Oldroyd-B Fluid Model Research Articles

A local meshless method for the numerical solution of multi-term time-fractional generalized Oldroyd-B fluid model

This work presents an accurate and efficient method, for solving a two dimensional time-fractional Oldroyd-B fluid model. The proposed method couples the Laplace transform (LT) with a radial basis functions based local meshless method (LRBFM). The suggested numerical scheme first uses the LT which transform the given equation to an elliptic equation in LT space, and then it utilizes the LRBFM to solve transformed equation in LT space, and then the solution is converted back into the time domain via the improved Talbot's scheme. The local meshless methods are widely recognized for scattered data interpolation and for solving PDEs in complex shaped domains. The adaptability, simplicity, and ease of use are features that have led to the popularity of local meshless methods. The local meshless methods are easy and straightforward, they only requires to solve linear system of equations. The main objective of using the LT is to avoid the computation of costly convolution integral in time-fractional derivative and the effect of time stepping on accuracy and stability of numerical solution. The stability and the convergence of the proposed numerical scheme are discussed. Further, the Ulam-Hyers (UH) stability of the proposed model is discussed. The accuracy and efficiency of the suggested numerical approach have been demonstrated using numerical experiments on five different domains with regular nodes distribution.

Significance of heat passage in four-phase Oldroyd-B nanofluid with solar thermal radiations through a cone: A study of entropy analysis

The studies of non-Newtonian fluids are extremely important because of their unlimited and extensive usage and applications in different mechanisms and processes. The current work carried out the visualization of thermal energy in the Oldroyd-B fluid model by inserting different types of nanoparticles, which are used to promote thermal performance. The flow is assumed to be passed through a cone with electro-magneto-hydrodynamic effect and thermal radiation and exponential external heat source. The modeled problem appears in the form of coupled nonlinear PDEs, which are transformed into corresponding ODEs by engaging the appropriate transformation. The solution of these transformed equations is calculated by using the finite element procedure. The utilization of tetra-hybrid nanoparticles improves the thermal performance and it is recorded that by inserting these particles fluid temperature increases significantly. It is worth mentioning that a finite element scheme is an authentic procedure to tackle highly nonlinear problems. The influence of multiple parameters such as M,E*,γ1,γ2 are examined and discussed in detail across the velocity profile whilst parameters behavior namely M,Ec,E* and Qs is observed graphically across the temperature profile. It was noticed through computed results that the velocity profile depicts enhanced behavior for E*,γ1,γ2 whereas, it illustrates reduced demeanor. Moreover, the Temperature profile illustrates accelerated behavior for M,Ec,E* and Qs. Moreover, skin friction and Nusselt number impact under distinct parameters are also presented graphically and show excellent agreement.

The Combined Effect of Gravity Modulation and Throughflow on Thermal Instability in the Hele-Shaw Cell Filled with Oldroyd-B Nanofluid

This paper shows the combined effect of throughflow and gravity modulation on the stability of Oldroyd-B nanofluid filled in Hele-Shaw cell. Nanofluid compared to the base fluid has higher thermal conduction. The thermal conductivity of nanofluid increased and thus increases the amount of energy transferred. The Oldroyd-B fluid model is important because of its numerous applications such as production of plastic sheet and extrusion of polymers through a slit die in polymer industry, biological solution pant tars glues, etc. In linear stability analysis, we found the expression of the critical Hele-Shaw Rayleigh number by using the normal mode method. Two-term Fourier series method is used for non-linear stability analysis and is also considered the Brinkman model for flow of nanofluid in Hele-Shaw cell. In linear stability analysis, we observed that there is no effect of Oldroyd-B nanofluid, which means that Deborah number (λ1) and retardation parameter (λ2) do not affect the stability analysis. Oldroyd-B nanofluid is similar to ordinary nanofluid in linear analysis. In non-linear analysis, Deborah number, retardation parameter, throughflow, gravity modulation, and Hele-Shaw number play a major role in heat/mass transfer. Enhancement in both heat/mass transfer in the system while increasing throughflow and Deborah number. An increment in Hele-Shaw number (Hs), decreases heat/mass transfer in the system.

