Oldroyd-B Fluid Research Articles

Towards the exact solutions of Burger’s fluid flow through arteries with fractional time derivative magnetic field and thermal radiation effects

We consider the unsteady flow of Burger fluid within a circular cylindrical tube, driven by a time-dependent pressure gradient, a body acceleration and a magnetic field acting normal to the flow direction. The solutions of the fractional constitutive equations governing the unsteady Burger’s fluid flow through arterial walls were obtained via the Laplace transform and the finite Hankel transform. The effects of magnetic field on parameters such as blood temperature and velocity were studied by Caputo time-fractional derivatives. We note that the solutions of many particular models such as fractional Oldroyd-B fluid, fractional Maxwell fluid, fractional second grade fluid and fractional Newtonian fluid models can be recovered from the solutions of the fractional constitutive equations governing the unsteady Burger’s fluid flow by particularizing the material coefficients (i.e. special and limiting cases of the earlier Burger’s fluid model). The numerical computations have been carried out to analyze the effects of fractional parameter α, similarity parameter β, relaxation time λ1, retardation time λ3, radius of the circular cylinder R0 and material parameter λ2 on the blood velocity and temperature. Some interesting flow and temperature characteristics are presented graphically and discussed. The study reveals that blood velocity, temperature and fractional parameters are reduced in the presence of magnetic field. The importance of this study can be found in the application fields of magnetic field control of biotechnological processes, bio magnetic device technology, biomedical engineering, medicine, etc.

Numerical simulation for bio-convection flow of magnetized non-Newtonian nanofluid due to stretching cylinder/plate with swimming motile microorganisms

The nanotechnology era has led to latest advancement in improving energy resources, which play a significant importance in the development of industrial sectors and engineering. The main purpose of current article is to address the Wu’s slip impact in bio-convection flow of Oldroyd-B fluid containing nanoparticles configured by stretching cylinder/plate in the presence of swimming motile microorganisms. The most desirable type of non-Newtonian fluid, such as Oldroyd-B fluid is employed to evaluate the prominent parameters. The particular characteristics including thermal radiation and well-known activation energy are also involved for the present flow scenario. To examine the inspiration of thermophoresis diffusion and Brownian motion on Oldroyd-B nanofluid, the Buongiorno’s model has been addressed. The appropriate conversion is employed to reformulate the governing system of partial differential equations to dimensionless nonlinear ordinary differential structures. The nonlinear dimensionless ODE’s are computed numerically by utilizing bvp4c solver via MATLAB. The behavior of controlling parameters against velocity distribution, temperature field, nanoparticle concentration and microorganism concentration is scrutinized through figures and tables.

Thermal analysis of MHD convective slip transport of fractional Oldroyd-B fluid over a plate

The prime concern of this study is to analyze the generalized time-dependent magnetohydrodynamic (MHD) slip transport of an Oldroyd-B fluid near an oscillating upright plate. The plate is nested in a porous media under the action of ramped heating and nonlinear thermal radiation. Caputo–Fabrizio (CF) and Atangana–Baleanu (ABC) derivatives are utilized to constitute fractional partial differential equations that establish slip flow, shear stress, and heat transfer phenomena. Primarily, Laplace transformation is applied to dimensionless fractional models, and later Stehfest’s numerical algorithm is invoked to anticipate solutions of momentum and heat equations in principal coordinates. Moreover, computed solutions of velocity and energy fields are authenticated by Durbin’s and Zakian’s Laplace inversion algorithms. The relations for skin friction and Nusselt number are evaluated in terms of velocity and temperature gradients to efficiently anticipate shear stress and rate of heat transfer at the solid–fluid interface. The respective outcomes are manifested through tables. A critical examination of the current model is carried out and repercussions of variation in implanted parameters on temperature and momentum profiles are graphically elucidated. For the sake of comparison, three limiting fractional models, named second grade, Maxwell, and viscous models, are proposed for the isothermal and ramped temperature cases. Consequently, the observed outcomes affirm that under the isothermal condition, a generalized Maxwell fluid performs the swiftest slip transport compared to other models. Inversely, a second grade fluid specifies the highest velocity profile under ramped temperature case.

