Oldroyd-B Fluid Research Articles

Numerical analysis of combined electroosmotic-pressure driven flow of a viscoelastic fluid over high zeta potential modulated surfaces

We report a numerical study on the mixed electroosmotic and pressure-driven transport of an Oldroyd-B fluid through a microchannel having high surface charge modulated walls. We report an augmentation in the net-throughput for higher surface potentials and thinner electrical double layers. We have shown that the enhanced fluid elasticity is responsible for the generation of asymmetric flow structures inside the micro-channel. A great augmentation in the streaming current is achieved by increasing the strength of surface potential or reducing the thickness of the electrical double layer. By accounting for the nonlinear fluid behavior and nonlinear nature of ionic transport, we show that the electrochemical parameters such as zeta potential, the relative strength of the applied electric field and pressure gradient, followed by the thickness of the electrical double layer, contribute largely toward altering the net-throughput inside the micro-channel. We observe the formation and shifting of re-circulation zones due to the complex interaction of the fluid rheology and asymmetric surface potential at the channel walls. The results of the present study hold the key toward understanding the complex fluid flow mimicking bio-fluid transport in the microfluidic platform under the mixed influence of electroosmotic forcing and pressure gradient.

磁场作用下Oldroyd-B流体的非稳态驻点流动

磁场作用下Oldroyd-B流体的非稳态驻点流动

Study of Heat Transfer under the Impact of Thermal Radiation, Ramped Velocity, and Ramped Temperature on the MHD Oldroyd-B Fluid Subject to Noninteger Differentiable Operators

This theoretical study explores the impact of heat generation/absorption with ramp wall velocity and ramp wall temperature on the magnetohydrodynamic (MHD) time-dependent Oldroyd-B fluid over an unbounded plate embedded in a porous surface. The mathematical analysis of fractional governing partial differential equations has been established using systematic and powerful techniques of Laplace transform with its numerical inversion algorithms. The fractionalized solutions have been traced out separately through all fractional differential operators. Nondimensional parameters along with Laplace transformation are used to find the solution of temperature and velocity profiles. Fractional time derivatives are used to analyze the impact of fractional parameters (memory effect) on the dynamics of the fluid. While making a comparison, it is observed that the fractional-order model is the best to explain the memory effect as compared to classical models. The obtained solutions are plotted graphically for different values of physical parameters. Our results suggest that the velocity profile decreases by increasing the effective Prandtl number. Furthermore, the existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity.

Linear instability of viscoelastic pipe flow

Abstract

High-order efficient numerical method for solving a generalized fractional Oldroyd-B fluid model

This paper investigates the high-order efficient numerical method with the corresponding stability and convergence analysis for the generalized fractional Oldroyd-B fluid model. Firstly, a high-order compact finite difference scheme is derived with accuracy $$O\left( \tau ^{\min {\{3-\gamma ,2-\alpha }\}}+h^{4}\right) $$ , where $$\gamma \in (1,2)$$ and $$\alpha \in (0,1)$$ are the orders of the time fractional derivatives. Then, by means of a new inner product, the unconditional stability and convergence in the maximum norm of the derived high-order numerical method have been discussed rigorously using the energy method. Finally, numerical experiments are presented to test the convergence order in the temporal and spatial direction, respectively. To precisely demonstrate the computational efficiency of the derived high-order numerical method, the maximum norm error and the CPU time are measured in contrast with the second-order finite difference scheme for the same temporal grid size. Additionally, the derived high-order numerical method has been applied to solve and analyze the flow problem of an incompressible Oldroyd-B fluid with fractional derivative model bounded by two infinite parallel rigid plates.

