Axisymmetric Fluid Flow Research Articles

Numerical investigation of an axisymmetric, dissipative, and unstable micropolar fluid flow over a stretched Riga plate incorporating mixed convection and chemical reaction

AbstractThe demand to improve the thermal performance of industrial working fluids and materials for better quality in engineering and household devices has spurred numerous studies on non‐Newtonian viscous fluids under various conditions. Researchers have explored different structures and geometries to understand and enhance the thermal propagation of fluid particles. As such, this research aims to investigate the effects of two‐dimensional unsteady boundary layer flow phenomena of a dissipative micropolar fluid over a radially stretching Riga plate when first‐order slip, thermal and solutal boundary conditions, mixed convection, and thermal radiation are all considered. Ordinary differential equations are the governing equations resulting from converting partial differential equations. The boundary layer conditions are altered and numerically solved using the Runge–Kutta fourth‐order shooting approach. Graphs and tables are used to visually analyze the physical attributes of temperature, concentration, velocity distributions, skin friction, Nusselt number, and Sherwood in relation to various factors. The results reveal significant insights into the impact of mixed convection and chemical reactions on the flow characteristics and dimensions. These findings have important implications for various engineering applications, particularly in enhancing industrial systems' heat and mass transfer processes, providing practical knowledge for improving thermal performance in real‐world applications.

Influence of carbon nanotube suspensions on Casson fluid flow over a permeable shrinking membrane: an analytical approach

The present work employs the single-wall carbon nanotube (SWCNT) and multiwall carbon nanotube (MWCNT) models on axisymmetric Casson fluid flow over a permeable shrinking sheet in the presence of an inclined magnetic field and thermal radiation. By exploiting the similarity variable, the leading nonlinear partial differential equations (PDEs) are converted into dimensionless ordinary differential equations (ODEs). The derived equations are solved analytically, and a dual solution is obtained as a result of the shrinking sheet. The dual solutions for the associated model are found to be numerically stable once the stability analysis is conducted, and the upper branch solution is more stable compared to lower branch solutions. The impact of various physical parameters on velocity and temperature distribution is graphically depicted and discussed in detail. The single wall carbon nanotubes have been found to achieve higher temperatures compared to multiwall carbon nanotubes. According to our findings, adding carbon nanotubes volume fractions to convectional fluids can significantly improve thermal conductivity, and this can find applicability in real world applications such as lubricant technology, allowing for efficient heat dissipation in high-temperatures, enhancing the load-carrying capacity and wear resistance of the machinery.

Axisymmetric Hydromagnetized Heat Transfer across a Stretching Sheet with Joule Heating and Radiation

This investigation thoroughly analyses magnetohydrodynamics axisymmetric fluid flow and heat transfer over an exponentially stretching sheet in the presence of radiation and Joule heating effects. The governing partial differential equation is obtained and converted into coupled ordinary differential equations using a suitable similarity transformation. This transformation is also used to re-model the governing system to modify ODEs and boundary conditions using the BVP4C MATLAB) package. The effects of the involved physical parameters, such as suction/injection parameter, magnetic parameter, Prandtl number, Eckert number, and radiation parameter on velocity and temperature profiles are shown graphically. The effects of various parameters on Nusselt number and skin friction coefficient are shown in tabular form. It has been determined that the presence of a magnetic field improves a fluid's thermal behavior. Furthermore, increasing the magnitude of the magnetic field reduces the fluid's radial velocity.

Iterative Methods for Solving the Fractional form of Axisymmetric Squeezing Fluid Flow between Tow Infinite Parallel Plates with Slip Boundary Conditions

Iterative Methods for Solving the Fractional form of Axisymmetric Squeezing Fluid Flow between Tow Infinite Parallel Plates with Slip Boundary Conditions

