Viscoelastic Solutions Research Articles

Polymer concentration regimes from fractional microrheology

In this work, a framework for deriving theoretical equations for mean squared displacement (MSD) and fractional Fokker–Planck is developed for any arbitrary rheological model. The obtained general results are then specified for different fractional rheological models. To test the novel equations extracted from our framework and bridge the gap between microrheology and fractional rheological models, microrheology of polystyrene in tetrahydrofuran solutions at several polymer concentrations is measured. By comparing the experimental and theoretical MSDs, we find the fractional rheological parameters and demonstrate for the first time that the polymer concentration regimes can be distinguished using the fractional exponent and relaxation time data because of the existence of a distinct behavior in each regime. We suggest simple approximations for the critical overlap concentration and the shear viscosity of viscoelastic liquidlike solutions. This work provides a more sensitive approach for distinguishing different polymer concentration regimes and measuring the critical overlap concentration and shear viscosity of polymeric solutions, which is useful when conventional rheological characterization methods are unreliable due to the volatility and low viscosity of the samples.

Frequency-domain axisymmetric and thermomechanical viscoelastic analysis of thermoplastic composite pipe

ABSTRACT Thermoplastic composite pipe (TCP), composed of polymers and composite laminates, shows significant potential for deep-water offshore oil field development due to its lightweight and high strength. However, current mechanical studies primarily focus on the elastic domain, ignoring the critical viscoelasticity of non-metallic materials. To solve this, we introduce a comprehensive theoretical model that incorporates viscoelastic properties under both axisymmetric and thermal loads, considering radial convective thermal gradients and axial heat conduction. This model accurately predicts TCP's mechanical behavior by using stiffness coefficients, differential geometry, and radial-axial temperature transfer curves. By applying the principle of elastic-viscoelastic correspondence, we obtain viscoelastic solutions in the frequency domain, showing strong agreement with Finite Element (FE) models particularly under cyclic loading. Viscoelasticity introduces larger equivalent axial stiffness and viscoelastic damping within complex structures, which become more obvious with temperature fluctuations.

Preparation and application of wormlike micelles generated from a rosin-based aggregation-induced emission surfactant through coordinating aggregation

Fluorescent nanomaterials have drawn considerable attentions due to their high fluorescence sensitivity, excellent signal stability and tunable luminescent properties. A bio-based aggregation-induced emission (AIE) surfactant (Sodium 4-(tetraphenylstyrene)maleate, MPA-TPE-Na) was prepared from rosin, which showed typical AIE characteristic, obvious solvatochromism and a large Stokes shift (>100 nm). AIE viscoelastic solutions were further prepared by complexing MPA-TPE-Na and cetyltrimethylammonium bromide (CTAB) through coordinating aggregation and their microstructure, fluorescence properties and viscoelasticities were investigated. The aggregates in the viscoelastic solutions were wormlike micelles. As the concentration of MPA-TPE-Na increased, the fluorescence intensity of the viscoelastic solutions increased, and their viscosity increased at first and then decreased. The fluorescence emission intensity of the viscoelastic solutions was barely affected by the change in pH. But reducing the pH could increase its viscosity. This system can specifically recognize Fe3+ without any organic solvent and has anti-interference ability. The present work provided a bio-based fluorescent nanomaterial and verified the feasibility of preparing aqueous AIE nanomaterials by modifying AIE groups with rosin skeleton.

A Meta-Analytical Way of Systematizing the Use of Hyaluronan Gels for the Relief of Osteoarthritis, Compared with New Treatment Alternatives.

Hyaluronic acid, in the form of a gel or viscoelastic colloidal solution, is currently used for the viscosupplementation of joints affected by osteoarthritis, but its effectiveness is under debate in relation to newer alternatives. Based on meta-analytical arguments, the present article reinforces the opinion that there are still no decisive arguments for its complete replacement but for its use adapted to the peculiarities of the disease manifestation and of the patients. A "broad" comparison is first made with almost all alternatives studied in the last decade, and then a meta-regression study is performed to compare and predict the effect size induced by viscosupplementation therapy and its main challenger of clinical interest, the platelet-rich plasma treatment. If they are computerized, the developed models can represent tools for clinicians in determining the appropriateness of the option or not for viscosupplementation in a manner adapted to the pain felt by the patients, to their age, or to other clinical circumstances. The models were generated using algorithms implemented in the R language and assembled in different R packages. All primary data and necessary R scripts are provided in accordance with the philosophy of reproducible research. Finally, we adhere in a documented way to the opinion that HA-based products, currently under circumspection, are still clinically useful.