Interaction of a pair of in-line bubbles ascending in an Oldroyd-B liquid: A numerical study

In this paper, the interaction between two initially circular in-line bubbles during their rise in a viscoelastic liquid under gravity is numerically simulated by weakly compressible smoothed particle hydrodynamics (WC-SPH). The background fluid is assumed to obey Oldroyd-B rheological model and the surface tension between two phases is evaluated by continuum surface tension (CST) method. First, it is shown that the obtained results for two benchmark problems, including two rising bubbles in a Newtonian fluid and a single rising bubble in a viscoelastic fluid, are in good agreement with previously published results. Then, together ascending of two unequal in-line bubbles in an Oldroyd-B viscoelastic liquid is simulated. Two different configurations are considered for the position of larger bubble and the center-of-mass of the bubbles and its velocity are presented for each case. Also, the differences of velocity and stress distributions in the background liquid are evaluated for two configurations. Based on the obtained results, it could be said that when the larger bubble is placed above the smaller one, merging does not occurred and the upper bubble has a dual cusped trailing edge. In addition, the effects of Deborah number, polymer concentration, density and viscosity ratios, Reynolds number, and Bond number are investigated on rising bubbles. To the best of authors’ knowledge, it is the first time the simultaneous rising of two bubbles in Oldroyd-B fluids is investigated.

Dynamics of an elastoviscoplastic droplet in a Newtonian medium under shear flow

The dynamics of a single elastoviscoplastic (EVP) drop immersed in plane shear flow of a Newtonian fluid is studied by 3D direct numerical simulations using a finite-difference and level-set method combined with the Saramito model for the EVP fluid. This model gives rise to a yield stress behavior, where the unyielded state of the material is described as a Kelvin-Voigt viscoelastic solid and the yielded state as a viscoelastic Oldroyd-B fluid. Yielding of an initially solid drop of Carbopol is simulated under successively increasing shear rates. We proceed to examine the roles of nondimensional parameters on the yielding process; in particular, the Bingham number ($Bi$), capillary number ($Ca$), Weissenberg number ($Wi$), and ratio of solvent and total drop viscosity. We find that all of these parameters, and not only $Bi$, have a significant influence on the drop dynamics. Numerical simulations predict that the volume of the unyielded region inside the droplet increases with $Bi$ and $Wi$, while it decreases with $Ca$ at low $Wi$ and $Bi$. A new regime map is obtained for the prediction of the yielded, unyielded, and partly yielded modes as a function of $Bi$ and $Wi$. The drop deformation is studied and explained by examining the stresses in the vicinity of the drop interface. The deformation has a complex dependence on $Bi$ and $Wi$. At low $Bi$, the droplet deformation shows a nonmonotonic behavior with an increasing $Wi$. In contrast, at moderate and high $Bi$, droplet deformation always increases with $Wi$. Moreover, it is found that the deformation increases with $Ca$ and with the solvent to total drop viscosity ratio. A simple ordinary differential equation model is developed to explain the various behaviours observed numerically. The presented results are in contrast with the heuristic idea that viscoelasticity in the dispersed phase always inhibits deformation.

Dynamics of coupled reacted flow of Oldroyd-B material induced by isothermal/exothermal stretched disks with Joule heating, viscous dissipation and magnetic dipoles

Current investigation presents the heat and mass transfer analysis for steady flow Oldroyd-B fluid induced by isothermally and exothermally stretching disks. The novel features of Joule heating, chemical reaction and Ohmic dissipations are also utilized in the energy and concentration equations. A non-dimensional set of transformations are introduced to convert the coupled partial differential system into a system of ordinary differential equations. The analytical solution of formulated dimensionless equations is obtained by using homotopy analysis method. The solution convergence is ensured carefully. The physical exploration of various dimensionless parameters on pressure, velocity, temperature and concentration profiles is presented. It is observed that heat transfer at lower disk increases with increment of Deborah number, Archimedes number and distance parameter. The rate of mass transfer at both surfaces of disk is enhanced for larger values of activation energy parameter and Deborah number.

Impact of heat generation/absorption of magnetohydrodynamics Oldroyd-B fluid impinging on an inclined stretching sheet with radiation

In this paper, we have investigated thermally stratified MHD flow of an Oldroyd-B fluid over an inclined stretching surface in the presence of heat generation/absorption. Similarity solutions for the transformed governing equations are obtained. The reduced equations are solved numerically using the Runge–Kutta Fehlberg method with shooting technique. The influences of various involved parameters on velocity profiles, temperature profiles, local skin friction, and local Nusselt number are discussed. Numerical values of local skin friction and local Nusselt number are computed. The significant outcomes of the study are that the velocity decreases when the radiation parameter R_{d} is increased while the temperature profile is increased for higher values of radiation parameter R_{d} in case of opposing flow, moreover, growth in Deborah number beta_{2} enhance the velocity and momentum boundary layer. The heat transfer rate is decrease due to magnetic strength but increase with the increased values of Prandtl and Deborah numbers. The results of this model are closely matched with the outputs available in the literature.

