Flow Of Fractional Maxwell Fluid Research Articles

Analysis of physiological pulsating flow of fractional Maxwell fluid in a locally narrow artery

The purpose of this paper is to provide a novel reference for the early diagnosis and treatment of atherosclerosis. Two-dimensional governing equations of fractional-order Maxwell fluid flow in a local stenotic artery are established, taking real physiological pulsating blood flow at inlet into consideration. Drawing support from the finite difference method as well as the L1 formula, vorticity and stream functions are introduced to acquire numerical solutions for velocity, stream function, and pressure. The distribution of blood flow in narrowed arteries within a real physiological pulse cycle is discussed. Furthermore, the influences of the degree of stenosis δ, the stenosis length parameter L0, fractional order parameter α, and relaxation time λ on crucial medical indicators, including the time average of the wall shear stress, oscillatory shear index, relative residence time, and pressure distribution are revealed. The results show that the deceleration and reversal phases of real physiological pulsatile flow critically affect the progression of arterial stenosis, and increasing the fractional order parameter α weakens the development of stenosis, while increasing λ has the opposite effect. This study is expected to serve as a reference for formulating standards of key medical indicators in the early diagnosis of vascular stenosis.

Unsteady Falkner-Skan flow of fractional Maxwell fluid towards a stretched wedge with buoyancy effects

The majority of researches for Falkner-Skan flow are dependent on the classical constitutive relations of viscoelastic fluids. Fractional Maxwell fluid model is introduced to depict Falkner-Skan flow innovatively in the paper. Moreover, the momentum equation studying the effects of buoyancy force is established. Analogy to constitutive relevance for fractional Maxwell fluid, fractional derivative is brought in Fourier’s law and Fick’s law. It is worth mentioning that heat source and chemical reaction are discussed. Finite difference method integrated with L1-algorithm is utilized to address the fractional governing equations, whose convergence is verified by constructing an example with accurate solution. Furthermore, the influences of pertinent physical parameters are analyzed diagrammatically. A fascinating phenomenon is discovered that all the velocity profiles initially rise to a maximal value due to the impact of buoyancy force and then decrease to the free flow velocity. Besides, the temperature and concentration distributions first increase slightly while decline significantly, which indicates the thermal relaxation and mass relaxation characteristic of Maxwell fluid.

A Comparative Study of Natural Convection Flow of Fractional Maxwell Fluid with Uniform Heat Flux and Radiation

This paper focuses on the comparative study of natural convection flow of fractional Maxwell fluid having uniform heat flux and radiation. The well‐known Maxwell fluid equation with an integer‐order derivative has been extended to a non‐integer‐order derivative, i.e., fractional derivative. The explicit expression for the temperature and velocity is acquired by utilizing the Laplace transform (LT) technique. The two fractional derivative concepts are used (Caputo and Caputo–Fabrizio derivatives) in the formulation of the problem. Utilizing the Mathcad programming, the effect of certain embedded factors and fractional parameters on temperature and velocity profile is graphically presented.

Axisymmetric convection flow of fractional Maxwell fluid past a vertical cylinder with velocity slip and temperature jump

A novel finite volume method is developed to investigate the axisymmetric convection flow and heat transfer of fractional viscoelastic fluid past a vertical cylinder. Fractional cylindrical governing equations are formulated by fractional Maxwell model and generalized Fourier's law. The velocity slip and temperature jump boundary conditions are considered across the fluid-solid interface. Numerical results are validated by exact solutions of special case with source terms. The effects of fractional derivative parameter and boundary condition parameters on flow and heat transfer characteristics are discussed. The viscoelastic fluid performs evident shear thickening property in the fractional Maxwell constitutive relation. Moreover, the boundary condition parameters have remarkable influence on velocity and temperature distributions.

Heat transfer and second order slip effect on MHD flow of fractional Maxwell fluid in a porous medium

This work explores the effect of second order slip on magnetohydrodynamic (MHD) flow of a fractional Maxwell fluid on a moving plate and a comparison between two numerical algorithms (Tzou and Stehfest’s algorithm). The problem is formulated for Maxwell fluid with Caputo-time fractional derivatives. Semi analytical solutions are derived using Laplace transform. The solution is obtained using numerical technique of Laplace transform Stehfest’s algorithm. To insight the physical behavior of the fluid, a graphical illustration is made. The influence of fractional parameter, the magnetic force, the porosity parameter, the slip parameters are analyzed and discussed. A tabular and graphical comparisons with Tzou’s algorithm are made for the sake of validation of the present results.

