Maxwell Viscoelastic Fluid Research Articles

Well-posedness result for the flow of Maxwell viscoelastic fluid of White-Metzner type

In this paper, we investigate the flow characteristics of an unsteady quasistatic Maxwell viscoelastic fluid of White-Metzner type within a three-dimensional bounded domain. Our objective is to establish the well-posedness of the resulting partial differential equations initial boundary value problem, both locally and globally in time, under the condition of small initial data. To demonstrate the existence of a solution, we employ an iterative method that transforms our problem into a sequence of linear subproblems. At each iteration, we tackle both elliptic and hyperbolic problems. The convergence of this iterative process provides the solution to the original problem.

Numerical analysis of velocity slip and magnetic Soret effect on dissipative Maxwell liquid motion about a stretching wall with heat source/sink

The main aim of present numerical analysis is to explore the effects of viscous dissipation and velocity slip on the two-dimensional steady-state viscous incompressible flow of Maxwell fluid over a stretching sheet under the infleunce of magnetic field. Novel collective effects of heat source/sink and Soret impacts have been included in the governing equations to explore the salient features of heat and mass transport mechanism. Further, the velocity slip is introduced into the boundary conditions to depict the momentum transport behavior in the flow region. A typical Maxwell fluid model is deployed to separate the non-Newtonian flow behavior from that of classical Newtonian fluids. However, the visco-elastic Maxwell fluid finds its abundant applications in various fields of engineering and medicine such as plastic sheet drawing, metallurgy, polymer sheet extrusion, chemical engineering, electronic cooling, injection molding and nuclear cooling and many others. Inspired by these applications, authors have made an attempt to disclose the magneto-thermo salient features of slip flow of Maxwell fluid over stretching wall under Soret effect. The current physical situation results the highly nonlinear coupled two-dimensional steady-state partial differential equations and which are not amenable to any of the direct techniques. Due to this, the suitable similarity transformations are deployed to reduce the dimensional complexity of the constructed partial differential equations. A robust Matlab-based bvp4c scheme is utilized as a basic tool to produce the similarity solutions of the governing equations. The computer generated numerical data is presented in view of flow, temperature and concentration profiles including physical quantities of interest like skin-friction coefficient, heat and mass transport rates for the various values of physical parameters range such as, 0 ≤ M ≤ 1 , 0 ≤ β ≤ 1 , − 0.3 ≤ λ ≤ 0.6 , − 0.2 ≤ Q ≤ 0.2 , 0 ≤ Ec ≤ 2.2 , 1.2 ≤ Pr ≤ 2.2 , 0 ≤ Sr ≤ 0.5 and 1.2 ≤ Sc ≤ 2.2 . Accordingly, it is noticed that, enhancing magnetic parameter decreases the Maxwell fluid flow and amplifies the temperature and concentration fields. Enlarging Maxwell fluid parameter decreases the velocity field and increases the temperature and concentration profiles. Amplified slip parameter diminished the Maxwell flow inside the flow regime. Increasing heat source/sink parameter amplifies the temperature field. Further, magnifying Soret number amplifies the concentration field. Magnitude of skin-friction coeffiecient enlarged with amplified magnetic and Maxwell fluid parameters. Heat and mass transport rates decayed with enhancement in heat source/sink and Soret parameters. Finally, it is described that, the present similarity solutions showing good agreement with the previously reported solutions in the literature and this fact confirms the accurateness of the used numerical method and the generated similarity solutions.

