non-Newtonian Viscoelastic Fluid Research Articles

Numerical investigation of MHD free convection flow of a non-Newtonian fluid past an impulsively started vertical plate in the presence of thermal diffusion and radiation absorption

A numerical investigation is carried out on an unsteady MHD free convection flow of a well-known non-Newtonian visco elastic second order Rivlin-Erickson fluid past an impulsively started semi-infinite vertical plate in the presence of homogeneous chemical reaction, thermal radiation, thermal diffusion, radiation absorption and heat absorption with constant mass flux. The presence of viscous dissipation is also considered at the plate under the influence of uniform transverse magnetic field. The flow is governed by a coupled nonlinear system of partial differential equations which are solved numerically by using finite difference method. The effects of various physical parameters on the flow quantities viz. velocity, temperature, concentration, Skin friction, Nusselt number and Sherwood number are studied numerically. The results are discussed with the help of graphs. We observed that the velocity decreases with an increase in magnetic field parameter, Schmidt number, and Prandtl number while it increases with an increase in Grashof number, modified Grashof number, visco-elastic parameter and Soret number. Temperature increases with an increase in radiation absorption parameter, Eckert number and visco-elastic parameter while it decreases with increasing values of radiation parameter, Prandtl number and heat absorption parameter. Concentration increases with increase in Soret number while it decreases with an increase in Schmidt number and chemical reaction parameter.

Modeling the Viscoelastic Behavior of Amorphous Shape Memory Polymers at an Elevated Temperature

Shape memory polymers (SMPs) are soft active materials, their special property is the ability to hold a temporary shape and when exposed to a suitable trigger, they come back to their original shape. These external stimuli can be temperature, light or electro-magnetic fields. Amorphous SMPs are a class of thermally-activated SMPs that rely on glass transition to retain their temporary shape. Above the glass transition temperature (T > Tg), (amorphous SMPs exhibit finite deformation and viscoelastic behavior. In this work we develop a model to capture the viscoelastic behavior of the amorphous SMPs at elevated temperatures. The model uses an approach that was initially developed to study non-Newtonian viscoelastic fluids. We accomplish this by developing a multi-branch model based on the theory of multiple natural configurations using the maximization of the rate dissipation to determine the evolution of the natural configurations. We apply our model to study several different deformations at an elevated temperature T = 130 °C and show that this approach is able to capture the viscoelastic behavior of these polymers. The predictions of the theory are then compared with experimental results.

Electro-osmotically driven MHD flow and heat transfer in micro-channel

A theoretical analysis is presented for electro-osmotic flow (EOF) of blood in a hydrophobic micro-channel with externally applied magnetic field. The lumen of micro-channels is assumed to be porous medium in addition to the consideration of permeability of the channel walls. The effects of slip velocity and thermal-slip are taken into consideration. The governing equations in the electrical double layer (EDL) together with the Poisson–Boltzmann equation and the body force exerted by the applied potential are furthermore considered. The flow is governed by the non-Newtonian viscoelastic fluid model. These equations along with the thermal energy equation are approximated by assuming that the channel height is much greater than the thickness of electrical double layer consisting the stern and diffusive layers. The problem is solved analytically and the computed results have presented graphically for various values of the dimensionless parameters. The results presented here have significant impact on the therapeutic treatment in hyperthermia as well as in controlling blood flow and heat transfer in micro-channels.

Analysis of boundary layer in MHD flow of non-Newtonian visco-elastic fluid on stretching sheet

This article aims to the study of fluid flow and heat transfer in non-Newtonian viscoelastic fluid magnetic hydrodynamics steady laminar flow is expanded on a horizontal plane. Among the many processes in chemical engineering, metallurgy, polymer extrusion process involves cooling the molten liquid is drawn into the cooling system, the production of paper and glass. In this process, the rate of cooling and shrinking influences very much on the final quality of the product. Equations for fluid flow and heat transfer analysis solutions are helping homotopy analysis. In this regard and in order to validate the results of the homotopy analysis, we are comparing the results of this study and other researchers published the results will be accepted. Also, the influence of various parameters on curves, speed and temperature have been investigated.