Topology optimization for blood flow considering a hemolysis model

In the past years, topology optimization has been studied for designing fluid flow devices, such as channels, valves and pumps, and also considering non-Newtonian fluid flows, such as blood. When considering blood flow devices, it is important to quantify and minimize the blood damage (given mainly by hemolysis). However, up to now, in topology optimization, hemolysis has been minimized in an indirect manner, by considering shear stress (or even energy dissipation) as the objective function to indirectly minimize hemolysis. This approach may give a general idea of where hemolysis may or may not appear, but the actual distribution of hemolysis can not be easily correlated. Therefore, a more direct measure may be better to evaluate hemolysis. The direct way to measure hemolysis is by considering the hemolysis index, which is given from a differential equation model (a “hemolysis model”). In this work, the hemolysis index computed though a hemolysis model is included in the topology optimization formulation. In order to illustrate this approach, the design of a 2D swirl flow device, which is based on an axisymmetric fluid flow with or without rotation around an axis, is considered. One relevant example in the field of blood flow devices is the design of blood pumps, which has been previously considered in topology optimization with the aim of indirectly reducing hemolysis. More specifically in terms of pump design for 2D swirl flow, the design of a Tesla-type blood pump is considered. A Tesla-type pump is a bladeless fluid flow device, in which the boundary layer effect is used for pumping the fluid. This principle of operation may lead to a smaller induction of blood damage. Together with the hemolysis index, the topology optimization is formulated by considering the relative energy dissipation for indirectly maximizing efficiency. The fluid is modeled considering a non-Newtonian fluid model, and the fluid flow is solved with the finite element method. In order to model the solid material to block the fluid flow, the traditional formulation of fluid topology optimization is augmented with the “Brinkman-Forchheimer model”. Also, an additional penalization is considered in the non-Newtonian viscosity. The optimization problem is solved with IPOPT (Interior Point Optimization algorithm).

Mathematical modeling of the dynamics of a hydroelastic system—A hollow cylinder with inhomogeneous initial stresses and compressible fluid

This work attempts to present mathematical modeling of the dynamics of the hydroelastic system consisting of a hollow cylinder with inhomogeneous initial stresses and a compressible barotropic inviscid fluid which filled the interior of the cylinder. The motion of the cylinder is described with the 3D linearized theory of elastic waves in bodies with initial stresses; however, the flow of the fluid is described with the linearized Euler equations for compressible inviscid fluid. Formulations of the boundary conditions on the outer surface of the cylinder and compatibility conditions between the cylinder and fluid on the interior surface of the cylinder are presented. Concrete formulations are made for the axisymmetric case, and general aspects of the solution methods of the formulated problems are considered. Under these considerations, two types of problem are selected: (1) the axisymmetric longitudinal wave propagation and (2) fluid flow profile on the outer free surface of the cylinder—the “circular” radial moving load. Numerical results are presented and discussed for the first type of problem. In particular, it is established that the character of the influence of the inhomogeneous initial stresses on the wave propagation velocity in the hydroelastic system under consideration depends on the dimensionless wavenumber. The perspective of future investigations is also presented and discussed.

Effects of inertia on the slow rotation of a slip spherical particle

The steady rotational motion of a spherical particle with frictionally slip surface about a diameter in a quiescent unbounded fluid is studied analytically for a small but finite Reynolds number Re. The Navier–Stokes equation governing the axisymmetric fluid flow around the particle is solved by using a regular perturbation method. The expansion expression for the retarding torque exerted by the fluid on the particle good to O(Re3) is obtained as a function of the scaled slip coefficient of the particle in closed form. This perturbation analysis shows that the perturbed fluid velocity field is of O(Re), the same as that for the translation of the particle, but the first correction to the hydrodynamic torque occurs at O(Re2), much weaker than that to the hydrodynamic drag force acting on a translating particle which is still of O(Re). The hydrodynamic torque is found to be a monotonic increasing function of the Reynolds number and a monotonic decreasing function of the scaled slip coefficient, similar to the effect of fluid inertia on the hydrodynamic force on a slip particle undergoing translation. The inertial effect on the hydrodynamic torque, which can be a sensitive function of the slip coefficient and vanishes as the particle surface is fully slip, is generally negligible for the case of Re<3 but significant as Re is greater than about 10.