Revolutionizing energy flow: Unleashing the influence of MHD in the presence of free convective heat transfer with radiation

This study investigates the complex interplay between radiation and magneto-flow on a porous, perpendicular plate immersed in a viscoelastic Maxwell fluid. The significance lies in understanding how the Lorentz force shapes dynamics and energy transfer in such systems, which is crucial for various industrial applications. Utilizing a comprehensive model that accounts for heat generation and absorption, we transform partial differential equations into ordinary ones through flow similarity analysis, providing valuable insights into the system's behavior. Employing the bvp4c solver in MATLAB, we evaluate velocity and energy profiles in Maxwell fluid flow. Graphical representations allow for a thorough examination of the influence of thermophysical parameters. Our findings reveal an intensified velocity profile attributed to prolonged material relaxation times.Furthermore, temperature profiles progressively increase with higher radiation and porous parameters. These results hold significant implications for industrial applications, particularly in Maxwell fluids' heat transport studies. Insights from this research can inform the design and optimization of systems such as ovens, boilers, cross-flow heat exchangers, and solar panels, enhancing efficiency and performance. Overall, this study contributes novel insights that advance understanding beyond previous efforts in the literature, paving the way for further exploration in this field. The primary finding of this study indicates that as the Rayleigh number increases, the velocity profile experiences an increase, whereas the temperature profile shows a decrease.

Contribution of rational design and fractional rheology on magnetic nanoparticle-based drug targeting in a microvessel with Saffman force

Magnetic nanoparticles based drug targeting is one of the prominent drug targeting methods due to non-invasive treatments, and recovery efficiency. The aim of the present problem is to analyze the trajectories of drug carrier particles and the total volume fraction of magnetic nanoparticles required for capturing purposes close to the tumor region. Due to the complex nature of blood, the viscoelastic Maxwell fluid relation is used to describe blood, and the flow of nanoparticles is investigated using momentum equations with the time-variant Caputo-Fabrizio fractional order expression to capture memory effects. The rational design of the nanoparticles such as size and shape with different aspect ratio along particle-particle interaction, Saffman force and external magnetic force are incorporated in the governing equation. The velocity profile of the fluid is represented in the form of the inverse of Laplace and Hankel transform. The velocity profile is solved by numerical integration and trajectories of the drug carrier particles analyzed by using the fourth order Runge-Kutta method by developing an algorithm. The conclusion drawn from the study shows that drug carriers lead towards the tumor region with long term memory effects, and it is easily captured at the tumor region. Viscoelastic rheology capture possibly opposes the drugs carrying magnetic nanoparticles to capture at tumor regions following a similar phenomenon by Saffman force. Spherical shaped drugs carrying magnetic nanoparticles are more prominent to be targeted to the tumor region than other shaped drugs carrying magnetic nanoparticles. The present study will help biomedical engineers and nanomedicine researchers develop magnetic devices and the next generation of drug carrier particles to treat cancerous tumors.

Alternating Current Electroosmotic Flow of Maxwell Fluid in a Parallel Plate Microchannel with Sinusoidal Roughness.

The EOF of a viscoelastic Maxwell fluid driven by an alternating pressure gradient and electric field in a parallel plate microchannel with sinusoidal roughness has been investigated within the Debye-Hückel approximation based on boundary perturbation expansion and separation of variables. Perturbation solutions were obtained for the potential distribution, the velocity and the mean velocity, and the relation between the mean velocity and the roughness. There are significant differences in the velocity amplitudes of the Newtonian and Maxwell fluids. It is shown here that the velocity distribution of the viscoelastic fluid is significantly affected by the roughness of the walls, which leads to the appearance of fluctuations in the fluid. Also, the velocity is strongly dependent on the phase difference θ of the roughness of the upper and lower plates. As the oscillation Reynolds number ReΩ increases, the velocity profile and the average velocity um(t) of AC EOF oscillate rapidly but the velocity amplitude decreases. The Deborah number De plays a similar role to ReΩ, which makes the AC EOF velocity profile more likely to oscillate. Meanwhile, phase lag χ (representing the phase difference between the electric field and the mean velocity) decreases when G and θ are increased. However, for larger λ (e.g., λ > 3), it almost has no phase lag χ.