Features of Cattaneo-Christov double diffusion theory on the flow of non-Newtonian Oldroyd-B nanofluid with Joule heating

This research deals the flow and heat transfer of the upper convected Oldroyd-B fluid over a rotating disk. The magnetic field is applied normal to the disk. With the presence of nanoparticle, the Cattaneo–Christov theory is used rather than classical Fourier’s and Fick’s laws for the study of heat and mass transport mechanisms. The Joule heating term is also added into heat equation. This theory predicts the influence of thermal and solutal relaxation times on the boundary layers. Von Karman similarity approach is utilized to convert the partial differential equations into ordinary differential equations. A homotopic approach for obtaining the analytical series solutions is carried out. The graphical results are obtained for velocity fields, temperature and concentration distributions. Comparisons are made for limiting case between numerical and analytical solutions and found in good agreement. Results reveal that the thermal and solutal relaxation time parameters are affected the temperature and concentration distributions in decreasing manner, respectively.

Flow and Heat Transfer Property of Oldroyd-B-Fluid-Based Nanofluids Containing Cylindrical Particles in a Pipe

Flow and heat transfer property of Oldroyd-B-fluid-based nanofluids containing cylindrical particles are studied in a pipe with circular cross-section in the range of Reynolds number (Re) from 100 to 2000, Weissenberg number (We) from 0.1 to 2, particle aspect ratio (β) from 2 to 16 and particle volume concentration (Φ) from 0.1% to 2.5%. The motion equation of Oldroyd-B fluid with particles, the equation for probability density function of particle orientation and convection-diffusion equation for particles are solved numerically. The numerical method used in the simulation is validated by comparing with the available results. The effects of Re, We, β and Φ on the friction factor (f), Nusselt number (Nu) and ratio of energy performance evaluation criterion (PECt/PECf) for Oldroyd-B-fluid-based nanofluids to that for Oldroyd-B fluids are discussed. The results showed that the values of f and Nu of Oldroyd-B-fluid-based nanofluids are larger than that of water-based nanofluids and that of pure Oldroyd-B fluids. The values of f increase with increasing Re, We and Φ, but with decreasing β. The values of Nu and PECt/PECf are enhanced with increasing Re, We, β and Φ. The increase of f is larger than that of Nu at lower Re, but is less than that of Nu at higher Re. It is more effective to use Oldroyd-B-fluid-based nanofluids with cylindrical nanoparticles to improve the heat transfer at the conditions of higher Re, We, β and Φ. Finally, the correlation formula of PECt/PECf as a function of Re, We, β and Φ is derived.

3D nanofluid flow over exponentially expanding surface of Oldroyd-B fluid

Fluid motion is caused by the surface stretching, the temperature difference or the concentration difference etc. In this study, we will focus exclusively on the 3D nanofluid flow due to expanding surface of Oldroyd-B fluid which is extended in two directions. The flow over expanding surface has several applications in engineering and industrial processes for instance plastic sheet extrusion, hot rolling, paper processing, wire drawing, plastic films painting, and fiber glass etc. In current investigation, we have discussed the nanofluid flow over an expanding surface for Oldroyd-B fluid. It is possible to use nanofluids to enhance the fluid’s thermal conductivity. The equations that governs the flow are converted into nonlinear coupled ODE’s. The problem’s series solution was found using the method of homotopy analysis. Effects of Deborah number, thermophoretic and Brownian diffusion parameters, Prandtl and Schmidt numbers on the flow field are explored and discussed graphically. The relaxation/retardation times are noted to have contrasting effects on fluid velocity. Further, the diffusion parameter of nanoparticles enhance the temperature and nanofluid concentration.