Numerical investigation on the enhanced heat transfer characteristics of non-Newtonian viscoelastic fluids in microchannel with chip arrays

Elastic turbulence is an efficient heat transfer method at microscale. In this work, we conduct a systematic investigation on the flow and heat transfer performances of viscoelastic polymer solutions in microchannels with chip arrays by means of high-fidelity numerical simulations. Focusing on the effects of fluid elasticity [i.e. polymer relaxation time (λ)] and flow Reynolds number (Re), we find that the synergistic interplay between inertial and elastic forces is strategically exploited to amplify convection, thereby facilitating an enhanced heat transfer performance. For highly elastic fluid, the Nusselt number (Nu) can be improved by 76.13 % compared to that of less elastic fluid, while the pressure drop is reduced appropriately. In addition, as the fluid elasticity increases, the pressure drop decreases and eventually converges to a constant. In the zone of elastic turbulence, the fluid reinforces the convective heat transfer, which can be ascribe to the deformation of long-chain polymer molecules. Particularly, we consider the effect of temperature-dependent λ on the heat transfer performance. Our results demonstrate that the increased temperature-dependent λ decreases the value of Nu, and the variation between values of variable and constant λ is reduced with increasing Re or λ. Hence, in some cases of large fluid elasticity or high Re, it is possible to safely ignore the impact of temperature-dependent λ with an acceptable accuracy. The present work provides important insights into the enhanced heat transfer via elastic turbulence, which could guide the applications in the field of chip cooling.

The pH dependent structural and viscoelastic behavior of Ovomucin-Complex isolated from egg white under alkaline conditions

Ovomucin-Complex (OVM) is responsible for providing the natural gel-like properties of egg white, especially in alkali-induced egg white gels. In this study, OVM was modified by alkaline to produce gel-type materials. The structure, physicochemical and viscoelastic properties of OVMs under different pH (7–12) were probed using FTIR, HPLC, SEM, CLSM and rheometer. The results of rheological measurements in linear viscoelastic region revealed that alkaline modified OVMs exhibited a soft viscoelastic gel in alkaline conditions, with the transition occurring near pH 8, compared with a viscoelastic solution at neutral pH. In addition to the pH-dependent gelation behavior of OVMs, further rheological studies under nonlinear deformations reveal shear thinning and an apparent yield stress, which were also highly affected by pH. The results from HPLC and molecular interactions suggest that the alkaline modification led to the depolymerization of OVMs in alkaline conditions, enhancing the formation of intermolecular disulfide bonds, electrostatic force and hydrophobic interactions. The differences in these mechanical properties were also reflected in the OVM structure. The SEM and CLSM images demonstrated that the arrangement of gel pores under pH 10 conditions is denser and well-distributed than those under other conditions. The FTIR results verified that alkaline modification leads to the decreased content of β-sheet. Nevertheless, prolonged exposure to pH 12.0 resulted in a gradual liquefaction of the gel due to increased electrostatic repulsion and surface hydrophobicity, as well as the reduced disulfide bond and an increase in the disordered structure. These findings provide a novel insight for the development of mucin gel foods.

A mesh-free framework for high-order simulations of viscoelastic flows in complex geometries

The accurate and stable simulation of viscoelastic flows remains a significant computational challenge, exacerbated for flows in non-trivial and practical geometries. Here we present a new high-order meshless approach with variable resolution for the solution of viscoelastic flows across a range of Weissenberg numbers. Based on the Local Anisotropic Basis Function Method (LABFM) of King et al. (2020), highly accurate viscoelastic flow solutions are found using Oldroyd B and PPT models for a range of two dimensional problems — including Kolmogorov flow, planar Poiseulle flow, and flow in a representative porous media geometry. Convergence rates up to 9th order are shown. Three treatments for the conformation tensor evolution are investigated for use in this new high-order meshless context (direct integration, Cholesky decomposition, and log-conformation), with log-conformation providing consistently stable solutions across test cases, and direct integration yielding better accuracy for simpler unidirectional flows. The final test considers symmetry breaking in the porous media flow at moderate Weissenberg number, as a precursor to a future study of fully 3D high-fidelity simulations of elastic flow instabilities in complex geometries. The results herein demonstrate the potential of a viscoelastic flow solver that is both high-order (for accuracy) and meshless (for straightforward discretisation of non-trivial geometries including variable resolution). In the near-term, extension of this approach to three dimensional solutions promises to yield important insights into a range of viscoelastic flow problems, and especially the fundamental challenge of understanding elastic instabilities in practical settings.