MHD Maxwell nanofluid flow over a stretching cylinder in porous media with microorganisms and activation energy

The main aim of this study is to investigate the significance of activation energy in the flow of a Maxwell fluid over a stretching cylinder. Additionally, the heat and mass fluxes of viscoelastic Maxwell fluids, thermal radiation, porous media, Brownian motion, heat generation/absorption, and thermophoresis over a stretching cylinder porous media containing gyrotactic microorganisms are also discussed in the flow. The governing nonlinear PDEs were converted into ODEs using similarity transformation. The transformed ODEs are tackled numerically by employing the Bvp4c scheme. This method contains a three-stage Lobatto IIIa collocation formula that provides continuous solutions up to fourth-order accuracy. Impacts of all physical parameters are illustrated in the form of graphs. The emerging parameters of the surface friction and heat/mass flux coefficients were tabulated. The results showed that the temperature and associated boundary layer thickness decreased with higher heat generation/absorption parameter values. Increasing the radiation parameter improves the temperature of the fluid, and increasing the activation energy parameter improves the thickness of the concentration boundary layer. The results of our research were compared with those of the existing literature and found to be in good agreement.

A steady flow of MHD Maxwell viscoelastic fluid on a flat porous plate with the outcome of radiation and heat generation

Maxwell fluids display viscous flow on a long timescale but exhibit additional elastic resistance during rapid deformations. Among various types of rate-type fluids, the Maxwell fluid has achieved prominence in numerous study fields. This viscoelastic fluid has viscous and elastic properties. Due to their reduced complexity, this Maxwell fluid is utilized used in the polymeric industries. We have established a mathematical model based on the applications. This article examines the mathematical and graphical analysis for steady-state magnetohydrodynamic flow in a horizontal flat plate of Maxwell viscoelastic fluid for a permeable medium with heat and thermal radiation. The non-dimensional and similarity transformation used to frame the partial differential equations with restored ordinary differential equations. The shooting technique is originated to find solutions to nonlinear boundary value problems with the help of MATLAB software via the Runge-Kutta Fehlberg method. The primary idea behind this strategy is to change the boundary conditions of boundary value problems into initial value problems. Several plots illustrate the leading parameters such as Prandtl number (Pr), Deborah number (De), Eckert number (Ec), heat generation (Q), radiation (Rd), Lewis number (Le), magnetic parameter (M), and thermal slip condition (β) on the velocity profile and energy transfer behaviour. We validated our results with published work. The most significant impact of this study is that the Nusselt number drops as the Eckert number rises and climbs when heat radiation increases. The skin friction coefficient increases as Deborah number increases.

Heat and mass transport of MHD viscoelastic fluid flow towards a permeable stretching cylinder

Heat and mass transport of MHD flow of viscoelastic Maxwell fluid due to a stretching cylinder on a porous medium with the impact of curvature parameter, Schmidt number, Deborah number and chemical reaction are investigated. Radiation, MHD, Brownian motion and thermophoresis effects are also considered for modelling. A set of (PDEs) partial differential equations was used to define the mathematical description of the flow. These equations were turned into nonlinear (ODEs) ordinary differential equations via similarity transformations. Since these PDEs are challenging to solve via the analytical method, we compute the solutions using the RK45 technique using inbuilt software bvp4c. This article's critical findings and novelty present the answers for the various physical parameters in two distinct geometries; among them, one represents the cylinder (curvature parameter αc = 1), and other represents the horizontal plate (curvature parameter αc = 0). The Maxwell fluid parameter elevates the temperature and concentration contour for both the plate and cylinder. Further, the velocity of the viscoelastic fluid displays inconsistent behaviour for the Deborah number and curvature parameter. In addition, we compared the acquired numerical result to existing work and discovered that the current numerical results are in remarkable agreement.

Simultaneous features of MHD and radiation effects on the UCM viscoelastic fluid through a porous medium with slip conditions

In this article, we analyzed upper-convected Maxwell (UCM) viscoelastic fluid flow in a permeable medium. Cattaneo–Christov (CC) heat flux theory is utilized for heat transfer phenomena. Impacts of thermal radiation, thermal slip condition and magnetohydrodynamic (MHD) are considered in modeling of the physical phenomena under investigation. The developed equations of fluid flow model are transformed to non-linear ordinary differential equations (ODEs) with some suitable similarity transformations. Numerical solution of ODEs with boundary conditions are investigated and the results are depicted through graphs and analyzed accordingly. From the present results, we concluded that velocity is declining for magnetic parameter; temperature is rising with thermal radiation and magnetic parameters while it shows reducing behavior for thermal slip parameter. Nusselt number observes decreasing behavior for larger values of porosity parameter, magnetic parameter, Deborah number, velocity slip and thermal slip parameters while opposite behavior is seen for radiation and thermal relaxation parameters. Furthermore, the accuracy of the current data was determined by comparing the heat transfer rate for several values of the porosity parameter to previously published results.

