Class Of non-Newtonian Fluids Research Articles

Falkner–Skan boundary layer flow of a fluid with pressure-dependent viscosity past a stretching wedge with suction or injection

In this paper we study the boundary layer flow of a particular class of non-Newtonian fluids, namely piezo-viscous fluids, past a stretching wedge (Falkner–Skan flow). These fluids are essentially Navier–Stokes fluids with pressure-dependent viscosity. We consider the two-dimensional steady flow and introduce some similarity variables, so that the problem is reduced to a third-order nonlinear BVP. We solve the problem numerically by means of a shooting procedure combined with Newton’s method, and we find local similarity solutions. We investigate the behaviour of the velocity field, of the drag and of the thickness of the boundary layer for different values of the involved parameters, making a comparison between the piezo-viscous and the Newtonian case. We find that, depending on some material parameters, the effect of pressure is that of reducing or increasing the boundary layer with respect to the Newtonian case.

Impact of Flow, Heat and Mass Transfer of Newtonian and Non-Newtonian Nanofluids Flow over a Non-Darcy Stretching Sheet in the Context of Fuel Applications

The study of flow, heat, and mass transfer of Newtonian and non-Newtonian nanofluid over porous media holds paramount significance in the context of fuel industries, contributing to enhanced efficiency, reduced emissions, and sustainable energy production. This investigation provides a concise overview of the critical role played by porous media in various aspects of the fuel sector. In the oil and gas industry, porous reservoir formations exhibit complex fluid dynamics characterized by non-Darcy flow, influencing recovery rates of hydrocarbons. Understanding the relationship between flow, heat, and mass transfer within these porous reservoirs is essential for reservoir engineers and fuels the quest for maximizing resource extraction. The Sisko nanofluid model is one of the most sought-after mathematical model which prophesies the interesting features of Newtonian and non-Newtonian (dilatant and Pseudoplastic nature) fluids. In contemporary years, a new class of non-Newtonian fluids with nanoparticle suspensions are gaining popularity as it is beneficial in enhancing thermal efficiency in several applications such as warming/cooling of home appliances and micro-electronics etc. However, the modeling on this class of non-Newtonian fluids is limited. In light of above, this work predicts the stream, heat and mass transmission behavior of nanofluids using Sisko fluid model. Stretching sheet with porous medium has been used for this study with addition with magnetic field, thermal radiation, Brownian motion and thermophoresis. The non-linearity issues in this fluid flow are addressed in the prevailing work using suitable similarity transformations. The non-linear dimensional coupled P.D.E are converted into nonlinear dimensionless coupled O.D.E. These equations are solved using MATLAB by implementing four-stage Lobatto IIIa formula. The impacts of copious physical parameters of flow, energy and mass transfer insights are discussed. From the outcomes of current work, it is perceived that increasing the perviousness of the porous medium reduces the fluid mobility. Further, for increased values of Prandtl number the heat transfer coefficient increases ensuing in more heat transfer. Flow, heat, and mass transfer over porous media are integral to fuel industries, influencing resource extraction, energy conversion, and product quality

Analytical approach for micropolar fluid flow in a channel with porous walls

This article aims to analyze and reach new physical achievements in a well-known nonlinear problem of two-dimensional, steady, and steady micropolar fluid flow between two parallel permeable porous walls. Micropolar fluids are considered a class of non-Newtonian fluids. The nonlinear governing equations of this problem were analyzed using two analytical methods. The achievements and novelty of this article, apart from showing the application of two mathematical methods in solving non-linear equations, are more about achieving new results that are obtained from solving the governing equations of this article. From the results, it is obvious that with the raise of the coupling parameter, other dimensionless parameters increase, except for the dimensionless microrotation. Also, when the spin gradient viscosity parameter increases, all the average values of the mentioned dimensionless parameters increase. From the problem's solution, it is clear that when the micro-inertia density ratio increases across the channel, all the average values of the dimensionless parameters decrease except for the dimensionless flow function characteristics. Also, when the Peclet number for the heat diffusion parameter is changed, it only affects the dimensionless temperature profile. When the Peclet number for the mass diffusion parameter is changed, it only affects the dimensionless concentration profile.