Unified derivation of thin-layer reduced models for shallow free-surface gravity flows of viscous fluids

We propose a unified framework to derive thin-layer reduced models for some shallow free-surface flows driven by gravity. It applies to incompressible homogeneous fluids whose momentum evolves according to Navier–Stokes equations, with stress satisfying a rheology of viscous type (i.e. the standard Newtonian law with a constant viscosity, but also non-Newtonian laws generalized to purely viscous fluids and to viscoelastic fluids as well). For a given rheology, we derive various thin-layer reduced models for flows on a rugous topography slowly varying around an inclined plane. This is achieved thanks to a coherent simplification procedure, which is formal but based on a mathematically clear consistency requirement between scaling assumptions and the approximation errors in the differential equations. The various thin-layer reduced models are obtained depending on flow regime assumptions (either fast/inertial or slow/viscous). As far as we know, it is the first time that the various thin-layer reduced models investigated here are derived within the same mathematical framework. Furthermore, we obtain new reduced models in the case of viscoelastic non-Newtonian fluids, which extends Bouchut and Boyaval (2013).

Convective Heat Transfer and MHD Viscoelastic Nanofluid Flow Induced by a Stretching Sheet

In this paper we have investigated the viscoelastic nano-fluid flow and heat transfer over a stretching sheet in the presence of magnetic field. The effects of Brownian motion and thermophoresis are taken into account. The flow is governed by the viscoelastic non-Newtonian fluid obeying Walter’s liquid $$B'$$ fluid model. The combined effects of stratifications (thermal and concentration) in the mixed convective flow past over a stretching surface is analyzed. The non-linear boundary layer equations together with the boundary conditions are reduced to a system of coupled non-linear ordinary differential equations by using the similarity transformations. The transformed equations are solved numerically by developing a finite difference scheme along with the Newton’s linearization technique. The study shows that the thermal boundary layer thickness appreciably increases with the increasing effects of Brownian motion, thermophoresis and magnetic field strength. However, the viscoelasticity of the nanofluid has reducing effect on thermal boundary layer thickness.

Investigation of heat transfer for cooling turbine disks with a non-Newtonian fluid flow using DRA

A non-Newtonian viscoelastic fluid flow passes through the porous wall of an axisymmetric channel on a turbine disc for cooling application. The present article solves the couple equations (momentum and heat transfer) of a non-Newtonian fluid flow in an axisymmetric channel with a porous wall for turbine cooling applications by using the Duan–Rach Approach (DRA). The precious achievement of the present work is introducing a new and efficient approximate analytical technique that this method allows us to find a solution without using numerical methods to evaluate the undetermined coefficients. The approximate analytical investigation is carried out for different values of the embedding parameters namely: Reynolds number, Prandtl number, injection Reynolds number and power law index. The DRA results indicate that Nusselt number has direct relationship with Reynolds number, Prandtl number and power law index. Also the results were compared with numerical solution in order to verify the accuracy of the proposed method. It is seen that the current results in comparison with the numerical ones are in excellent agreement.

A Review of Computational Hemodynamics in Middle Cerebral Aneurysms and Rheological Models for Blood Flow

Cerebrovascular accidents are the third most common cause of death in developed countries. Over recent years, CFD simulations using medical image-based anatomical vascular geometries have been shown to have great potential as a tool for diagnostic and treatment of brain aneurysms, in particular to help advise on the best treatment options. This work aims to present a state of the art review of the different models used in CFD, focusing in particular on modeling blood as a viscoelastic non-Newtonian fluid in order to help understand the role of the complex rheological nature of blood upon the dynamics of middle cerebral aneurysms. Moreover, since the mechanical properties of the vessel walls also play an important role in the cardiovascular system, different models for the arterial structure are reviewed in order to couple CFD and computational solid dynamics to allow the study of the fluid–structure interaction (FSI).