Dynamics of unsteady axisymmetric of Oldroyd-B material with homogeneous-heterogeneous reactions subject to Cattaneo-Christov heat transfer

In several industrial and engineering applications, the Catteno-Christov heat flux plays a major role in the flow and heat transport of non-Newtonian fluids. Therefore, the goal of this study is to investigate the characteristics of homogeneous-heterogeneous reactions in the axisymmetric flow of Oldroyd-B materials using heat conduction analysis. The heat transfer phenomenon is examined from the non-Fourier heat flux model perspective. The governing flow field equations are developed using the rheological formulation of the Oldroyd-B fluid model, which is transformed into a set of nonlinear differential equations by utilizing the proper similarity conversions. The series solutions for the velocity, thermal, and solutal distribution are derived. The physical behaviors of relevant parameters are discussed in detail. The findings reveal that for the curvature parameter, the fluid velocity improves near the cylinder surface and no motion occurs away from the surface, while this predicts the dual behavior on temperature and concentration distributions. Further, fluid relaxation and retardation time exhibit opposite behavior on fluid velocity. Additionally, the results demonstrate that the homogeneous response parameter exhibits contradicting behavior on the concentration field while the thermal relaxation parameter lowers the temperature field.

Thermal investigation into the Oldroyd-B hybrid nanofluid with the slip and Newtonian heating effect: Atangana–Baleanu fractional simulation

The significance of thermal conductivity, convection, and heat transportation of hybrid nanofluids (HNFs) based on different nanoparticles has enhanced an integral part in numerous industrial and natural processes. In this article, a fractionalized Oldroyd-B HNF along with other significant effects, such as Newtonian heating, constant concentration, and the wall slip condition on temperature close to an infinitely vertical flat plate, is examined. Aluminum oxide (Al2O3) and ferro-ferric oxide (Fe3O4) are the supposed nanoparticles, and water (H2O) and sodium alginate (C6H9NaO7) serve as the base fluids. For generalized memory effects, an innovative fractional model is developed based on the recently proposed Atangana–Baleanu time-fractional (AB) derivative through generalized Fourier and Fick’s law. This Laplace transform technique is used to solve the fractional governing equations of dimensionless temperature, velocity, and concentration profiles. The physical effects of diverse flow parameters are discussed and exhibited graphically by Mathcad software. We have considered 0.15≤α≤0.85,2≤Pr⁡≤9,5≤Gr≤20,0.2≤ϕ1,ϕ2≤0.8,3.5≤Gm≤8, 0.1≤ Sc ≤0.8, and 0.3≤λ1,λ2≤1.7. Moreover, for validation of our present results, some limiting models, such as classical Maxwell and Newtonian fluid models, are recovered from the fractional Oldroyd-B fluid model. Furthermore, comparing the results between Oldroyd-B, Maxwell, and viscous fluid models for both classical and fractional cases, Stehfest and Tzou numerical methods are also employed to secure the validity of our solutions. Moreover, it is visualized that for a short time, temperature and momentum profiles are decayed for larger values of α, and this effect is reversed for a long time. Furthermore, the energy and velocity profiles are higher for water-based HNFs than those for the sodium alginate-based HNF.

Hydrodynamic clustering of two finite-length flagellated swimmers in viscoelastic fluids.

Clustering of flagellated microswimmers such as sperm is often mediated by hydrodynamic interactions between them. To better understand the interaction of microswimmers in viscoelastic fluids, we perform two-dimensional simulations of two swimming sheets, using a viscoelastic version of the smoothed dissipative particle dynamics method that implements the Oldroyd-B fluid model. Elasticity of sheets (stiff versus soft) defines two qualitatively different regimes of clustering, where stiff sheets exhibit a much more robust clustering than soft sheets. A formed doublet of soft sheets generally swims faster than a single swimmer, while a pair of two stiff sheets normally shows no speed enhancement after clustering. A pair of two identical swimmers is stable for most conditions, while differences in the beating amplitudes and/or frequencies between the two sheets can destroy the doublet stability. Clustering of two distinct swimmers is most stable at Deborah numbers of De = τω ≈ 1 (τ is the relaxation time of a viscoelastic fluid and ω is the beating frequency), in agreement with experimental observations. Therefore, the clustering of two swimmers depends non-monotonically on De. Our results suggest that the cluster stability is likely a dominant factor which determines the cluster size of collectively moving flagellated swimmers.