Physics-Informed Neural Networks for Bingham Fluid Flow Simulation Coupled with an Augmented Lagrange Method

As a class of non-Newtonian fluids with yield stresses, Bingham fluids possess both solid and liquid phases separated by implicitly defined non-physical yield surfaces, which makes the standard numerical discretization challenging. The variational reformulation established by Duvaut and Lions, coupled with an augmented Lagrange method (ALM), brings about a finite element approach, whereas the inevitable local mesh refinement and preconditioning of the resulting large-scaled ill-conditioned linear system can be involved. Inspired by the mesh-free feature and architecture flexibility of physics-informed neural networks (PINNs), an ALM-PINN approach to steady-state Bingham fluid flow simulation, with dynamically adaptable weights, is developed and analyzed in this work. The PINN setting enables not only a pointwise ALM formulation but also the learning of families of (physical) parameter-dependent numerical solutions through one training process, and the incorporation of ALM into a PINN induces a more feasible loss function for deep learning. Numerical results obtained via the ALM-PINN training on one- and two-dimensional benchmark models are presented to validate the proposed scheme. The efficacy and limitations of the relevant loss formulation and optimization algorithms are also discussed to motivate some directions for future research.

Viscoplastic corner eddies

When viscous fluid in a corner is disturbed, eddies can form in the absence of inertia. Examples of flow configurations in which this motion occurs include flow through an abrupt contraction and over a cavity. Six decades ago, Moffatt (J. Fluid Mech., vol. 18, 1964, pp. 1–18) calculated the slow viscous flow of Newtonian fluids in sharp corners, detailing his eponymous ‘Moffatt eddies’. In this study we examine corner flows of viscoplastic materials, a class of non-Newtonian fluids which exhibit solid-like behaviour for stresses below a yield stress. Specifically, we consider a Bingham fluid, for which the material is perfectly rigid at stresses below the yield stress. While a static unyielded plug forms at the tip of the corner, eddies analogous to those found by Moffatt can also form. We examine these viscoplastic eddies numerically, by computing finite element solutions using the augmented-Lagrangian method, and analytically, by employing a viscoplastic boundary layer formulation and scaling arguments. We measure the depth of the static plug as a function of the Bingham number (dimensionless yield stress), show that the process of a new eddy forming as the Bingham number is decreased is driven by the pressure in the yielded fluid adjacent to the static plug, and provide a heuristic argument for the critical Bingham number at which this occurs.

Unsteady non-Newtonian fluid flow with heat transfer and Tresca\u2019s friction boundary conditions

We consider an unsteady non-isothermal flow problem for a general class of non-Newtonian fluids. More precisely the stress tensor follows a power law of parameter p, namely sigma = 2 mu ( theta , upsilon , | D(upsilon ) |) |D( upsilon ) |^{p-2} D(upsilon ) - pi mathrm{Id} where θ is the temperature, π is the pressure, υ is the velocity, and D(upsilon ) is the strain rate tensor of the fluid. The problem is then described by a non-stationary p-Laplacian Stokes system coupled to an L^{1}-parabolic equation describing thermal effects in the fluid. We also assume that the velocity field satisfies non-standard threshold slip-adhesion boundary conditions reminiscent of Tresca’s friction law for solids. First, we consider an approximate problem (P_{delta }), where the L^{1} coupling term in the heat equation is replaced by a bounded one depending on a small parameter 0 < delta ll 1, and we establish the existence of a solution to (P_{delta }) by using a fixed point technique. Then we prove the convergence of the approximate solutions to a solution to our original fluid flow/heat transfer problem as δ tends to zero.