MHD mixed convection stagnation-point flow of a viscoelastic fluid towards a stretching sheet in a porous medium with heat generation and radiation

An analysis was carried out to study the effect of thermal radiation on magnetohydrodynamic boundary layer flow and heat transfer characteristics of a non-Newtonian viscoelastic fluid near the stagnation point of a vertical stretching sheet in a porous medium with internal heat generation–absorption. The flow is generated because of linear stretching of the sheet and influenced by the uniform magnetic field that is applied horizontally in the flow region. Using a similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically using an accurate implicit finite difference scheme. A comparison of the obtained results with previously published numerical results is done and the results are found to be in good agreement. The effects of the viscoelastic fluid parameter, magnetic field parameter, nonuniform heat source–sink, and the thermal radiation parameter on the heat transfer characteristics are presented graphically and discussed. The values of the skin friction coefficient and the local Nusselt number are tabulated for both cases of assisting and opposing flows.

In an attempt to generalize wall slip in fluid flows using a series expansion of the wall shear stress: Case of non-Newtonian [Phan–Thien–Tanner fluid

In this paper, we address a new wall slip formulation based on a series expansion of both differential and exponential forms of wall shear stress. As this is initially considered as an infinite series, we use a truncated version of it to get a slip law having three slip coefficients, where we have considered the exponential form only. We use our new truncated triple-slip-coefficients wall slip law to analyze a particular class of viscoelastic non-Newtonian fluid. This special case follows the Phan–Thien–Tanner fluid model. Moreover, for this fluid, we identify Weissenberg number as one salient parameter affecting slip. In particular, our new model is tested on a familiar planar Couette and planar Poiseuille flow problem, where two parallel and infinitely long plates have been used. Furthermore, slip-dependent analytical expressions for field quantities such as velocity and shear stress at the walls and beyond, are derived and numerically analyzed for both problems. In addition, the pressure and flow-rate are derived for various slip coefficients for Poiseuille flow case.Our results obtained prove reasonable as represented by physically realistic plots herein. This feasibility is especially dictated by the velocity profile across channel width for both application problems. Thus, we can infer from all these, that this new model has the potential of providing results which can match experimental data, that is, if the three slip-coefficients are properly chosen.

An improved particle method for simulation of the non-isothermal viscoelastic fluid mold filling process

A non-isothermal molding filling process for a non-Newtonian viscoelastic fluid is investigated in this work. An extended smoothed particle hydrodynamics with diffusive term and kernel gradient correction (extended SPH_DTKGC) method is first presented to simulate the non-isothermal molding filling for the viscoelastic fluid based on the coupled eXtended Pom-Pom (XPP) and thermal power-law model. Meanwhile, a suitable discrete temperature scheme in the SPH frame is proposed. And a new way to treat the zig-zag boundary is given and expected to deal with arbitrary shaped rigid wall. Subsequently, the merits of the proposed boundary treatment are demonstrated by a spin-down problem and the filling process in a C-shaped mould. The ability of the extended SPH_DTKGC to simulate the viscoelastic free surface flow is verified by the several classical problems. Two benchmark problems are presented to display the reliability of the proposed temperature scheme. The non-isothermal filling process for a power-law fluid is performed to show the feasibility of the extended SPH_DTKGC to simulate the non-isothermal mold filling process. Then the extended SPH_DTKGC method combined with other improvements is applied to the non-isothermal filling processes based on the coupled XPP and power-law model. Especially, the influences of the parameters of the XPP model on the physical quantities, such as the first normal stress difference and the temperature field, are numerically predicted.

On the global existence for a regularized model of viscoelastic non-Newtonian fluid

We study the generalized Oldroyd model with viscosity depending on the shear stress behaving like $\mu (\mathbf {D}) \sim | \mathbf {D} |^{p-2}$ ($p>{6/5}$), regularized by a nonlinear stress diffusion. Using the Lipschitz truncation method we prove glob

Analysis of Viscoelastic Fluid Flow over a Suddenly Moved Flat Plat

The velocity field and the associated tangential tension corresponding to the flow of the viscoelastic fluid over an infinite rigid plate are determined in this paper. The characteristic of the non-Newtonian viscoelastic fluid flow is analyzed using the Stehfest method of the numerical inversion of Laplace transform. It indicates that the flow of the viscoelastic fluid is very sensitive to the material constants. Finally, some comparative diagrams concerning the velocity and tangential tension profiles are presented.