Dynamic Transitions and Bifurcations for a Class of Axisymmetric Geophysical Fluid Flow

In this article, we aim to classify the dynamic transitions and bifurcations for a family of axisymmetric geophysical fluid problems of a generic fourth-second order structure. A transition theorem is established by reducing the governing partial differential equations to a complex-valued ordinary differential equation, derived by employing approximate invariant manifolds. We develop an algorithm for the numerical determination of the transition/bifurcation types. Finally we apply the transition theorem and algorithm to examine the baroclinic instability in a two-layer quasi-geostrophic system in an annular channel and with different bathymetry profiles. Our numerical results show that with concave bathymetry the transition (bifurcation) is always continuous (supercritical Hopf bifurcation), whereas for convex bathymetry a jump transition (subcritical Hopf bifurcation) may occur in the basic azimuthal currents that rotate in the same direction.

Experimental Evidence of Enhanced Adsorption Dynamics at Liquid-Liquid Interfaces under an Electric Field.

In this work, we investigate the adsorption of surface-active compounds at the water-oil interface subjected to an electric field. A fluid system comprising a pendent water drop surrounded by an asphaltene-rich organic phase is exposed to a DC uniform electric field. Two subfractions of asphaltenes having contrasting affinities to the water-oil interface are used as surface-active compounds. The microscopic changes in the drop shape, as a result of asphaltene adsorption, are captured and the drop profiles are analyzed using our in-house code for axisymmetric drop shape analysis (ADSA) under an electric field. The estimates of dynamic interfacial tension under different strengths of the field (E0) and concentrations of the asphaltene subfractions (C) are used to calculate adsorption dynamics and surface excess. The experimental observations and careful analyses of the data suggest that the externally applied electric field significantly stimulates the mass-transfer rate at the liquid-liquid interface. The enhancement in mass transport at the water-oil interface can be attributed to the axisymmetric electrohydrodynamic fluid flows generated on either side of the interface. The boost in mass transport is evident from the growing decay in equilibrium interfacial tension (γeq) and increased surface excess (Γeq) upon increasing strength of the applied electric field. The mass-transfer intensification does not increase monotonously with the electric field strength above an optimum E0, which is in agreement with the previous theoretical studies in the literature. However, these first explicit experimental measurements of adsorption at an interface under an electric field suggest that the optimum E0 is determined by characteristics of the surface-active molecules.

Approximation solution of the squeezing flow by the modification of optimal homotopy asymptotic method

The approximate solution of the squeezing axisymmetric fluid flow between infinite plates is discussed in the present paper. An optimal homotopy analysis method with a modification function technique is proposed to solve a class of nonlocal boundary value problems, namely squeezing axisymmetric fluid flow equation. We first transform the nonlocal boundary value problems into an equivalent integral equation, and then the optimal homotopy analysis technique is utilized for an approximate solution. The numerical results confirm the reliability of the present method as it tackles such nonlocal problems without any limiting assumptions. The proposed method is tested upon squeezing axisymmetric fluid flow equation from the literature and the results are compared with the available approximate solutions including perturbation method (Ran et al. in Commun Nonlinear Sci Numer Simul, 2007. https://doi.org/10.1016/j.cnsns ), homotopy perturbation method (Ran et al. 2007), homotopy analysis method (Ran et al. 2007), and optimal homotopy asymptotic method (Idrees et al. in Math Comput Model 55:1324–1333, 2012). The convergence and error analysis of the proposed method is discussed. It can be said that squeezing the axisymmetric fluid flow equation exists in different dynamical behaviors. In addition, the physical behaviors of these new exact solutions are given with two and three-dimensional graphs.

Renormalization and energy conservation for axisymmetric fluid flows

We study vanishing viscosity solutions to the axisymmetric Euler equations without swirl with (relative) vorticity in L^p with p>1. We show that these solutions satisfy the corresponding vorticity equations in the sense of renormalized solutions. Moreover, we show that the kinetic energy is preserved provided that p>3/2 and the vorticity is nonnegative and has finite second moments.