Investigation of the structural viscosity of oil films on the friction surface with fullerene compositions

The paper presents theoretical studies of changes in the structural viscosity of oil films on the friction surface with fullerene compositions in the field of action of electrostatic forces of the friction surface and the base lubricant. A feature of the use of fullerene additives in lubricants is that fullerenes are readily soluble in a wide class of organic and inorganic solvents. At the same time, poor solubility of fullerenes in technical oils (mineral, semi-synthetic and synthetic). The purpose of this work is to carry out theoretical studies of changes in the structural viscosity of oil films on the friction surface with fullerene compositions in the field of action of electrostatic forces of the friction surface and the base lubricant. On the basis of the working hypothesis, it was theoretically established that for a thin oil film, located in the field of action of electrostatic forces of the friction surface, it is necessary to consider the structural dynamic viscosity of the lubricant, which at the friction surface has a gel structure, and as the electrostatic forces from the friction surface decrease, the gel structure transforms into the sol structure. It is shown that the value of the structural viscosity of the considered aggregates is comparable with the viscosity of polymers or bitumen. Moreover, the viscosity of the gel structure is four orders of magnitude higher than the viscosity of the sol structure. An increase in the concentration of fullerenes leads to an increase in the dynamic viscosity of aggregates. It is theoretically shown that the structure of the oil film, which corresponds to the structure of the gel, belongs to the class of non-Newtonian fluids. With an increase in the sliding speed, the dynamic viscosity of such structures decreases by a factor of 4, which explains the destruction of micelle clusters and the appearance of rotational motions of elastic flocks. It is assumed that this will lead to a decrease in the value of the coefficient of friction. It is shown that for the gel structure, the concentration of fullerenes in the bulk of the base lubricant does not have a large effect on the structural viscosity. Conversely, for the structure of a sol, the concentration of fullerenes has a significant effect on the value of the structural dynamic viscosity.

The use of a general convected time derivative to compute the Reynolds stress tensor for a compressible turbulent flow

This paper deals with the turbulence closure problem associated with the Reynolds-averaged Navier–Stokes equations for compressible flows. Due to the known limitations faced by the turbulent closure model based on the Boussinesq hypothesis, additional tensors are needed in order to capture the complete Reynolds stress tensor. Models such as this are in the group of the so-called nonlinear eddy viscosity models. The methodology here presented consists mainly in translating the coefficients obtained via orthogonal projection of the Reynolds stresses that are calculated from a large eddy simulation onto a given basis of tensors. In addition, these coefficients can be seen as turbulent parameters which have analogous interpretation in a class of non-Newtonian fluids. The proposed closure, expressed in terms of the mean strain-rate and its Gordon–Schowalter convected derivative, has a concise and clear physical interpretation. In addition to the turbulent viscosity, parameters associated with the Gordon–Schowalter convected derivative are incorporated to help the interpretation of the nonlinear turbulent model. The methodology is applied to a compressible flow through a narrow channel with a series of holes of cylindrical shape. This configuration is representative of what is generally found in a Hole-Pattern turbomachinery seal. Different number of holes are tested in order to evaluate the influence of neighborhood holes in the analysis. The comparison between the Boussinesq hypothesis and the extended model shows how the latter one outperforms the former. Even though the nonlinear model has shown some limitations, there are still tensorial subspaces of the Reynolds stress tensor obtained from the LES approach that the present nonlinear model could not reach. In addition, the physical coefficients did not present strong similarities for the different configurations tested, what can be a challenge for constructing a complete closure model.

Flow of a new class of non-Newtonian fluids in tubes of non-circular cross-sections.

Fluids described by constitutive relations wherein the symmetric part of the velocity gradient is a function of the stress can be used to describe the flows of colloids and suspensions. In this paper, we consider the flow of a fluid obeying such a constitutive relation in a tube of elliptic and other non-circular cross-sections with the view towards determining the velocity field and the stresses that are generated at the boundary of the tube. As tubes are rarely perfectly circular, it is worthwhile to study the structure of the velocity field and the stresses in tubes of non-circular cross-section. After first proving that purely axial flows are possible, that is, there are no secondary flows as in the case of many viscoelastic fluids, we determine the velocity profile and the shear stresses at the boundaries. We find that the maximum shear stress is attained at the co-vertex of the ellipse. In general tubes of non-circular cross-section, the maximum shear stress occurs at the point on the boundary that is closest to the centroid of the cross-section. This article is part of the theme issue 'Rivlin's legacy in continuum mechanics and applied mathematics'.

Interior regularity to the steady incompressible shear thinning fluids with non-Standard growth

We consider weak solutions to the equations of stationary motion of a class of non-Newtonian fluids which includes the power law model. The power depends on the spatial variable, which is motivated by electrorheological fluids. We prove the existence of second order derivatives of weak solutions in the shear thinning cases.

