The numerical simulation of two-dimensional fluid flow in T-shaped and Y-shaped channels having a single moving indented wall is performed by the finite element method in the Arbitrary Lagrangian-Eulerian frame. The motion of the indented wall is defined as a hyperbolic function, and it is located at a small segment at the bottom wall in the parent channel. The smallest value of the wall oscillation period causes the waviest core flow in the main channel, resulting in bigger vortices and greater flow separation region in the branches, especially during the outward indentation motion. This flow disturbance pattern is found more severe in T-channel as compared to that of in Y-channel.

The article presents the mixed finite element formulation for examining the biomagnetic fluid dynamics as governed by the Navier–Stokes equation, coupled with energy and magnetic expressions. Both ferrohydrodynamics and magnetohydrodynamics describe the additional magnetic effects. For model discretization, the Galerkin weighted residual method was performed. Departing from a good agreement with existing findings, a biomagnetic flow (blood) in a straight rectangular conduit was then simulated in the presence of a spatially changing magnetic distribution. By virtue of negligible spatial variation influence from the magnetic field, the effects of Lorentz force were not presently considered. It was further found that the model accurately exhibits the formation and distribution of vortices, temperature, and skin friction located adjacent to and remotely from the source of magnetic load following a rise in the magnetic intensity.

The effect of a catheter on blood flow and heat transfer characteristics of a Carreau fluid model is investigated mathematically using the perturbation method involving appropriate small parameters. Physically, this study relates to the surgical technique when a catheter is injected eccentrically into an artery. The model describes fluid flowing in the gap between eccentric tubes where the inner tube is uniform and rigid representing the moving catheter while the other tube represents an artery with overlapping stenosis. A complete perturbation solution up to the first order is presented whereby a validation exercise carried out shows that previously published solutions involving Newtonian fluids may have some typographical errors. The present results obtained show that the axial velocity, wall shear stress, and temperature in the case of the eccentric catheter are higher than that of the concentric catheter. The average Nusselt number is enhanced with increasing catheter radius and the velocity of the catheter while it decreases with increased Weissenberg number, Prandtl number, and Eckert number. These results agree with physiological observations that the risks and complications associated with catheterization are alleviated when the eccentric position of the catheter is considered.

This paper discusses the effect of different geometric representations of stenosis on the numerical solution of one-dimensional unsteady blood flow in stenotic blood vessel (or stenosis) taking into account fluid-structure interaction. In the formulation, a collapsible pressure-area constitutive relation is added to the coupled mass and momentum equations to allow for the interaction between the cross sectional area, volumetric flow rate and pressure of the flow and hence the prevalence of the one-dimensional fluid-structure interaction. The formulation is stabilized by employing Streamline-Upwind Petrov-Galerkin scheme. Non-reflecting boundary conditions are imposed based on the method of characteristics. Flow characteristics and the geometrical effects of the stenosis are then discussed. Numerical results show that stenosis with irregular shape is more prone to collapse as compared to the smooth one for a given baseline conditions. This study, thus, highlights the importance of representing the shape of the stenosis as close as possible as it might give information otherwise missing in the simplistic smooth representation of the stenosis.

This study is focus on generalized power law model of blood flow in a stenosed bifurcated artery under the effect of different types of stenosis. Stenosis can cause the narrowing of the artery that may reduce the flow of blood supply to the heart, and this may lead to the heart attacks. The geometry of the bifurcated artery with different classification of stenosis locations is considered in order to shows four possible morphologies formation of plaque from healthy artery to disease artery. The bifurcated artery is modelled as a two-dimensional rigid wall since the wall of a disease artery is reported to be less flexibility. Few assumptions are considered such as blood are incompressible, laminar, steady and characterized as the generalized power-law model. Simulation results are obtained using COMSOL Multiphysics 5.2, which is a software that based on the finite element method to solve this problem. Results concerning the effect of different locations of stenosis on generalized power law model of the blood flow characteristic such as streamlines pattern are discussed.

An investigation of drug transport in the lumen as well as in the tissue, in the presence of absorbing interface is studied. The streaming blood is considered as a power-law fluid, whereas, the transport of luminal and tissue drug as a convection-diffusion process. Predicted results show the length of flow separation increases with increasing Re. Simulation predicts the diminishing tissue content with increasing wall absorption parameter. The luminal concentration reaches its quasi steady-state more rapidly than that in the tissue. (C)2021 L&H Scientific Publishing, LLC. All rights reserved.

