with repaired tetralogy of Fallot (rToF) to further understand the pathophysiological mechanisms as this could be a potential marker for pulmonary valve replacement (PVR) in these patients. Patients with rToF and pulmonary regurgitation (PR) > 20% ( n = 18) and healthy control subjects ( n = 15) underwent MRI, including four-dimensional flow. A subset of patients ( n = 8) underwent PVR and MRI after surgery. Time-resolved hemodynamic forces were quantified using 4D-flow data and indexed to ventricular volume. Patients had higher systolic and diastolic left ventricular (LV) hemodynamic forces compared with control subjects in the lateral-septal/LV outflow tract ( P = 0.011 and P = 0.0031) and inferior-anterior ( P < 0.0001 and P < 0.0001) directions, which are forces not aligned with blood flow. Forces did not change after PVR. Patients had higher RV diastolic forces compared with control subjects in the diaphragm-right ventricular (RV) outflow tract (RVOT; P < 0.001) and apical-basal ( P = 0.0017) directions. After PVR, RV systolic forces in the diaphragm-RVOT direction decreased ( P = 0.039) to lower levels than in control subjects ( P = 0.0064). RV diastolic forces decreased in all directions ( P = 0.0078, P = 0.0078, and P = 0.039) but were still higher than in control subjects in the diaphragm-RVOT direction ( P = 0.046). In conclusion, patients with rToF and PR had LV hemodynamic forces less aligned with intraventricular blood flow compared with control subjects and higher diastolic RV forces along the regurgitant flow direction in the RVOT and that of tricuspid inflow. Remaining force differences in the LV and RV after PVR suggest that biventricular pumping does not normalize after surgery. NEW & NOTEWORTHY Biventricular hemodynamic forces in patients with repaired tetralogy of Fallot and pulmonary regurgitation were quantified for the first time. Left ventricular hemodynamic forces were less aligned to the main blood flow direction in patients compared with control subjects. Higher right ventricular forces were seen along the pulmonary regurgitant and tricuspid inflow directions. Differences in forces versus control subjects remain after pulmonary valve replacement, suggesting that altered biventricular pumping does not normalize after surgery.

scholarly journals Dual-series equations formulation for static deformation of plates with a partial internal line support

2007 ◽  
Vol 34 (3) ◽  
pp. 221-248 ◽  
Author(s):  
Yos Sompornjaroensuk ◽  
Kraiwood Kiattikomol
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Hankel Transform ◽  
Internal Line ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Distributed Load ◽  
Dual Series Equations ◽  
Finite Hankel Transform ◽  
Standard Techniques

The paper deals with the application of dual-series equations to the problem of rectangular plates having at least two parallel simply supported edges and a partial internal line support located at the centre where the length of internal line support can be varied symmetrically, loaded with a uniformly distributed load. By choosing the proper finite Hankel transform, the dual-series equations can be reduced to the form of a Fredholm integral equation which can be solved conveniently by using standard techniques. The solutions of integral equation and the deformations for each case of the plates are given and discussed in details.

Practical numerical considerations for the Alekseev–Mikhailenko method

1990 ◽  
Vol 27 (8) ◽  
pp. 1023-1030 ◽  
Author(s):  
P. F. Daley ◽  
F. Hron
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Integral Transforms ◽  
Hankel Transform ◽  
Radial Symmetry ◽  
Hyperbolic Partial Differential Equations ◽  
Finite Integral ◽  
Finite Hankel Transform ◽  
Difference Methods ◽  
New Generation

Programs that utilize the Alekseev–Mikhailenko method are becoming viable seismic interpretation aids because of the availability of a new generation of supercomputers. This method is highly numerically accurate, employing a combination of finite integral transforms and finite difference methods, for the solution of hyperbolic partial differential equations, to yield the total seismic wave field.In this paper two questions of a numerical nature are addressed. For coupled P–Sv wave propagation with radial symmetry, Hankel transforms of order 0 and 1 are required to cast the problem in a form suitable for solution by finite difference methods. The inverse series summations would normally require that the two sets of roots of the transcendental equations be employed, corresponding to the zeroes of the Bessel functions of order 0 and 1. This matter is clarified, and it is shown that both inverse series summations may be performed by considering only one set of roots.The second topic involves providing practical means of determining the lower and upper bounds of a truncated series that suitably approximates the infinite inverse series summation of the finite Hankel transform. It is shown that the number of terms in the truncated series generally decreases with increasing duration of the source pulse and that the truncated series may be further reduced if near-vertical-incidence seismic traces are avoided.

Generalized finite Hankel transform

2006 ◽  
Vol 17 (1) ◽  
pp. 39-44 ◽  
Author(s):  
Moustafa El-shahed ◽  
M. Shawkey
Keyword(s):  
Hankel Transform ◽  
Finite Hankel Transform
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