Radiative heat transfer enhancement in MHD porous channel flow of an Oldroyd-B fluid under generalized boundary conditions

This study explains the transient free convection phenomenon in a vertical porous channel subject to nonlinear thermal radiation. The infinite vertical channel encloses magnetohydrodynamic (MHD) flow of an Oldroyd-B fluid. The left channel wall possesses time-dependent velocity , while the right wall exhibits no motion. The momentum and temperature field equations are developed on the bases of momentum conservation law and Fourier’s principle of heat transfer. Laplace transformation technique and Durbin’s numerical inversion method are jointly incorporated to compute the solutions of the formulated problem. The influences of flow and material parameters on heat transfer and fluid velocity are graphically scrutinized with physical aspects. The numerical computations for skin friction and temperature gradient are tabularized to comprehensively examine the wall shear stress and heat transfer rate. Finally, velocity fields for Maxwell fluid, second grade fluid, and viscous fluid are traced out as limiting cases and their comparison is drawn with the velocity field of an Oldroyd-B fluid. Besides this, some newly published results are also deduced from the acquired solutions. It is observed that increasing the magnitude of radiation parameter Rd rapidly enhances the rate of heat transfer at the right channel wall while an inverse behavior of Nusselt number is witnessed at the left channel wall. The Maxwell fluid and second grade fluid indicate the swiftest and slowest channel flow rates respectively. The shear stress specifies dual nature for relaxation and retardation parameters subject to static and moving wall. Additionally, it is found that the flow of an Oldroyd-B fluid is retarded by a magnetic field.

Transient magnetohydrodynamic flow and heat transfer of fractional Oldroyd-B fluids in a microchannel with slip boundary condition

The unsteady magnetohydrodynamic flow of viscoelastic fluids through a parallel plate microchannel under the combined influence of magnetic, electro-osmotic, and pressure gradient forcings is investigated. The fractional Oldroyd-B fluid is used for the constitutive equation to simulate the viscoelastic behavior of fluid in the microchannel. Considering the important role of slip boundary condition in microfluidics, the Navier slip model at wall is adopted. The Laplace and Fourier cosine transforms are performed to derive the analytical expression of velocity distribution. Then, by employing the finite difference method, the numerical solution of the velocity distribution is given. In order to verify the validity of our numerical approach, numerical solutions and analytical solutions of the velocity distribution are contrasted with the exact solutions of the Newtonian fluid in previous work, and the agreements are excellent. Furthermore, based on the values of the velocity distribution for the fully developed flow, the energy equation including volumetric Joule heating, electromagnetic couple effect, and energy dissipation is solved to give the temperature distribution in the microchannel by using the finite difference method. Finally, the influence of fractional parameters and pertinent system parameters on the fluid flow and heat transfer performance and the dependence of the dimensionless Nusselt number Nu on the Hartmann number Ha and Brinkman number Br are discussed graphically.

A Chebyshev Based Spectral Method for Solving Boundary Layer Flow of a Fractional-Order Oldroyd-B Fluid

A Chebyshev Based Spectral Method for Solving Boundary Layer Flow of a Fractional-Order Oldroyd-B Fluid

Comprehensive analysis of integer-order, Caputo-Fabrizio (CF) and Atangana-Baleanu (ABC) fractional time derivative for MHD Oldroyd-B fluid with slip effect and time dependent boundary condition