Partial regularity of a certain class of non-Newtonian fluids

We study the partial regularity of weak solution to a certain class of non-Newtonian fluids (1.1)–(1.3), the existence of weak solution to such system had been provided by D. Pierre and H. Norbert in [40]. In particular, we prove that the regularity point in QT is an open set with full measure, and we obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In this paper we confined ourselves to considered the case p=2 and space dimension d=2.

Unique solvability for a class of non-Newtonian fluids for a reacting mixture with vacuum

In this paper,we consider a class of non-Newtonian fluids for a reacting mixture in one-dimensional bounded interval, provided the initial data satisfying a compatibility condition. The main ingredient is that we allow the initial density vacuum.

Similarity treatment for MHD free convective boundary layer flow of a class of non-Newtonian fluids

Deductive group symmetry treatment is applied to derive the similarity transformations for the free convective boundary layer flow of a class of non-Newtonian fluids past over a two-dimensional surface and flowing under the influence of transverse magnetic field. Numerical solutions are obtained for particular Non-Newtonian fluid model namely Prandtl Eyring fluid, in a graphical form . The important physical quantities like velocity distribution, skin friction coefficient and temperature variations are discussed.

MATHEMATICAL ANALYSIS OF A ONE-DIMENSIONAL MODEL FOR AN AGING FLUID

We study mathematically a system of partial differential equations arising in the modeling of an aging fluid, a particular class of non-Newtonian fluids. We prove well-posedness of the equations in appropriate functional spaces and investigate the longtime behavior of the solutions.

Finite Velocity of the Propagation of Perturbations for a Class of Non-Newtonian Fluids

In this paper, we consider the initial boundary value problem of a class of non-Newtonian fluids. We obtain that finite velocity of the propagation of perturbations.

Global Existence and Uniqueness of Solution for a Class of Non-Newtonian Fluids

In this paper, we consider a class of non-Newtonian fluids in one-dimen- sional bounded interval. The global existence and uniqueness of solution are investi- gated.

On the Generalized Brinkman Number Definition and Its Importance for Bingham Fluids

In this technical note we discuss the importance of using a generalized Brinkman number definition for laminar pipe flow of a Bingham fluid, when viscous dissipation effects are relevant. We show that adapting the Brinkman number definition commonly used for Newtonian fluids directly to the more general class of non-Newtonian fluids does not calculate correctly the ratio between heat generated by viscous dissipation and heat transfer at the wall and leads to a distortion of the graphical representation of the Nusselt number, Nu, rendering difficult, if not impossible, the comparisons of the Nu behavior between different Brinkman numbers. The use of the proposed generalized Brinkman number removes these problems and simultaneously it has the merit of being independent of any reference apparent viscosities.

Global well-posedness of viscoelastic fluids of Oldroyd type in Besov spaces

We investigate a system of equations concerning an incompressible viscoelastic fluid of the Oldroyd type which describes one class of non-Newtonian fluid with memory. Making use of a regularization method in conjunction with Bony’s paraproduct decomposition, we obtain the existence and uniqueness of a small global solution for the above system in the Besov spaces B 2 , ∞ s with s > d 2 , and which implies global well-posedness for small data in H s with s > d 2 , since the Sobolev space H s is embedded in B 2 , ∞ s .

Group classification of three-dimensional boundary layer equations of a class of non-Newtonian fluids

Group classification of three-dimensional boundary layer equations of a class of non-Newtonian fluids in which thee stress is an arbitrary function of rates of strain is made. Group classification of the equations with respect to shear stress is done by using equivalence transformations. Special cases such as arbitrary stress, Newtonian fluids and power-law fluids are treated.

Group classification of unsteady boundary layer equations of a class of non-Newtonian fluids

Two dimensional unsteady boundary layer equations of a general model of non-Newtonian fluids were investigated in this study. In this model, the shear stress is taken as an arbitrary function of the velocity gradient. Group classification of the equations with respect to shear stress is done using two different approaches: (1) classical theory (2) equivalence transformations. Both approaches yield identical results. It is found that the principle Lie Algebra extends only for cases of Newtonian and Power-Law flows.