Spreading of a viscoelastic drop on a solid substrate

We study the spreading of Newtonian viscous (aqueous glycerin solution) and viscoelastic (aqueous polymer solution) drops on solid substrates with different wettabilities. For drops of the same zero-shear viscosity, we find in the early stages of spreading that viscoelastic drops (i) spread faster and (ii) their contact radius shows a different power law vs time than Newtonian drops. We argue that the effect of viscoelasticity is only observable for experimental time scales of the order of or larger than the internal relaxation time of the viscoelastic polymer solution. We attribute this behaviour to the shear thinning of the viscoelastic polymer solution. When approaching the contact line, the shear rate increases and the steady-state viscosity of the viscoelastic drop is lower than that of the Newtonian drop. We support our experimental findings with a simple (first-order) perturbation model that qualitatively agrees with our findings.

Investigating Non-Newtonian Fluid Behavior in Hydrocyclones Via Computational Fluid Dynamics

Expert researchers examine complex patterns of pressure, viscosity, and velocity in a CFD study of viscoelastic food inside hydrocyclones to obtain a detailed grasp of particle behavior and fluid dynamics. Velocity profiles show how fluids and particles flow through the hydrocyclone in complex ways, while pressure distributions show where high and low pressure is found, regions that are critical for maximizing separation efficiency. Furthermore, the analysis of viscosity fluctuations clarifies the intricate relationship between fluid rheology and flow dynamics, providing information on how food's viscoelastic characteristics affect particle trajectories and separation efficiency. Utilizing this comprehensive examination, scientists hope to optimize the design and functioning parameters of the hydrocyclones, which will in turn improve the efficacy and efficiency of particle separation procedures in viscoelastic food solutions. This will ultimately lead to improvements in food processing technology and product quality. Researchers look into the impact of geometric elements on flow patterns and separation efficiency in addition to these characteristics, such as hydrocyclone size and inlet configurations. Additionally, they investigate how different operating parameters, such rotational speed and flow rate, affect how well the hydrocyclone handles viscoelastic food items. Through the integration of these complex analyses, researchers hope to create all encompassing models that can precisely forecast and optimize the behavior of viscoelastic food flows inside hydrocyclones, opening the door to improved process control and food sector product quality.

New long tail gemini surfactant in aqueous solution: Self-assembly, rheological properties and responsiveness to hydrocarbon

Gemini surfactants are promising to replace conventional monomeric surfactants in various applications. In this paper, a new gemini surfactant with long unsaturated oleyl tails and bis(hydroxyethyl) ammonium head groups linked by butyl spacer was synthesized. Its critical micelle concentration in salt-free water (12 µM) is much lower than for its monomeric analog (220 µM). Without any additives this surfactant can form viscoelastic solutions with the viscosity of up to 1 kPa·s and elastic modulus of 15 Pa at the conditions, when the viscosity of the single-chained monomeric analog is close to that of pure water. These are one of the highest values reported so far for C18-tailed gemini surfactants without additives. The structure of the gemini surfactant solutions was studied by cryo-TEM and SAXS. Cryo-TEM revealed the presence of closed-looped micelles coexisting with linear wormlike micelles as well as the regular spacing between the micelles arising from strong electrostatic repulsion between them. The SAXS curves were well-fitted by a form-factor of core–shell cylinder, which yielded the radius of the core and the thickness of the shell equal to 1.4 nm each. Addition of n-decane induced the drop of viscosity by 6 orders of magnitude accompanied by the transformation of wormlike micelles into microemulsion droplets with 4.4 nm radius. Such gemini surfactants providing high viscoelasticity to aqueous solution that is responsive to added hydrocarbon are promising for the application in oil recovery as thickeners of fracturing fluids that can be cleaned up without any breakers at the backflow of oil.