<p style='text-indent:20px;'>This article is focused on the slip effect in the unsteady flow of MHD Oldroyd-B fluid over a moving vertical plate with velocity <inline-formula><tex-math id="M1">\begin{document}$ U_{o}f(t) $\end{document}</tex-math></inline-formula>. The Laplace transformation and inversion algorithm are used to evaluate the expression for fluid velocity and shear stress. Fractional time derivatives are used to analyze the impact of fractional parameters (memory effect) on the dynamics of the fluid. While making a comparison, it is observed that the fractional-order model is best to explain the memory effect as compared to the classical model. The behavior of slip condition as well as no-slip condition is discussed with all physical quantities. The influence of dimensionless physical parameters like magnetic force <inline-formula><tex-math id="M2">\begin{document}$ M $\end{document}</tex-math></inline-formula>, retardation time <inline-formula><tex-math id="M3">\begin{document}$ \lambda_{r} $\end{document}</tex-math></inline-formula>, fractional parameter <inline-formula><tex-math id="M4">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula>, and relaxation time <inline-formula><tex-math id="M5">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula> on fluid velocity has been discussed through graphical illustration. Our results suggest that the velocity field decreases by increasing the value of the magnetic field. In the absence of a slip parameter, the strength of the magnetic field is maximum. Furthermore, it is noted that the Atangana-Baleanu derivative in Caputo sense (ABC) is the best to highlight the dynamics of the fluid.</p>

Finite element solution of nonlinear convective flow of Oldroyd-B fluid with Cattaneo-Christov heat flux model over nonlinear stretching sheet with heat generation or absorption

In this study, a two-dimensional boundary layer flow of steady incompressible nonlinear convective flow of Oldroyd-B fluid over a nonlinearly stretching sheet with Cattaneo-Christov heat flux model and heat generation or absorption is examined. The governing equations of the boundary layer flow which are highly nonlinear partial differential equations are converted to the ordinary differential equations using similarity transformations and then the Galerkin finite element method (GFEM) is used to solve the proposed problem. The effect of local Deborah numbers β1 and β2, local buoyancy parameter λ, Prandtl number Pr, Deborah number γ, and heat generation/absorption parameter δ on the temperature and the velocity as well as heat transfer rate and shear stress are discussed both in graphical and tabular forms. The result shows the enlargement in the local buoyancy parameter λ will improve the velocity field and the heat transfer rate of the boundary layer flow. Moreover, our present work evinced both local skin friction coefficient and heat transfer rate step up if we add the values of non-linear stretching sheet parameter and local heat generation/absorption parameter has quite the opposite effect. The numerically computed values of local skin friction coefficient and local Nusselt number are validated with available literature and evinced excellent agreement.

Oldroyd-B fluid flow over a rotating disk subject to Soret–Dufour effects and thermophoresis particle deposition

In this study, an investigation of magnetohydrodynamics flow of Oldroyd-B fluid by a rotating disk with the influence of thermophoresis on the deposition of particles is discussed. Additionally, the Soret–Dufour effects are taken into consideration. The von Karman transformation is used and the numerical results are obtained through BVP Midrich technique in Maple. The results are given through graphical structure and tabular form. The solutions of the governing equations are obtained and presented graphically in the form of velocity fields, temperature and concentration distributions. The results of local Stanton number (or inward axial thermophoretic deposition velocity) are presented through table. Results reveal that axial thermophoretic velocity enhances with the enlargement of relative temperature difference parameter and thermophoretic coefficient.

LOCAL AND NONLOCAL DIFFERENTIAL OPERATORS: A COMPARATIVE STUDY OF HEAT AND MASS TRANSFERS IN MHD OLDROYD-B FLUID WITH RAMPED WALL TEMPERATURE

Study of heat and mass transfers is carried out for MHD Oldroyd-B fluid (OBF) over an infinite vertical plate having time-dependent velocity and with ramped wall temperature and constant concentration. It is proven in many already published articles that the heat and mass transfers do not really or always follow the classical mechanics process that is known as memoryless process. Therefore, the model using classical differentiation based on the rate of change cannot really replicate such dynamical process very accurately, thus, a different concept of differentiation is needed to capture such process. Very recently, a new class of differential operators were introduced and have been recognized to be efficient in capturing processes following the power-law, the decay law and the crossover behaviors. For the study of heat and mass transfers, we applied the newly introduced differential operators to model such flow and compare the results with integer-order derivative. Laplace transform and inversion algorithms are used for all the cases to find analytical solutions and to predict the influences of different parameters. The obtained analytical solutions were plotted for different values of fractional orders [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] on the velocity field. In comparison, Atangana–Baleanu (ABC) fractional derivatives are found to be the best to explain the memory effects than the classical, Caputo (C) and Caputo–Fabrizio (CF) fractional derivatives. Some calculated values for Nusselt number and Sherwood number are presented in tables. Moreover, from the present solutions, the already published results were found as limiting cases.