Heat and mass flux analysis of magneto-free-convection flow of Oldroyd-B fluid through porous layered inclined plate

The present work examines the analytical solutions of the double duffusive magneto free convective flow of Oldroyd-B fluid model of an inclined plate saturated in a porous media, either fixed or moving oscillated with existence of slanted externally magnetic field. The phenomenon has been expressed in terms of partial differential equations, then transformed the governing equations in non-dimensional form. On the fluid velocity, the influence of different angles that plate make with vertical is studied as well as slanted angles of the electro magnetic lines with the porous layered inclined plate are also discussed, associated with thermal conductivity and constant concentration. For seeking exact solutions in terms of special functions namely Mittag–Leffler functions, G-function etc., for Oldroyd-B fluid velocity, concentration and Oldroyd-B fluid temperature, Laplace integral transformation method is used to solve the non-dimensional model. The contribution of different velocity components are considered as thermal, mass and mechanical, and analyse the impacts of these components on the fluid dynamics. For several physical significance of various fluidic parameters on Oldroyd-B fluid velocity, concentration and Oldroyd-B fluid temperature distributions are demonstrated through various graphs. Furthermore, for being validated the acquired solutions, some limiting models such as Newtonian fluid in the absence of different fluidic parameters. Moreover, the graphical representations of the analytical solutions illustrated the main results of the present work and studied various cases regarding the movement of plate.

Temporal second-order finite difference schemes for variable-order time-fractional generalized Oldroyd-B fluid model

In this paper, we study the variable-order generalized time fractional Oldroyd-B fluid model, use the reduced order method and the L2-1? method to establish the differential format with second-order accuracy, prove the stability and convergence of the format, and give numerical examples to illustrate the effectiveness of the differential format.

Two fast numerical methods for a generalized Oldroyd-B fluid model

This work proposes two fast and efficient numerical methods for a generalized Oldroyd-B fluid model with fractional derivatives. The fast evaluations of the Riemann–Liouville fractional derivatives are developed based on convolution quadrature generated by the backward Euler and the second-order backward difference methods. By using these fast algorithms in time and employing the finite element method in space, two fully discrete schemes are established for the considered problem. Further, we discuss the error estimates of these numerical schemes based on the property of the initial value and the right hand function instead of the regularity assumption of the exact solution. Finally, some numerical tests are presented to verify the effectiveness of the numerical schemes and confirm the theoretical results.

Magneto-Oldroyd-B fluid flow over an exponentially accelerated vertical porous plate with heat source and reactive agents

ABSTRACT The present research work describes about flowing magnetohydrodynamic generalized Oldroyd-B liquid model in an exponentially accelerated vertical porous boundless device with heat source and reacting species and heat source. The fully developed Oldroyd-B fluid model is stimulated by heat source/sink and species reaction and vertical device under the influence of gravity. The physical flow equation is modelled in the form of partial derivative which is mutated into the dimensionless partial derivative equations by invoking suitable non-dimensional variables. The partial system of derivative equations is tackled by employing perturbation technique. The outcomes for the velocity flow field, thermal and species distributions are exhibited graphically. Computed outcomes for the plate friction, heat gradient and Sherwood number are provided in table. Furthermore, correlation in terms of validation has been tabulated. Some obtained results show that an increase in heat source and time reduces velocity plots but increase the rate of particle temperature. Owing to the Lorentz force produced by the imposed magnetic field, the velocity alongside velocity degenerates. Time parameter compliments the fluid temperature, particle concentration and fluid transport. The heat transfer rate accelerates with higher Prandtl number and heat source, but mass transfer rate retards with higher Schmidt number.