Analytical prediction for time-dependent interaction of a circular tunnel excavated in strain-softening rock mass

Viscoelastic plastic solutions for tunnel excavation in strain-softening rock mass and tunnel-rock interaction are proposed based on the Mohr-Coulomb and the Generalized Zhang-Zhu (GZZ) strength criterion considering stress path. The solutions are verified by numerical simulations, results show that the theoretical solutions are close to the simulated data. The evolutions of rock stresses, strains, displacements and support pressure were investigated and the influences of residual strength parameter, support stiffness, support timing, initial support pressure and viscosity coefficient on the rock deformation and the support pressure are discussed by proposed solution. It is found that strain-softening results in large deformation and high support pressure, with stiffer support and a larger viscosity coefficient contributing to even greater support pressure. Ductile support is recommended at the first stage to release the energy and reduce the support pressure by allowing a relatively large deformation. The support pressure, especially the additional support pressure at the second stage will be much smaller if a higher initial support pressure is applied at the first stage. This can not only control the displacement rate of surrounding rock and improve the tunnel stability at the first stage by exerting sufficient support pressure immediately after tunnel excavation, but also greatly reduce the pressure acted on permanent support and improve the structure stability at the second stage. Therefore, to avoid the instability of support structure, ductile support, which could not only deform continuously but also provide sufficient high support pressure, is recommended at the first stage.

Reversal of particle Migration for viscoelastic solution at high solvent viscosity

The imbalance of normal stress around a particle induces its transverse migration in pressure-driven viscoelastic flow, offering possibilities for particle manipulation in microfluidic devices. Theoretical predictions align with experimental evidence of particles migrating towards the center-line of the flow. However, these arguments have been challenged by both experimental and numerical investigations, revealing the potential for a reversal in the direction of migration for viscoelastic shear-thinning fluids. Yet, a significant property of viscoelastic liquids that remains largely unexplored is the ratio of solvent viscosity to the sum of solvent and polymer viscosities, denoted as β. We computed the lift coefficients of a freely flowing cylinder in a bi-dimensional Poiseuille flow with Oldroyd-B constitutive equations. A transition from a negative (center-line migration) to a positive (wall migration) lift coefficient was demonstrated with increasing β values. Analogous to inertial lift, the changes in the sign of the lift coefficient were strongly correlated with abrupt (albeit small) variations in the rotation velocity of the particle. We established a scaling law for the lift coefficient that is proportional, as expected, to the Weissenberg number, but also to the difference in rotation velocity between the viscoelastic and Newtonian cases. If the particle rotates more rapidly than in the Newtonian case, it migrates towards the wall; conversely, if the particle rotates more slowly than in the Newtonian case, it migrates towards the center-line of the channel. Finally, experiments in microfluidic slits confirmed migration towards the wall for viscoelastic fluids with high viscosity ratio.

The strain gradient viscoelasticity full field solutions for Mode-I and Mode-II crack problems

The impacts of size and viscosity become distinctly evident when considering micro- and nano-scale phenomena for advanced materials with micro- and nanostructures. In this study, the mechanical behavior of the advanced material is characterized by using the strain gradient viscoelasticity theory, and a novel solution is presented for the mode-I and mode-II cracks, which is formulated based on the strain gradient viscoelasticity theory, employing the Wiener-Hopf method. Besides, the gradient-dependent viscoelastic crack solutions are directly derived by applying the correspondence principle that aligns strain gradient viscoelasticity with strain gradient elasticity within the Maxwell's standard linear solid model. Relative to the influence of elastic strain gradient effects, the involvement of viscous gradient effects instigates a reinforcement to the stress field around the crack tip, thereby offering a more reasonable representation of advanced materials crack behavior. When the viscosity effect is omitted or as time tends to infinity, the solutions based on strain gradient viscoelasticity theory converges to those on the classical strain gradient elasticity theory.

Ordered mesoporous nanofibers mimicking vascular bundles for lithium metal batteries.

Hierarchical self-assembly with long-range order above centimeters widely exists in nature. Mimicking similar structures to promote reaction kinetics of electrochemical energy devices is of immense interest, yet remains challenging. Here, we report a bottom-up self-assembly approach to constructing ordered mesoporous nanofibers with a structure resembling vascular bundles via electrospinning. The synthesis involves self-assembling polystyrene (PS) homopolymer, amphiphilic diblock copolymer, and precursors into supramolecular micelles. Elongational dynamics of viscoelastic micelle solution together with fast solvent evaporation during electrospinning cause simultaneous close packing and uniaxial stretching of micelles, consequently producing polymer nanofibers consisting of oriented micelles. The method is versatile for the fabrication of large-scale ordered mesoporous nanofibers with adjustable pore diameter and various compositions such as carbon, SiO2, TiO2 and WO3. The aligned longitudinal mesopores connected side-by-side by tiny pores offer highly exposed active sites and expedite electron/ion transport. The assembled electrodes deliver outstanding performance for lithium metal batteries.