NEAR-WELL ZONE CLEANING

The size of the zone of wave action on the formation is determined when the sucker rod pump is operated with a rocker-type drive. An axisymmetric fluid flow to a well is considered against the depression permanently acting on a stratum of infinite length. Reversion of fluid flow influences on the change in nature of the rock wettability in vicinity of well. This change stimulates increasing its production rate. The results of experiments on a flat laboratory stratum model are presented.

Axisymmetric Flow Through a Cylinder with Porous Medium

The present work is a struggle to establish a mathematical appearance of the conduct of axisymmetric fluid flow in a moving cylinder confined in a porous medium. The fluid is assumed to be flowing through the annular region formed between two concentric smooth cylinders for the case when the outer cylinder is kept fixed while the inner cylinder is assumed to be moving with a constant velocity along the axial direction and is also assumed to be rotating with a constant angular velocity with reference to the centre line along the axial axis. Firstly, the conducting equations of motion are obtained in the form of a system of coupled non-linear partial differential equations with corresponding boundary conditions. The system is then transformed into a new set of coupled non-linear ordinary differential equations using a set of suitable similarity transformation. The problem is then solved using the fourth order numerical technique, the Runge-Kutta-Shooting method. The concluding results are derived for non- dimensional coupled differential equations. In the end the results are graphically presented and the behaviour of porosity parameter over the fluid flow is examined. The observed results indicated that with increasing values of the Reynolds’s numbers the non-dimensional linear and axial velocities also increases.

Study of magneto-hydrodynamics (MHD) impacts on an axisymmetric Casson nanofluid flow and heat transfer over unsteady radially stretching sheet

The current study is presented to probe the impacts of thermal radiation and mixed convection of axisymmetric Casson fluid flow in the presence of magnetic field along with nano-particles. The flow is provoked because of unsteady radially stretching sheet. The solution of transformed ordinary differential equations is attained by utilizing Keller-box finite difference method (IFDM). The influence of different parameters on flow features is sketched through various graphs and results are tabulated and argued briefly. The convection conditions on the wall temperature and concentration are also exerted in the study. Finally, a comparison is established with existing literature to support our results and a good agreement is found which corroborates our work. A decline in both velocity and temperature is witnessed with the rise in Casson parameter. It is also observed that with the rise Brownian motion and Thermophoresis parameters, the temperature of the fluid rises but concentration profile decreases in start and then start increasing. The fluid concentration in its boundary layer decreases with the increase of heavier species, the parameter of the reaction rate and the exponent of power law for fluid having Prandtl number = 10.0, 15.0, and 20.0. Moreover, the fluid velocity depreciates with the rise in unsteadiness parameter while a significant decrease in temperature is noted. The outcomes of study are quite useful in fabrication of magnetic nano-materials and high temperature treatment of magnetic nano-polymers.

Safety factor for time-dependent axisymmetric flows of barotropic gas and ideal incompressible fluid

The safety factor q(r, z, t) is proved to be a material conservation law for the time-dependent axisymmetric barotropic compressible gas flows and ideal incompressible fluid flows with constant density ρ. Infinite families of conserved quantities connected with the safety factor are derived. The existence of maximal vortex rings and vortex blobs which are frozen into the axisymmetric inviscid gas and fluid flows is demonstrated. A stratification in the space of ideal gas and fluid flows is obtained: if two axisymmetric states of the barotropic gas or fluid with constant density ρ are dynamically connected, then their total numbers of vortex rings must be equal (the same for the total numbers of vortex blobs) and the infinitely many corresponding conserved quantities must coincide.

Latitudinally deforming rotating sphere

In this study, we consider a sphere with a surface that is fully covered by a stretchable elastic material. The radius of the sphere is fixed and it is also rotating about its radial axis. We investigate how the axisymmetric motion of a triggered fluid flow around the sphere is affected by the presence of both sphere rotation and latitudinal stretching. Considering that the deformation over the sphere commences at the pole, the problem is formulated such that the fluid flow near the pole is similar to the induced flow due to a linearly stretchable rotating disk, which has been described well in previous studies. When the rotation is omitted, the flow develops two-dimensionally under the action of pure stretching; otherwise, a three-dimensional axisymmetric fluid flow occurs, which is computed at each latitudinal angle both numerically and using a perturbation approach. The solution with wall deformation is different from the traditional character of the solution due to a solely rotating sphere. This solution is then used to compute the surface shears due to the physical drag and torque acting over the sphere. The contribution of wall stretching reduces the drag, whereas high rotation suppresses the effects of stretching to enhance the drag. More torque is required to rotate the sphere when both stretching and rotation mechanisms are in action.