PEGAFEM-V: A new petrov-galerkin finite element method for free surface viscoelastic flows

The recently proposed finite element (FE) formulation for viscoelastic flows that allows the use of equal order linear interpolants for all variables and simultaneously does not suffer from the high Weissenberg number problem, is extended to free surface flows. The coupling of this Petrov-Galerkin stabilized FE formulation with the quasi-elliptic mesh generator allows us to obtain stable numerical solutions in highly deformed meshes and for very high values of the Weissenberg number (Wi). We present benchmark solutions in three free surface flows: the axisymmetric filament stretching, the elastocapillary-driven formation of bead-on-a-string, and the 2-dimensional, planar extrudate swell flow. In all cases, we attain converged solutions for values of Wi that have never been reached before by FE. The accuracy and robustness of the proposed numerical scheme are illustrated by achieving mesh and time step convergence under extreme mesh deformation conditions such as the bead-on-a-string (BOAS) formation during filament stretching. The formulation is enriched further with a discontinuity capturing scheme that enhances the quality of the solution around singularities dramatically. Finally, our simulations reveal for the first time the existence of lip-vortices in the steady planar extrudate-swell flow of Oldroyd-B fluids, which converge with mesh refinement.

Stabilized variational formulation of an oldroyd-B fluid flow equations on a Graphic Processing Unit (GPU) architecture

The governing equations of the flow of an oldroyd-B fluid are discretized using the finite element method. To overcome the convective nature of the momentum equation, the Galerkin/Least-Squares Finite Element Method (GLS/FEM) is used while the Discrete Elastic–Viscous Stress-Splitting (DEVSS) method is used to overcome the instability due to the absence of diffusion in the constitutive equations. The discretized equations are implemented on a hybrid system between the Graphics Processing Unit (GPU) architecture using Compute-Unified-Device-Architecture (CUDA) and a multi-core CPU. The implementation is applied successfully to simulate the blood flow in abdominal aortic aneurysm. To accelerate application performance on the GPU several optimized approaches are adopted. The most significant approach is the coloring technique that is used to assemble the global matrix. Numerical experiments show that the hybrid CPU-GPU implementation has a 26 time speedup over the multi-core CPU implementations.

An Oldroyd-B solver for vanishingly small values of the viscosity ratio: Application to unsteady free surface flows

This work is concerned with time-dependent axisymmetric free surface flows of Oldroyd-B fluids for any value of ▪, the ratio of solvent to total viscosities. The Oldroyd-B constitutive equation is dealt with by employing a novel technique to calculate the conformation tensor while an EVSS transformation allows the solution of the momentum equations coupled with the free surface stress conditions: this avoids numerical instabilities that can arise when using small values of ▪. The convergence of this new methodology is verified on pipe flow and also by comparing results from the literature for the time-dependent impacting drop problem. This approach is then used to predict the time-dependent free surface flow after a viscoelastic drop impacts a solid surface for ▪ values in the range [0, 1]. The impacting drop problem is investigated for polymer solutions containing a small solvent contribution (▪) or without any solvent viscosity (▪). In addition, a study of the bouncing drop problem for different values of ▪, Weissenberg and Reynolds numbers is undertaken.

Numerical investigation of hematocrit variation effect on blood flow in an arterial segment with variable stenosis degree

Numerical simulations of blood flow in arteries are important in the understanding and diagnosis of many cardiovascular diseases, such as atherosclerosis and arterial stenosis. More realistic mathematical models representing blood rheology offer a better understanding of these diseases. In this study, blood is considered an Oldroyd-B fluid with a shear-thinning property and a shear rate-dependent relaxation time that is adopted by fitting experimental data. The Quemada model is used to represent the shear-thinning property with hematocrit variation. The stabilized finite element method is used to obtain numerical solutions. Hemodynamics factors, such as the wall shear stress (WSS), axial velocity, wall pressure, and recirculation zones are examined for different flow conditions. The effects of the variation in both the hematocrit value and the relaxation time for different stenosis degrees are considered. Results indicate that the hematocrit value should be considered for blood flow simulations as it significantly affects the WSS and vortex shape.