Viscoelastic solution of optimal reserved deformation for deep soft rock tunnels with large deformation

In the construction process of soft rock tunnels, determining a reasonable amount of reserved deformation is important to ensure the tunnel stability. This article presents the viscoelastic solution of reserved deformation for deep soft rock tunnels considering the support effects. Based on the analytical solution of the Burgers model, the expression of surrounding rock displacement was derived by considering reserved deformation and optimal reserved deformation. Subsequently, based on numerical simulation experiments, the variation laws and errors of the numerical and analytical solutions of the expressions of reserved deformation and surrounding rock displacement were analyzed. To gain a better understanding of the factors that affect reserved deformation, the factors influencing the expression of optimal reserved deformation were analyzed. The errors in the numerical simulation and analytical solution results were within 10%. This study could provide a theoretical basis for determining the amount of reserved deformation and analyzing the variation law of surrounding rock affected by the amount of reserved deformation.

Cavitation in viscoelastic dilute polymer solutions through a Venturi nozzle

This research experimentally examines the influence of viscoelastic dilute water solutions of polyethylene oxide on Venturi cavitation. Variations in solutions are engineered to manipulate the viscoelastic properties that in turn affect cavitation patterns and attributes. The consequences of viscoelasticity and flow conditions on cavitation are quantified using dimensionless numbers, including the elasticity number (El), the Reynolds number (Re), and the pressure ratio (κ). The experiment identifies three distinct cavitation patterns in the solutions, with their transitions being impacted by alterations in El and κ. As El amplifies, the cavitation bubbles expand and get smoother, and the reentrant jet thickens and amplifies. The behavior of cavitation aligns with the model proposed by Zhang et al. [Phys. Fluids 31, 097107 (2019)], suggesting the critical role of the reentrant jet in the shedding of the cavity cluster. The study also substantiates that the reentrant jet intensifies with ascending El or Re. The collective influence of El, Re, and κ is discovered to shape the cavitation length and shedding frequency of cavity clusters. An increased El or a decreased Re reinforces the vorticity and the reentrant jet, which inevitably leads to a reduction in cavitation lengths and an uptick in the shedding frequency. Conversely, a larger El results in a more gradual response of the bubble to pressure alterations and pronounced rebounds, extending the cavitation length.

APPLICATION OF VISCOELASTIC SYSTEMS IN OIL PRODUCTION INTENSIFICATION PROCESSES

This paper provides an overview of viscoelastic behavior and the use of viscoelastic fluids (VBLs) in various oil production intensification processes. The first part provides basic models describing viscoelastic behavior and corresponding equations of state. Describes the method of testing under the action of harmonic vibrations (method of dynamic tests), possible options for its implementation and the determined rheological properties of the viscoelastic sample. To interpret the results of dynamic tests, a complex module is most often introduced, which consists of two components — the elastic modulus (G’) and the loss modulus (G’’). These dynamic modules and their relationship describe the behavior of the viscoelastic sample. It is shown that with respect to modules, it is possible to conclude on the type of sample - viscoelastic liquid or viscoelastic body. It is also noted that dynamic tests should be carried out in the area of low amplitudes of oscillating loads, in which the rheological properties do not depend on the applied stress or strain. The second part provides examples of viscoelastic systems used in operations such as water flow isolation, hydraulic fracturing, and modified acid treatments. The most common viscoelastic systems used in various technologies are solutions of surfactants and polymers of different structures. It is noted that in order to obtain a viscoelastic gel, polymer solutions are used with a crosslinker, while the rheological properties of surfactant solutions are controlled by external factors — pH, temperature, water mineralization. Viscoelastic surfactant solutions have an advantage over polymer solutions ‑ they are able to recover their properties after mechanical or thermal exposure due to the formation of supramolecular structures as a result of selforganization of surfactant molecules. The surfactant-based HLT property of reversibly collapsing and recovering is used, in particular, to reduce pressure losses to overcome friction. In flow-deflecting acid compositions, viscoelastic surfactants are mainly used, the most common of which are given in the second part of the article.

A Novel Fractional Brownian Dynamics Method for Simulating the Dynamics of Confined Bottle-Brush Polymers in Viscoelastic Solution.