Finite difference Laguerre-Legendre spectral method for the two-dimensional generalized Oldroyd-B fluid on a semi-infinite domain

In this paper, we study the numerical solution for a two-dimensional generalized Oldroyd-B fluid flowing on a semi-infinite domain. The second order θ scheme with the weighted and shifted Grünwald difference operator is derived to approximate the time derivatives with orders in (0,2). For the case of unbounded space, the Laguerre-Legendre spectral method is proposed. The fully discrete scheme is obtained and proved to be stable, convergent with accuracy O(τ2+N(1−s)/2+M1−r), where τ is the time step size, N,M are the polynomial degrees. We also implement some numerical examples to further support the theoretical analysis.

The centre-mode instability of viscoelastic plane Poiseuille flow

Abstract

Localized stress amplification in inertialess channel flows of viscoelastic fluids

Nonmodal analysis typically uses square-integrated quantities to characterize amplification of disturbances. However, such measures may be misleading in viscoelastic fluids, where polymer stresses can be strongly amplified over a small region. Here, we show that when using a localized measure of disturbance amplification, spanwise-constant polymer-stress fluctuations can be more amplified than streamwise-constant polymer-stress fluctuations, which is the opposite of what is observed when a square-integrated measure of disturbance amplification is used. To demonstrate this, we consider a model problem involving two-dimensional pressure-driven inertialess channel flow of an Oldroyd-B fluid subject to a localized time-periodic body force. Nonmodal analysis of the linearized governing equations is performed using recently developed well-conditioned spectral methods that are suitable for resolving sharp stress gradients. It is found that polymer-stress fluctuations can be amplified by an order of magnitude while there is only negligible amplification of velocity fluctuations. The large stress amplification arises from the continuous spectrum of the linearized problem, and may put the flow into a regime where nonlinear terms are no longer negligible, thereby triggering a transition to elastic turbulence. The results suggest an alternate mechanism that may be useful for understanding recent experimental observations of elastic turbulence in microchannel flows of viscoelastic fluids. • Nonmodal amplification of localized time-periodic body forces is examined. • Poiseuille flow of Oldroyd-B fluids is considered. • Stress fluctuations can be amplified much more than velocity fluctuations. • Stress amplification is highly localized in space. • Results suggest a mechanism for transition to elastic turbulence in microchannels.

Simulation of Oldroyd-B Viscoelastic Fluid in Axisymmetric Straight Channel by Using a Hybrid Finite Element/Volume Method

In this study, incompressible viscoelastic fluid through the axisymmetric circular channel is simulated with Oldroyd-B model. The simulation is performed based on a hybrid finite volume/element method, which consists of Taylor-Galerkin finite element discretisation, and a cell vertex fluctuation-distribution finite volume method. In this context, the momentum and continuity equations are treated with a finite element method, while a finite volume approach is applied to solve the Oldroyd-B constitutive model. Analytical expressions are presented for the velocity and stress components in fully developed channel flow of Oldroyd-B fluid. For this complex fluid, we see an excellent agreement between the analytic and the numerical solutions. The study of axisymmetric circular channel problem based on a hybrid numerical method represents a great challenge. The novelty here is to study the temporal convergence-rate of the system solution that is taken to be steady state, incompressible, axisymmetric, and laminar, which did not address by researchers previously. Here, the rate of convergence for all solution components is presented, where a large level of convergence is appeared for stress compared to the other solution components. Moreover, the pressure drops and stress response across the flow are provided with respect to difference in solvent-fraction and Weissenberg number . A significant effect from the viscoelastic parameters upon the level of the stress has been detected, while for the pressure response the change is semi-modest. For the stress response the findings reveal that, with decreasing solvent-fraction , the maxima level of stress components are strongly amplifies.