Natural convection of a viscoelastic Cattaneo–Christov fluid bounded by thick walls with finite thermal conductivity

Abstract The linear natural convection of a Maxwell viscoelastic fluid with Cattaneo–Christov heat flux constitutive equation, between two thick walls with finite thermal conductivity is investigated. The viscoelastic fluid and the heat flux have different relaxation times. The main interest is on the curves of criticality for different thicknesses ratio D and thermal conductivities ratio X. In the middle range of log X the curves of criticality stabilize depending on the other parameters of the problem. It is revealed that for some Prandtl numbers the curves of criticality remain higher for small X and lower for large X. However, increasing the Prandtl number this behavior is reversed. It is shown that this has important consequences in the order of the criticality curves when the heat flux relaxation time is increased. Depending on the Prandtl number, an increase of this relaxation time may decrease (destabilize) the curves of criticality until a minimum is reached, after which the curves start to increase (stabilize) again. For two different magnitudes of the viscoelastic relaxation time, the critical Rayleigh number, wavenumber and frequency of oscillation are plotted against log X for different magnitudes of D and the heat flux relaxation time.

Transport mechanism under temperature and concentration gradient for nano-sized species in Maxwell viscoelastic fluid over cylindrical object moving with non-uniform velocity

Non-Newtonian fluids have a wide range of engineering applications, which has drawn researchers to study their puzzling rheology as well as the transport of thermal and somatic energy behaviors. The researchers provide a variety of empirical models to describe the behavior of the non-Newtonian fluids because non-Newtonian fluids alter their flow behavior in response to the applied stress. This study considered a two-dimensional transport mechanism in viscoelastic fluid over convectively heated surface moving with non-uniform velocity is modelled via simplified conservation laws by considering temperature and concentration gradients. Axisymmetric PDEs are further transformed into their dimensionless forms under similarity principle. The associated set of models are solved numerically using finite element numerical technique. Convergent mesh free solutions are further utilized in exploring the underlying physics. The significant role of temperature gradient in transporting species observed whereas impact of compositional gradient in transferring the heat energy is investigated. Brownian motion of solid nano-sized structures in viscoelastic non-Newtonian fluid is rheological observed to strongly impact the simultaneous transport of heat and mass. Convectively heated surface is also responsible for thermal enhancement. Convective transport is being accelerated by convectively varying amount of species at the convectively heat surface of cylindrical body.

Spectral relaxation computation of Maxwell fluid flow from a stretching surface with quadratic convection and non-Fourier heat flux using Lie symmetry transformations

A mathematical model for nonlinear quadratic convection with non-Fourier heat flux in coating boundary layer flow of a Maxwell viscoelastic fluid is presented. Nonlinear quadratic thermal radiation and heat source/ sink effects are also considered. The transformations of Lie symmetry are employed. The resultant nonlinear differential equations with defined boundary conditions are numerically solved using the spectral relaxation technique (SRM), a robust computational methodology. Graphical visualization of the velocity and temperature profiles is included for a range of different emerging parameters. For skin friction and the Nusselt number, numerical data are also provided. There is a very strong correlation between the outcomes of this study and those published in the literature. Higher values of the nonlinear thermal radiation, mixed convection, thermal conductivity, nonlinear convection and heat source/ generation parameters increase temperature as well as the thickness of the thermal boundary layer. However, a higher Prandtl number, thermal relaxation parameter and heat sink/ absorption parameter all reduce temperature. Deborah number causes velocity to be raised (and momentum boundary layer thickness to be lowered), whereas raising nonlinear mixed convection parameter causes velocity to be decreased (and momentum boundary layer thickness to be increased), and a velocity overshoot is calculated. The models are applicable to simulations of high-temperature polymeric coatings in material processing.