Unsteady Couette Flow of a Thermally Conducting Viscoelastic Fluid under Constant Pressure Gradient in a Porous Medium

Unsteady Couette flow through a porous medium of an incompressible non-Newtonian viscoelastic fluid between two parallel horizontal porous plates is studied. A constant pressure gradient in the axial direction and a uniform suction and injection normal to the surface of the plates are applied. The two plates are kept at different but constant temperatures, heat transfer through the conducting fluid is considered, and viscous dissipation is not neglected. Numerical solutions for the governing momentum and energy equations are obtained using the finite difference method. The results show that the porosity of the medium and the departure from the Newtonian characteristics of the fluid to viscoelasticity result in a drop in the velocity of flow and a drop in temperature and change the transient duration. The suction and injection reduce both the velocity and temperature at the middle plane.

Unsteady boundary-layer flow over jerked plate moving in a free stream of viscoelastic fluid.

This study aims to investigate the unsteady boundary-layer flow of a viscoelastic non-Newtonian fluid over a flat surface. The plate is suddenly jerked to move with uniform velocity in a uniform stream of non-Newtonian fluid. Purely analytic solution to governing nonlinear equation is obtained. The solution is highly accurate and valid for all values of the dimensionless time 0 ≤ τ < ∞. Flow properties of the viscoelastic fluid are discussed through graphs.

Rheological characterisation of modified binders at mixing and compaction temperature

The mixing temperature for binders is normally chosen by the pavement engineer based on a specific ‘viscosity’ required during hot mix asphalt production. Majority of the unmodified binders exhibit Newtonian behaviour at the mixing temperature and hence the determination of the same is straight-forward. However, when modified binders are used, experiments using a rotational viscometer indicate that the binder exhibits viscoelastic non-Newtonian fluid characteristic even at very high temperature. Consequently, the ‘viscosity’ varies with time and the location where it is measured, and hence is not a unique property of the material. In this work, a thermodynamically consistent, frame-invariant viscoelastic non-Newtonian fluid model was developed to characterise the rheological properties of the binders tested in a rotational viscometer. In the investigation reported here, two types of modified binders, polymer and crumb rubber, and one unmodified binder were used. These binders were subjected to steady and variable shear rate experiments in a rotational viscometer. The viscoelastic non-Newtonian model developed was able to predict reasonably the response of binders subjected to various protocols. In addition, bituminous mixtures were fabricated at different mixing and compaction temperatures using these binders, and the evolution of volumetric properties was investigated. The experimental investigation on mixtures showed that for identical aggregate gradation, the apparent viscosity of the binders played a critical role on the final volumetric properties obtained.

Minimal model for zero-inertia instabilities in shear-dominated non-Newtonian flows

The emergence of fluid instabilities in the relevant limit of vanishing fluid inertia (i.e., arbitrarily close to zero Reynolds number) has been investigated for the well-known Kolmogorov flow. The finite-time shear-induced order-disorder transition of the non-Newtonian microstructure and the corresponding viscosity change from lower to higher values are the crucial ingredients for the instabilities to emerge. The finite-time low-to-high viscosity change for increasing shear characterizes the rheopectic fluids. The instability does not emerge in shear-thinning or -thickening fluids where viscosity adjustment to local shear occurs instantaneously. The lack of instabilities arbitrarily close to zero Reynolds number is also observed for thixotropic fluids, in spite of the fact that the viscosity adjustment time to shear is finite as in rheopectic fluids. Renormalized perturbative expansions (multiple-scale expansions), energy-based arguments (on the linearized equations of motion), and numerical results (of suitable eigenvalue problems from the linear stability analysis) are the main tools leading to our conclusions. Our findings may have important consequences in all situations where purely hydrodynamic fluid instabilities or mixing are inhibited due to negligible inertia, as in microfluidic applications. To trigger mixing in these situations, suitable (not necessarily viscoelastic) non-Newtonian fluid solutions appear as a valid answer. Our results open interesting questions and challenges in the field of smart (fluid) materials.