Variable heat source in stagnation-point unsteady flow of magnetized Oldroyd-B fluid with cubic autocatalysis chemical reaction

Understanding the flow behavior of non-Newtonian fluids required more research in terms of various aspects. Because the role of heat transfer in non-Newtonian flows is dominant due to its importance in technology. For these benefits, a theoretical investigation is carried out to analyze the time-dependent flow of non-Newtonian fluid with a focus on thermal and solutal transport. In the present study, we formulate a mathematical model for Oldroyd-B fluid by taking into account the effect of magnetic field. The governing flow field equations are constructed with the help of the rheological expression of Oldroyd-B fluid model. For physical relevance, the effects of non-uniform heat source/sink, Joule heating and thermal radiation with homogeneous-heterogeneous chemical reactions have been incorporated in stagnation point flow towards a stretching cylinder to modify the energy and concentration distributions. The highly non-linear ordinary differential equations are tackled analytically through the optimal homotopy analysis method (OHAM). Study reveals that, the strength of homogeneous and heterogeneous reactions leads to enhanced the concentration of the catalyst at the surface. Furthermore, the non-uniform heat source/sink parameter acts like a major controlling parameter for the heat transportation rate, and heat transport is also influenced by the surface-dependent heat source/sink.

Comparative Numerical Study of Thermal Features Analysis between Oldroyd-B Copper and Molybdenum Disulfide Nanoparticles in Engine-Oil-Based Nanofluids Flow

Apart from the Buongiorno model, no effort was ably accomplished in the literature to investigate the effect of nanomaterials on the Oldroyd-B fluid model caused by an extendable sheet. This article introduces an innovative idea regarding the enforcement of the Tiwari and Das fluid model on the Oldroyd-B fluid (OBF) model by considering engine oil as a conventional base fluid. Tiwari and Das’s model takes into account the volume fraction of nanoparticles for heat transport enhancement compared to the Buongiorno model that depends significantly on thermophoresis and Brownian diffusion impacts for heat transport analysis. In this paper, the thermal characteristics of an Oldroyd-B nanofluid are reported. Firstly, the transformation technique is applied on partial differential equations from boundary-layer formulas to produce nonlinear ordinary differential equations. Subsequently, the Keller-box numerical system is utilized to obtain final numerical solutions. Copper engine oil (Cu–EO) and molybdenum disulfide engine oil (MoS2–EO) nanofluids are considered. From the whole numerical findings and under the same condition, the thermodynamic performance of MoS2–EO nanofluid is higher than that of Cu–EO nanofluid. The thermal efficiency of Cu–EO over MoS2–EO is observed between 1.9% and 43%. In addition, the role of the porous media parameter is to reduce the heat transport rate and to enhance the velocity variation. Finally, the impact of the numbers of Reynolds and Brinkman is to increase the entropy.

Bioconvection oblique motion of magnetized Oldroyd-B fluid through an elastic surface with suction/injection

In recent research, it is worth mentioning that bioconvection usage has shown significant promise for environmentally friendly, sustainable “green” fuel cell technologies. In this context, the present problem definitely gives a boost to a deeper analysis of the Oldroyd-B fluid model in the presence of gyrotactic microorganisms. This study analyses oblique Oldroyd-B fluid with mixed convection on an elastic surface with interactive properties and gyrotactic microorganisms under the influence of suction/injection with zero heat and mass. The principal physical model is converted in a nonlinear system of ODEs employing proper similarity equations. The impact of all relative physical constrictions on velocity, temperature, concentration, and volume fraction of gyrotactic microorganisms is expressed geometrically. Physical scales like skin friction measurements, heat transfer rate, and mass transfer rate at the surface are calculated numerically.

Electrokinetic oscillatory flow and energy conversion of viscoelastic fluids in microchannels: a linear analysis

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.

Electroosmotic slip flow of Oldroyd-B fluid between two plates with non-singular kernel

In the present research article, we investigated the slip flow of an unsteady incompressible Oldroyd-B fluid model. The electroosmosis and the pressure gradient have been seized for the stimulation of flow. The progress of the fluid is treated to be as passage composed by two micro-parallel plates. The potential difference alive between hard surface and the fluid is taken to be non symmetric. The governing equations are established for an Oldroyd-B fluid by using newly defined Caputo–Fabrizio fractional derivative. We used Laplace transform for converting the problem into spacial coordinates after proposing the geometry free variables. To find inverse Laplace transform, numerical Stehfest algorithm is used in place of promoting an analytical expression for it. In order to have the validity of our obtained results, the tabular comparison of two different algorithms (Stehfest and Tzou) and graphical simulation have been investigated. The conclusions are also illustrated in terms of graphs and carry the report of slip flow effect as well as some pertinent parameters on the velocity of the fluid.