Exact Solution of the Equations of Axisymmetric Viscous Fluid Flow between Parallel Plates Approaching and Moving Apart from One Another

The exact solutions of the Navier-Stokes equations in a fluid layer in between parallel plates moving so that the distance varies in accordance with an arbitrary-power law are investigated. The no-slip condition is imposed on the plate boundary. The exact solutions of the Navier-Stokes equations are constructed as series in powers of the Reynolds number. The cases of the decelerated motion in accordance with the time-square-root law, the uniform motion, and the uniformly accelerated motion of the plates are studied in detail. In the first of the cases mentioned above the series converge and in the other cases the solution is determined by means of asymptotic series. The critical Reynolds number which corresponds to the development of backflow is determined.

Elasticity Change along the Aorta is a Mechanism for Supporting the Physiological Self-organization of Tornado-like Blood Flow

We performed an experimental study of the elastic properties of the aorta by several independent methods, including the elastometry of the porcine aorta in different stretching modes, aortography in an acute porcine experiment with various levels of blood pressure, and contrast multislice computed tomography (MSCT) of the aorta in a healthy volunteer. In previous studies, it was shown that the swirling nature of the blood flow in the heart chambers and the aorta may be described in terms of the hydrodynamic model of tornado-like self-organizing axisymmetric viscous fluid flows. The purpose of the study was to test the correspondence between the pattern of changes in the viscoelastic characteristics of the aorta walls and the conditions of the self-organization of the tornado-like flow in its lumen. Three independent methods, namely, postmortal elastometry, intravital panaortography, and MSCT of a healthy volunteer, have been used to show that the aorta elasticity monotonically decreases in the distal direction, this relationship being distorted with increasing radial load beyond the physiologically normal range. This distribution of elasticity along the aorta ensures that the geometric configuration of the aorta flow pass corresponds to the directions of the current lines of the tornado-like flow obtained from the precise solutions throughout the cardiac cycle. Thus, it has been established that the changes in the elastic properties along the aorta create the necessary hydrodynamic conditions for maintaining the tornado-like flow throughout the cardiac cycle in the physiological range of pressure.

Steady Flow Generated by a Core Oscillating in a Rotating Spherical Cavity

Steady flow generated by oscillations of an inner solid core in a fluid-filled rotating spherical cavity is experimentally studied. The core with density less than the fluid density is located near the center of the cavity and is acted upon by a centrifugal force. The gravity field directed perpendicular to the rotation axis leads to a stationary displacement of the core from the rotation axis. As a result, in the frame of reference attached to the cavity, the core performs circular oscillation with frequency equal to the rotation frequency, and its center moves along a circular trajectory in the equatorial plane around the center of the cavity. For the differential rotation of the core to be absent, one of the poles of the core is connected to the nearest pole of the cavity with a torsionally elastic, flexible fishing line. It is found that the oscillation of the core generates axisymmetric azimuthal fluid flow in the cavity which has the form of nested liquid columns rotating with different angular velocities. Comparison with the case of a free oscillating core which performs mean differential rotation suggests the existence of two mechanisms of flow generation (due to the differential rotation of the core in the Ekman layer and due to the oscillation of the core in the oscillating boundary layers).

Non–existence of potential vorticity in a stationary axisymmetric adiabatic fluid configuration

It is found that the value of relativistic potential vorticity is zero in the case of a stationary axisymmetric adiabatic fluid flows. The fluid’s vorticity flux vector lies in the level surfaces of constant entropy per baryon and thereby leads to conservation of fluid helicity.