In crowded fluids, polymer segments can exhibit anomalous subdiffusion due to the viscoelasticity of the surrounding environment. Previous single-particle tracking experiments revealed that such anomalous diffusion in complex fluids (e.g., in bacterial cytoplasm) can be described by fractional Brownian motion (fBm). To investigate how the viscoelastic media affects the diffusive behaviors of polymer segments without resolving single crowders, we developed a novel fractional Brownian dynamics method to simulate the dynamics of polymers under confinement. In this work, instead of using Gaussian random numbers ("white Gaussian noise") to model the Brownian force as in the standard Brownian dynamics simulations, we introduce fractional Gaussian noise (fGn) in our homemade fractional Brownian dynamics simulation code to investigate the anomalous diffusion of polymer segments by using a simple "bottle-brush"-type polymer model. The experimental results of the velocity autocorrelation function and the exponent that characterizes the subdiffusion of the confined polymer segments can be reproduced by this simple polymer model in combination with fractional Gaussian noise (fGn), which mimics the viscoelastic media.

Stability of Viscoelastic Solutions: BrijL4 and Sodium Cholate Mixtures with Metal Ions Across a Broad pH and Temperature Range.

The impact of pH, temperature, and metal ions on the rheological and interfacial properties of aqueous mixed surfactant solutions composed of anionic NaC (sodium cholate) and nonionic BrijL4 [polyoxyethylene (4) lauryl ether] surfactants has been investigated. The various compound systems were analyzed, considering variations in each selected factor. The results highlight the unique characteristics of the BrijL4/NaC mixture, suggesting its potential as a viable alternative to other existing surfactants. The synergistic effect between BrijL4 and NaC significantly reduces the critical micelle concentration (CMC) and improves the wetting properties on hydrophobic surfaces, surpassing those of single-component solutions. Additionally, sodium, calcium, and magnesium ions enhance surface wetting and decrease the CMC. Besides, the BrijL4/NaC solutions exhibit viscoelastic fluid behavior at higher surfactant concentrations. These viscoelastic BrijL4/NaC solutions demonstrate stability over various pH and temperature variations, exhibiting lower flow activation and scission energy values than those of other viscoelastic surfactant solutions. Notably, the BrijL4/NaC mixture has potential applications in gel-based foliar fertilizers and drug delivery systems. Furthermore, the rheological studies examine the impact of humic acid on the rheological properties of BrijL4/NaC mixture solutions, revealing that incorporating additional humic acids can achieve stable rheological properties.

Effect of fluid elasticity and shear thinning on heat transfer from a heated sphere at moderate Reynolds numbers

The drag and heat transfer characteristics of an isothermal sphere in a FENE-P-type viscoelastic fluid have been studied in the steady axisymmetric flow regime. The governing equations, namely, mass, momentum, and energy equations, together with FENE-P type viscoelastic constitutive equations, have been solved using the finite volume method based opensource CFD code OpenFOAM over the following ranges of conditions: Reynolds number, 1 ≤ Re ≤ 100 ; Prandtl number, 1 ≤ Pr ≤ 50 ; Weissenberg number, 0 ​ ≤ Wi ≤ 10 and polymer extensibility parameter, 10 ≤ L 2 ≤ 500 for a fixed value of the polymer viscosity ratio of β = 0.5 . At low Reynolds numbers, fluid viscoelasticity causes an upward and downward shifting in the axial velocity profiles with reference to that in a Newtonian fluid along the upstream and downstream axis of the sphere, respectively. However, such a shift progressively diminishes with the increasing Reynolds number. Furthermore, a “velocity overshoot” and/or a “negative wake” is also observed in a viscoelastic polymer solution at low Reynolds numbers, and this is accentuated with the increasing Weissenberg number. The separation of boundary layers is seen to be suppressed with the increasing Weissenberg number. The drag coefficient decreases with the Reynolds number irrespective of the fluid type and the corresponding dependence on the Weissenberg number is found to be non-monotonic depending upon the values of Re and L 2. The average Nusselt number always increases with the increasing values of Re, Pr, and Wi and with the decreasing value of L 2. A limited number of simulations have also been carried out to show the effect of the temperature-dependent viscosity of the fluid on the flow dynamics and heat transfer characteristics. Finally, simple correlations for the drag coefficient and average Nusselt number are presented which not only capture the functional dependence but also can be used for the interpolation of the present results for the intermediate values of the governing parameters in a new application.