Boundary layer flow of fractional Maxwell fluid over a stretching sheet with variable thickness

A novel investigation about the boundary layer flow of fractional Maxwell fluid over a stretching sheet with variable thickness is presented. By introducing new variables, the irregular boundary changes as a regular one. Solutions of the governing equations are obtained numerically where the L1-scheme is applied. Dynamic characteristicswith the effects of different parameters are shown by graphical illustrations. Three kinds of distributions versus power law parameter are presented, including monotonically increasing in nearly linear form at y =1, increasing at first and then decreasing at y =1.4 and monotonically decreasing in nearly linear form at y =2.

Numerical analysis for electroosmotic flow of fractional Maxwell fluids

The electroosmotic flow of fractional Maxwell fluid in a rectangular microchannel is studied in this paper. By means of the fractional Maxwell constitutive equation, and based on the experimental data, the nonlinear conjugate gradient method is proposed to get the viscoelastic parameters. Combined with the continuity equations and Cauchy momentum equations, the governing equations of velocity distribution are established. Besides, a fully discrete spectral method based on a difference method in the temporal direction and a Legendre spectral method in the spatial direction is introduced to solve the dimensionless governing equations. Finally, some results are presented to show the effectiveness of the proposed method.

Exact Solutions for the Flow of Fractional Maxwell Fluid in Pipe-Like Domains

AbstractThis paper presents an analysis of unsteady flow of incompressible fractional Maxwell fluid filled in the annular region between two infinite coaxial circular cylinders. The fluid motion is created by the inner cylinder that applies a longitudinal time-dependent shear stress and the outer cylinder that is moving at a constant velocity. The velocity field and shear stress are determined using the Laplace and finite Hankel transforms. Obtained solutions are presented in terms of the generalized G and R functions. We also obtain the solutions for ordinary Maxwell fluid and Newtonian fluid as special cases of generalized solutions. The influence of different parameters on the velocity field and shear stress are also presented using graphical illustration. Finally, a comparison is drawn between motions of fractional Maxwell fluid, ordinary Maxwell fluid and Newtonian fluid.

Flow of Fractional Maxwell Fluid in Oscillating Pipe-Like Domains

This paper presents an analysis for oscillating flows of fractional Maxwell fluid in the annular region between two infinite concentric circular cylinders. The fluid motion is created as both cylinders begin to oscillate around their common axis. The exact solutions are established using the sequential fractional derivatives Laplace transform and finite Hankel transform in terms of generalized G and R functions. Also, we obtain the solutions for ordinary Maxwell fluid and Newtonian fluid as special cases of the generalized solutions. Moreover, the effects of various parameters on the velocity field and shear stress are analyzed by graphical illustration. Finally, a comparison is drawn between motions of fractional Maxwell fluid, ordinary Maxwell fluid and Newtonian fluid.

Retraction Note: Flow of fractional Maxwell fluid between coaxial cylinders

This paper has been retracted. Too many duplicate passages have appeared in multiple articles. Professor Fetecau, the only contributor who cooperated with our investigations into this possible case of plagiarism is not involved in practices unworthy of scientists who uphold high academic standards. Many of the publications have been published with him as one of the contributors without his prior knowledge or consent.

RETRACTED ARTICLE: Flow of fractional Maxwell fluid between coaxial cylinders

This paper deals with the study of unsteady flow of a Maxwell fluid with fractional derivative model, between two infinite coaxial circular cylinders, using Laplace and finite Hankel transforms. The motion of the fluid is produced by the inner cylinder that, at time t = 0+, is subject to a time-dependent longitudinal shear stress. Velocity field and the adequate shear stress are presented under series form in terms of the generalized G and R functions. The solutions that have been obtained satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Maxwell and Newtonian fluids are obtained as limiting cases of general solutions. Finally, the influence of the pertinent parameters on the fluid motion as well as a comparison between the three models is underlined by graphical illustrations.