The effect of non-Newtonian biomagnetic power-law fluid in a channel undergoing external localised magnetic fields is investigated. The governing equations are derived by considering both effects of Ferrohydrodynamics (FHD) and Magnetohydrodynamics (MHD). These governing equations are difficult to solve due to the inclusion of source term from magnetic equation and the nonlinearity of the power-law model. Numerical scheme of Constrained Interpolation Profile (CIP) is developed to solve the governing equations numerically. Extensive results carried out show that this method is efficient on studying the biomagnetic and non-Newtonian power-law flow. New results show that the inclusion of power-law model affects the vortex formation, skin friction and heat transfer parameter significantly. Regardless of the power-law index, the vortex formation length increases when Magnetic number increases. The effect of this vortex however decreases with the inclusion of power-law where in the shear thinning case, the arising vortex is more pronounced than in the shear thickening case. Furthermore, increasing of power-law index from shear thinning to shear thickening, decreases the wall shear stress and heat transfer parameters. However for high Magnetic number, the wall shear stress and heat transfer parameters increase especially near the location of the magnetic source. The results can be used as a guide on assessing the potential effects of radiofrequency fields (RF) from electromagnetic fields (EMF) exposure on blood vessel.

This paper discusses the optimal control of pressure using the zero-gradient control (ZGC) approach. It is applied for the first time in the study to control the optimal pressure of hydrogen natural gas mixture in an inclined pipeline. The solution to the flow problem is first validated with existing results using the Taylor series approximation, regression analysis and the Runge-Kutta method combined. The optimal pressure is then determined using ZGC where the optimal set points are calculated without having to solve the non-linear system of equations associated with the standard optimization problem. It is shown that the mass ratio is the more effective parameter compared to the initial pressure in controlling the maximum variation of pressure in a gas pipeline.

The aim of this article is to use the Homotopy Analysis Method (HAM) to pinpoint the optimal location of leakage in an inclined pipeline containing hydrogen-natural gas mixture by obtaining quick and accurate analytical solutions for nonlinear transportation equations. The homotopy analysis method utilizes a simple and powerful technique to adjust and control the convergence region of the infinite series solution using auxiliary parameters. The auxiliary parameters provide a convenient way of controlling the convergent region of series solutions. Numerical solutions obtained by HAM indicate that the approach is highly accurate, computationally very attractive and easy to implement. The solutions obtained with HAM have been shown to be in good agreement with those obtained using the method of characteristics (MOC) and the reduced order modelling (ROM) technique.

The study on the effects of biological fluids in the presence of magnetic field is known as biomagnetic fluid dynamics (BFD) and the most common biological fluid that exhibit such magnetic properties is blood.An extensive research work has been done in this area due to its applications in medical and bioengineering.Basically, it is essential for a study to be justified according to certain benchmark before progressing.Hence, biomagnetic fluid flow in a lid driven cavity is numerically investigated by utilizing two numerical schemes: finite difference and finite element methods.The formulation adopted is consistent with the principles of ferrohydrodynamics.The mathematical model describes Newtonian blood flow under the influence of a spatially varying magnetic field.The model considers the biofluid as non-conducting.The flow is assumed to be two-dimensional, steady, laminar and isothermal.The implementation of finite element method shows stability issue due to extremely steep magnetic field gradient while finite difference method shows no issue.Due to this, a solution is proposed to alleviate the problem and the result for various magnetic field intensity presented.

The simultaneous effect of flexible wall and multiple stenoses on the flow and mass transfer of blood is investigated through numerical computation and simulations. The solution is obtained using the Marker and Cell technique on an axisymmetric model of Newtonian blood flow. The results compare favorably with physical observations where the pulsatile boundary condition and double stenoses result in a higher pressure drop across the stenoses. The streamlines, the iso-concentration lines, the Sherwood number, and the mass concentration variations along the entire wall segment provide a comprehensive analysis of the mass transport characteristics. The double stenoses and pulsatile inlet conditions increase the number of recirculation regions and effect a higher mass transfer rate at the throat, whereby more mass is expected to accumulate and cause further stenosis.

Biomagnetic fluid dynamics (BFD) is an important application in medical sciences and bioengineering research. Due to this, biomagnetic fluid flow through a stenosed bifurcated artery is numerically studied. A biomagnetic fluid can be found in a living creature and its flow is influenced by the present of a magnetic field. Blood is a typical biomagnetic fluid due to the interaction of intercellular protein, cell membrane and the haemoglobin. This study considered the flow to be incompressible, laminar, two-dimensional (2D), fully developed viscous flow of a Newtonian biomagnetic fluid (blood) in a stenosed bifurcated artery under the effect of a spatially varying magnetic field. A simplified mathematical model of BFD was developed only for isothermal case. Numerical results are obtained using COMSOL Multiphysics 5.2 based on finite element method (FEM). Results concerning the different values of magnetic field intensity produce a considerable effect on the blood flow characteristics such as the velocity profiles and the streamlines patterns. It is shown that the vortex at lower wall extends vertically while vortex at upper wall becomes shrink as the magnetic field strength increases. The location of the magnetic source also can affect the velocity at the daughter artery where the velocity at the lower wall of daughter artery is lower than the upper wall.