Prediction of shear thickening of particle suspensions in viscoelastic fluids by direct numerical simulation

Abstract

Flow of Oldroyd-B fluid caused by a rotating disk featuring the Cattaneo-Christov theory with heat generation/absorption

This article presented the Cattaneo-Christove heat and mass flux theories in the flow of Oldroyd-B fluid over a rotating disk. The flow configuration is due to the rotating as well as stretching of the disk. The heat generation/absorption and chemical reaction are also considered. For the formulation of heat and mass equations, the Cattaneo-Christov theories are used rather than Fourier's and Fick's laws. The von Karman's transformations are used to convert the partial differential equations into non-dimensional ordinary differential equations. The analytical series solutions are obtained by utilizing the homotopy analysis method (HAM) in Mathematica software. The graphical results are achieved in the form of velocity fields, temperature and concentration distributions. Results show that the temperature of the Odroyd-B fluid rises when the magnetic field parameter increases in some specific range. Further, the velocities show a reducing behavior against magnetic field parameter. It is observed that the temperature reduces as thermal relaxation time parameter increases. It is also be mentioned that the solutal relaxation time parameter is influenced on concentration distribution in decreasing trend.

Fractional study on heat and mass transfer of MHD Oldroyd-B fluid with ramped velocity and temperature

This study explores the time-dependent convective flow of MHD Oldroyd-B fluid under the effect of ramped wall velocity and temperature. The flow is confined to an infinite vertical plate embedded in a permeable surface with the impact of heat generation and thermal radiation. Solutions of velocity, temperature, and concentration are derived symmetrically by applying non-dimensional parameters along with Laplace transformation $(LT)$ and numerical inversion algorithm. Graphical results for different physical constraints are produced for the velocity, temperature, and concentration profiles. Velocity and temperature profile decrease by increasing the effective Prandtl number. The existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity. Velocity is decreasing for $kappa$, $M$, $Pr_{reff,}$ and $Sc$ while increasing for $G_{r}$ and $G_{c}$. Temperature is an increasing function of the fractional parameter. Additionally, Atangana-Baleanu $(ABC)$ model is good to explain the dynamics of fluid with better memory effect as compared to other fractional operators.

Microconfined electroosmotic flow of a complex fluid with asymmetric charges: Interplay of fluid rheology and physicochemical heterogeneity

Abstract We report a study on the micro-confined electroosmotic flow of an Oldroyd-B fluid over a surface having asymmetric charge modulation. We have employed a combination of regular and matched asymptotic expansion to obtain the analytical solution. We have also carried out a full numerical simulation of the physicochemical problem in order to assess the full parameter space of the problem. The analytical solution is shown to be in excellent agreement with the full numerical solution in the limiting conditions of thin electrical double layers and weakly viscoelastic fluids. We have used these solutions to describe the complex fluid flow pattern and the modified electroosmotic slip velocity. We have also highlighted the alteration in the net volumetric throughput and ionic current. We have subsequently presented the numerical solutions for the velocity field, flow rates, and streaming current by varying the physicochemical conditions at the surface and viscoelastic properties of the fluid. We report an augmentation in the electroosmotic slip velocity with the increase in relative strength. The symmetry breaking of flow and stress distributions are shown to affect the net-throughput and streaming current, which is indicative of the combined effect of phase angle, magnitude of charge distribution, and the fluid viscoelasticity. We have shown that the thickness of electrical double layer considerably affects the net-throughput and streaming current generation in the microchannel. Our results hold the key towards understanding the complex bio-fluid transport in a microchannel utilizing the electric field in the presence of non-uniform surface charge distribution.

Impact of irreversibility ratio and entropy generation on three-dimensional Oldroyd-B fluid flow with relaxation–retardation viscous dissipation

The study is concerned with entropy minimization on three-dimensional magnetohydrodynamic Oldroyd-B fluid flow with relaxation–retardation viscous dissipation and a mixed chemical reaction. A numerical solution of the nonlinear transport equations is obtained using an overlapping grid spectral collocation numerical scheme. We investigate strategies for entropy generation minimization in terms of system parameters such as the mixed convection parameter and changes in thermal and concentration fields under different conditions. Further, the findings on changes in the axial and transverse skin friction coefficients, the Nusselt number and the Sherwood number are presented.