The Efficient Finite Element Methods for Time-Fractional Oldroyd-B Fluid Model Involving Two Caputo Derivatives

In this paper, we consider the numerical schemes for a timefractional Oldroyd-B fluid model involving the Caputo derivative. We propose two efficient finite element methods by applying the convolution quadrature in time generated by the backward Euler and the second-order backward difference methods. Error estimates in terms of data regularity are established for both the semidiscrete and fully discrete schemes. Numerical examples for two-dimensional problems further confirm the robustness of the schemes with first- and second-order accurate in time.

Numerical simulation of particle focusing dynamics of DNA-laden fluids in a microtube

A CFD model considering inertial, elastic and drag forces was developed to simulate the focusing effect of microparticles in a dilute DNA solution passing through a microtube. The Oldroyd-B fluid model coupled with Lagrangian model was employed to describe the flow behavior of DNA solution and particle trajectory. The model was validated by comparing the patterns of particle beam and its width with experimental results. Particle focusing dynamics was investigated by analyzing the focusing behaviors, flow and particle velocity, and force distributions throughout the whole tube. The results indicated that particles far away from the centerline migrate faster than those near centerline. Investigations on the effect of DNA concentration, particle diameter and flow rate showed that increasing DNA concentration and particle diameter benefited the focusing efficiency while larger flow rate weakened the particle focusing. This computational model could serve as an effective tool to investigate the particle focusing dynamics.

Novel Numerical Analysis of Multi-Term Time Fractional Viscoelastic Non-Newtonian Fluid Models for Simulating Unsteady Mhd Couette Flow of a Generalized Oldroyd-B Fluid

Abstract In this paper, we consider the application of the finite difference method for a class of novel multi-term time fractional viscoelastic non-Newtonian fluid models. An important contribution of the work is that the new model not only has a multi-term time derivative, of which the fractional order indices range from 0 to 2, but also possesses a special time fractional operator on the spatial derivative that is challenging to approximate. There appears to be no literature reported on the numerical solution of this type of equation. We derive two new different finite difference schemes to approximate the model. Then we establish the stability and convergence analysis of these schemes based on the discrete H 1 norm and prove that their accuracy is of O(τ + h 2) and O(τ min{3–γs ,2–αq ,2–β}+h 2), respectively. Finally, we verify our methods using two numerical examples and apply the schemes to simulate an unsteady magnetohydrodynamic (MHD) Couette flow of a generalized Oldroyd-B fluid model. Our methods are effective and can be extended to solve other non-Newtonian fluid models such as the generalized Maxwell fluid model, the generalized second grade fluid model and the generalized Burgers fluid model.

A penalty immersed boundary method for viscoelastic particulate flows

We extend the penalty immersed boundary (pIB) method to investigate the interaction between circular rigid particles and a surrounding viscoelastic Oldroyd-B fluid. The basic idea of the pIB method is the splitting of an immersed boundary, which here is a rigid body, notionally into two Lagrangian components: one is a massive component carrying all mass of the rigid body, and the other is massless. These two components are connected by a system of stiff springs with zero rest length. The massive component has no direct interaction with the surrounding fluid and behaves as though in a vacuum, following the dynamics of a rigid body, in which the acting forces and torques are generated from the system of stiff springs that connects the two Lagrangian components. The massless component interacts with the surrounding Oldroyd-B fluid: it moves at the local fluid velocity and exerts force locally on the fluid. We verify the pIB method combined with Oldroyd-B fluid model by investigating the effects of the wall and elasticity of the fluid on the lateral position of a circular particle falling under the influence of gravity and by studying convergence of the numerical solutions. We also simulate the interaction between multiple circular particles and the surrounding Oldroyd-B fluid and compare the dynamics of the particles in various flow conditions.