Numerical analysis of viscoelastic Maxwell fluid flow through a radiative axisymmetric semi‐porous channel

AbstractThe non‐Newtonian fluids have abundant implications in versatile fields of chemical, mechanical, and biological engineering. Furthermore, the non‐Newtonian fluids flowing through the porous medium are very useful in petroleum and industrial engineering. Heat transport analysis with radiation has major appliances in fusion reactors, heat exchangers, solar energy, aircrafts engines, turbine cooling, and many others. Having all these important appliances in view, the present study is focused on the heat transfer analysis of an incompressible two‐dimensional viscoelastic magnetohydrodynamic Maxwell non‐Newtonian liquid flow in a porous space. The magnetic field is uniformly applied tangential to the flow direction and the lower‐channel wall is heated by induction as a consequence of the Lorentz force. The effect of thermal radiation is taken to foresee the physical occurrence of heat kinetics from an applied point of view. Similarity transformation is considered in reducing the governing partial differential equations into ordinary differential equations and a numerical solution is computed using the shooting technique. The results obtained are compared with the published literature. The effects of flow quantities are illustrated graphically and analyzed with physical meaning. In view of engineering applications, the effects of Reynolds on skin friction coefficient and rate of heat transfer are presented.

Unsteady flow of Maxwell viscoelastic fluid near a critical point

Unsteady flow of Maxwell viscoelastic fluid near a critical point

Unsteady Flows of a Maxwell Viscoelastic Fluid near a Critical Point with a Countercurrent at the Initial Moment

Unsteady Flows of a Maxwell Viscoelastic Fluid near a Critical Point with a Countercurrent at the Initial Moment

Effect of temperature on the reverse self-assembly of lecithin and sugar alcohol mixtures in a nonpolar solvent

It has been shown that the addition of sugar alcohols to lecithin solutions induces a transformation from reverse spherical micelles into reverse cylindrical micelles, resulting in the formation of viscoelastic Maxwell fluids. Herein, we systematically investigated the effects of temperature on the rheological parameters, such as the plateau modulus (Gp), relaxation time (tR), and zero-shear viscosity (η0), of lecithin and sugar alcohol mixtures in decane. The rheological properties upon heating of mixtures of lecithin and sugar alcohols with different numbers (3–6) of hydroxyl (–OH) groups and concentrations were studied in detail. Gp, tR, and η0 for all reverse cylindrical micelles decreased with temperature. This decrease can be attributed to a reduction in the lengths of the reverse cylindrical micelles, as evidenced by the small-angle X-ray scattering results at different temperatures. More importantly, the decay rates of Gp, tR, and η0 upon heating decreased more rapidly when the hydrogen bonds between the lecithin and sugar alcohol molecules were weaker as the hydrogen bonds were closely associated with the formation of the reverse self-assembled structure. This indicates that the driving force for the formation of reverse cylindrical micelles can be weakened by increasing the temperature.

Cattaneo–Friedrich and Crank–Nicolson analysis of upper-convected Maxwell fluid along a vertical plate

The concept of fractional derivative is used to solve a variety of viscoelastic fluid problems. However, researchers mostly overlooked the consequences of nonlinear convection in the fractional viscoelastic fluid models and were concerned only with situations where the governing equations are linear. Most importantly, the nonlinear fluid models, whether classical or fractional, are solved for steady-state conditions. To overcome these limitations, this research presents unsteady flow and heat transfer of nonlinear fractional upper-convected Maxwell (UCM) viscoelastic fluid along a vertical plate. The governing equations of the fractional Maxwell fluid are developed by introducing Friedrich shear stress and Cattaneo heat flux models to the classical UCM fluid model. An additional feature to the invention of the constructed fractional model is the consequence of an external magnetic field. Moreover, the considered model comprises nonlinear, coupled, fractional partial differential equations. Therefore, a numerical scheme is developed with the aid of the L1-approximation of Caputo derivative and the Crank–Nicolson method. The effects of different regulating parameters on fluid features have been thoroughly investigated. The obtained results are exhibited graphically and discussed in detail. It is observed that the skin friction increases for the velocity relaxation time parameter, but an opposite behavior is observed against the velocity fractional derivative parameter. Moreover, a significant enhancement is noticed in the Nusselt number for increasing estimates of the Prandtl number.