Transient flow modeling in gas well has always been a problem to the natural gas industry operators this is due to parameter changing with both space and time. Some previous investigations of gas flow in producing well have been limited to general use, because assumptions were introduced to simplify either gas properties or the basic differential equation. Dominantly in use today in the gas production industries are Correlations and Steady state solutions, but most of them does not give satisfactory results because their applications neglected the transient and compressibility aspect leading to limited set of calculated results. The present study is an attempted to present sufficient numerical results to permit meaningful conclusion to be drawn by developing a one-dimensional transient compressible model according to conservation of mass, momentum and energy that can investigate the transient behavior of flow characteristics in a producing gas well. The model retains all the terms in the partial differential equation and is solved numerically using the implicit Steger-Warming flux vector splitting method (FSM). Gas flow characteristics with respect to well depth are plotted at different time of production, geothermal gradients and thermal conductivities were also plotted, reflecting gas flow law and the characteristics of temperature distribution in the formation. The analysis provide a dynamic information on production for gas well. The results presented when utilized properly will provide a dependable for forecasting gas well prediction work and pressure performance analysis.

Unsteady non-Newtonian blood fow characterized by the generalized power-law model subjected to an external magnetic feld together with heat transfer through stenosed artery has been developed. The arterial segment is assumed to be a cylindrical tube and the arterial wall is considered to be fexible having cosine shaped stenoses a condition due to the abnormal narrowing of a blood vessel. The full equations comprising the governing equations of motion, heat equation, the initial and the boundary conditions are solved using numerical procedure involves the discretization of the equations using the Marker and Cell (MAC) method, where pressure along the artery is calculated iteratively using the Successive-Over-Relaxation (SOR) technique. The results demonstrated through the simulations that under the infuence of magnetic feld, the blood temperature distribution over the entire arterial segment increases. The present results also predict the effects of the generalized power-law index and the Prandtl number on the distribution of blood temperature.

This work focuses on the development of a mathematical model as a viable alternative to pinpoint locations of gas leaks in a pipeline. The transient non-isothermal flow of hydrogen-natural gas mixture is considered because hydrogen is often transported in the same pipeline as natural gas to reduce the transportation cost. The mathematical model developed took into consideration the effect of the mass ratio of gas mixture. The gas mixture was assumed to be homogeneous and the transient pressure wave was created by the sudden or instantaneous closure of a downstream shut-off valve to ensure the attainment of minimum pressure at the downstream end within a short time. The governing equations were numerically solved using the reduced order modelling (ROM) technique, which had not been previously applied on non-isothermal models involving gas mixtures. Numerical results observed that the mass ratio of hydrogen to natural gas should not be more than 0.5 to ensure that leakage does not occur before the estimated leak position. An increase in the mass ratio leads to an increase in the pressure and celerity wave, while the leak location and the amount of leak discharge decrease.

Achieving an accurate and efficient model for inclined bed therapy is ever-demanding. A new mathematical model for simulating airflow inside human trachea under resting and normal breathing scenario, where the influence of inclination angle on the unsteady flow is determined. The governing equations of motion consisting of unsteady, nonlinear, non-homogenous, Navier-Stokes equations are derived and numerically solved using the Marker and Cell method in Matlab code. Two-dimensional cylindrical coordinate system with appropriate initial and boundary conditions are used. The discretization is performed on uniform staggered grids. The pressure is calculated iteratively using the Successive-Over-Relaxation method. Quantities including the wall pressure, pressure drop, axial and radial velocity, volumetric flow rate, flow resistance and streamlines of airflow patterns are computed. The computed axial velocities for the horizontal position are agreed when compared with other experimental and numerical findings. An increase in the inclination angle is found to diminish the pressure drop inside the trachea. Thus, it generated a higher negative pressure in the lungs. Simulation results are demonstrated to be accurate when compared with the real situation. Excellent features of the results suggest that the proposed model based simulation procedure may contribute towards the development of precise and effective inclined bed therapy.

Transient pressure wave detection analysis to detect the location of leakage of non-isothermal flow in an inclined pipeline containing hydrogen-natural gas mixture is investigated. The governing equations are solved using the reduced order modelling technique. The effects of inclination angles, mass ratio of gas mixture and temperature change on the pressure and celerity waves in an inclined pipeline are discussed. The solutions for isothermal flow in a horizontal pipeline show good agreement with published results. For non-isothermal flow an increase in the mass ratio lead to an increase in the pressure and celerity waves, while the leak location and amount of leak discharge decrease. However, it is noted that the amount of leak discharge is still higher than that of isothermal flow. It is also observed that an increase in the inclination angle increases the pressure drop and leak discharge but the celerity wave and the leak location do not seem to be affected. Thus, to reduce the leak discharge, the inclination angle of the pipeline should be reduced and further, to ensure that leakage does not occur before the calculated leak position, the mass ratio of hydrogen to natural gas should not be more than 0.5.

Unsteady blood flow characterized by the generalized power law model in a stenosed artery subject to external body acceleration is considered numerically using the Marker and Cell finite difference discretization on staggered grid, where the pressure is calculated iteratively using the successive-over-relaxation method. The codes have been developed and the results analysed using Matlab. The focus of discussion is on the effects of body acceleration on the flow characteristics, in particular its effects on the wall pressure, pressure drop and the streamlines as these results have not yet been presented and discussed in previous works.