Transient Generalized Couette Flow of Viscoelastic Fluid Through a Porous Medium with Variable Viscosity and Pressure Gradient

The transient generalized Couette flow through a porous medium of a non-Newtonian viscoelastic fluid between two parallel porous plates is studied with heat transfer. A uniform suction from above and injection from below are applied perpendicular to the plates which are maintained at two fixed, but different, temperatures while the viscosity of the fluid is assumed to vary exponentially with temperature. The fluid is driven by a uniform horizontal exponential decaying pressure gradient. The coupled set of equations of motion and the energy equation is solved numerically using finite differences. The influence of the different physical parameters of the model on the velocity and temperature fields is investigated and presented.

Physiological flow of shear-thinning viscoelastic fluid past an irregular arterial constriction

The present investigation deals with the effect of the shape of a stenosis on the flow characteristics of blood, having shear-thinning viscoelastic rheological properties by using a suitable mathematical model. Keeping the relevance of the physiological situation, the mathematical model is developed by treating blood as a non-Newtonian shear-thinning viscoelastic fluid characterised by unsteady Oldroyd-3-constant model through an axisymmetric irregular arterial stenosis obtained from casting of a mildly stenosed artery (cf. Back et al., 1984). Comparison with the well-known cosine-shaped stenosis, in order to estimate the effect of surface roughness on the flow characteristics of blood, has however not been ruled out from the present study. Numerical illustrations are presented for a physiological flow, as well as for an equivalent simple pulsatile flow with equal stroke volume to that of the physiological flow, and the differences in their flow behaviour are recorded and discussed. The Marker and Cell method is developed in cylindrical co-ordinate system in order to tackle the highly nonlinear governing equations of motion. The effects of the quantities of significance such as Reynolds number, Deborah number, blood viscoelasticity and flow pulsatility, as well on the velocity components, pressure drop, wall shear stress and patterns of streamlines are quantitatively investigated graphically. Comparison of the results reveals that although the behaviour of two different pulses are similar at the same instant of time, there exist some important deviations in the flow pattern, pressure drop and wall shear stress as well. The present results also predict that the excess pressure drop across the cosine stenosis compared with the irregular one is consistent with several existing results in the literature which substantiate sufficiently to validate the applicability of the model under consideration.

Spectral analysis of turbulent viscoelastic and Newtonian channel flows

The one-dimensional spectra in the streamwise direction of the velocity and vorticity fields in turbulent channel flows of Newtonian and non-Newtonian viscoelastic fluids are presented for friction Reynolds numbers up to Reτ0=1000.The most striking feature induced by viscoelasticity is a marked drop, as rapid as k−5, in the energy level of the streamwise velocity spectra at high wave-numbers, and in agreement with experimental data by Warholic et al. (1999) [15]. The scaling of the streamwise velocity spectra for viscoelastic flow share some characteristics with the Newtonian spectra, but also exhibit unique properties. In particular, the logarithmic correction to the usual k−1 law at the intermediate scales (eddies with size one to ten times the distance from the wall), found by del Álamo et al. (2004) [7] in the case of Newtonian turbulence, still holds in viscoelastic flows; although, with different scaling coefficients. In contrast, the longest modes of the spectra of the streamwise velocity component are found to behave differently. These modes are longer in viscoelastic flows and their scaling with the channel centerline velocity, here confirmed for Newtonian flow, fails for high drag reduction viscoelastic turbulent flows.As for vorticity, it is found that the spectra of its cross-flow component in viscoelastic flows exhibit a significantly higher energy level at large scales, with a tendency towards a k−1 law for high drag reduction and high Reynolds number.