The Caputo–Fabrizio (CF) and Atangana–Baleanu in Caputo sense (ABC) fractional time‐derivative approach on transient free convection flow between two vertical parallel plates: A semi‐analytical solution

AbstractA comparative analysis on semi‐analytical solution of transient free convection flow of fractional Maxwell viscoelastic fluid between two vertical parallel plates has been investigated by employing the Caputo–Fabrizio (CF) and Atangana–Baleanus in Caputo sense (ABC) fractional time derivative. The semi‐analytical solutions for dimensionless temperature, velocity, skin friction, and mass flux are obtained using both approach (CF and ABC) and solution presented in the Laplace domain. The Riemann sum approximation was used to invert all solutions from the Laplace domain to the time domain. The influence of pertinent parameters on dimensionless temperature and velocity for both CF and ABC approach are presented graphically and in tabular form and thereafter discussed. The significant result obtained from this study is that both temperature and velocity in CF and ABC increase as the time and relaxation time parameter increases, while temperature and velocity via CF and ABC model decrease when the fractional parameter increases. It is also significant to note that, temperature, velocity, skin friction, and mass flux have a higher value in the CF model than the ABC model.

Numerical modeling of fractional viscoelastic non-Newtonian fluids over a backward facing step – Buoyancy driven flow and heat transfer

The unsteady flow and natural convection heat transfer of fractional Maxwell viscoelastic fluid over sudden expansion geometry such as vertical backward facing step is studied. The time–space fractional derivatives are calculated based on Caputo fractional derivative. The nonlinear governing equations are solved using finite difference method mixed with a L-1 algorithm. The step, upstream and downstream walls were set at a constant temperature. The range of step length is 0≤S≤0.5 and dimensionless temperature is 0.25≤θw≤1. The effects of velocity and temperature fractional derivatives (αand β) and various physical parameters, such as step length, dimensionless temperature, on Nusselt number, friction coefficient, profile of velocity and temperature, are investigated numerically. The results reveal that the fractional derivative parameters, the variation of wall temperature and step length have significant effects on the rate of heat transfer, the friction coefficient, the velocity and temperature of backward facing step. The average of Nusselt number variation increases with increasing of β and decreases of α parameters. The results show that the velocity and thermal boundary layer of the non-Newtonian fluid (ordinary Maxwell) is higher than Newtonian fluid. Also, the Nusselt number for the ordinary Maxwell fluid flow is greater than the Newtonian fluid flow. With the increase of the step length of backward facing step, the average Nusselt number, friction coefficient, velocity boundary layer, and temperature boundary layer increases. The obtained results can improve significantly the performance of the systems design that operate with the non-Newtonian fluids.

Effects of Exponential Variable Viscosity on Heat Transfer Flow of MHD Fractional Maxwell Fluid

This research article presents the unsteady natural convection of Maxwell viscoelastic fluid based on boundary layer heat transfer. The stretching sheet on lower wall of fluid with exponential time dependent viscosity is implemented. The fractional derivative based governing equations of Maxwell fluid model are derived. These governing equations are used to derive nonlinear coupled partial differential equations (PDEs) which involves space and time derivatives in convection terms. By employing the Finite Difference Method with L1-algorithm, to solve system of nonlinear coupled PDEs and presented via graphically. The effects of fractional and physical parameters on velocity, temperature and particular fractional parameters effect on average skin friction coefficient $$\bar{Cf}$$ and average Nusselt number $$\bar{Nu}$$ are discussed in details. For instance, the thickness of velocity boundary layer increases in response to increase in fractional parameter $$\alpha $$ , whereas heat conduction reduces in response to increase in fractional parameter $$\gamma $$ .