Insight into the Dynamics of Oldroyd-B Fluid Over an Upper Horizontal Surface of a Paraboloid of Revolution Subject to Chemical Reaction Dependent on the First-Order Activation Energy

In this study, the problem of two-dimensional non-Newtonian Oldroyd-B fluid flow over the upper horizontal paraboloid surface (UHPS) is investigated. The shape of a submarine, the bonnet of a car, the shape of the jet plane, and the shape of the upper pointed bullet are some daily life examples of the paraboloid surface. At a free stream, the Oldroyd-B fluid flow over UHPS is created by the reaction of the catalytic surface and the stretching between fluid layers. With the help of appropriate similarity parameters, the determining nonlinear coupled partial differential equations (PDE’s) are reduced into nonlinear coupled ordinary differential equations (ODE’s). The numerical solution of governing ODE’s is obtained by using the Runge–Kutta Fehlberg method associated with the shooting technique through MATLAB software. The numerical results are achieved for the velocity field, concentration, and temperature fields by varying different physical parameters like thickness parameter, reaction consumption parameter, fluid’s parameters, and velocity power index parameter. The obtained results are investigated numerically and graphically. The velocity field of fluid flow is a rising function of the thickness parameter. The temperature field is increasing with an extension in the quantity of the velocity index parameter. The concentration field is a growing function of the thickness parameter. The coefficient of local skin friction decreases due to the increment of the thickness parameter of the paraboloid surface.

A fractional study of generalized Oldroyd-B fluid with ramped conditions via local & non-local kernels

Abstract Convective flow is a self-sustained flow with the effect of the temperature gradient. The density is nonuniform due to the variation of temperature. The effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by mass transfer process; for instance condensation, evaporation and chemical process. Due to the applications of the heat and mass transfer combined effects in different field, the main aim of this paper is to do comprehensive analysis of heat and mass transfer of MHD unsteady Oldroyd-B fluid in the presence of ramped conditions. The new governing equations of MHD Oldroyd-B fluid have been fractionalized by means of singular and non-singular differentiable operators. In order to have an accurate physical significance of imposed conditions on the geometry of Oldroyd-B fluid, the ramped temperature, concentration and velocity are considered. The fractional solutions of temperature, concentration and velocity have been investigated by means of integral transform and inversion algorithm. The influence of physical parameters and flow is analyzed graphically via computational software (MATHCAD-15). The velocity profile decreases by increasing the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness and enlargement of the thermal effect. The classical calculus is assumed as the instant rate of change of the output when the input level changes. Therefore it is not able to include the previous state of the system called the memory effect. Due to this reason, we applied the modern definition of fractional derivatives. Obtained generalized results are very important due to their vast applications in the field of engineering and applied sciences.

MHD Oldroyd-B Fluid with Slip Condition in view of Local and Nonlocal Kernels

We examine the velocity field of an incompressible Oldroyd-B fluid over a horizontal plate of continual length in a permeable medium with magnetohydrodynamics effect. Firstly, the results for the dimensionless classical model (governing equation) have been studied analytically then the study is extended for different fractional operators. The relations to determine the velocity fields of this problem are found by Laplace transformation and different numerical inversion algorithms. The impact of physical parameters on velocity profiles is analyzed graphically for integer and non-integer models. Non-integer operators are used to analyzing the impact of fractional parameters on the fluid curves of the fluid.

An extensible lattice Boltzmann method for viscoelastic flows: complex and moving boundaries in Oldroyd-B fluids

Most biological fluids are viscoelastic, meaning that they have elastic properties in addition to the dissipative properties found in Newtonian fluids. Computational models can help us understand viscoelastic flow, but are often limited in how they deal with complex flow geometries and suspended particles. Here, we present a lattice Boltzmann solver for Oldroyd-B fluids that can handle arbitrarily shaped fixed and moving boundary conditions, which makes it ideally suited for the simulation of confined colloidal suspensions. We validate our method using several standard rheological setups and additionally study a single sedimenting colloid, also finding good agreement with the literature. Our approach can readily be extended to constitutive equations other than Oldroyd-B. This flexibility and the handling of complex boundaries hold promise for the study of microswimmers in viscoelastic fluids.Graphic abstract

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.