Effects Of non-Newtonian Parameters Research Articles

Study of the secondary droplet breakup mechanism and regime map of Newtonian and power law fluids at high liquid–gas density ratio

This work reports the numerical investigation of the secondary breakup of non-Newtonian droplets at different Weber Weg and Ohnesorge Ohl numbers. As part of this work, an in-house coupled level set volume of fluid solver is developed based on OpenFOAM libraries. It uses improved curvature calculation techniques like smoothening and the closest point search method. Flow is assumed to be axisymmetric. Approximately 95 different cases were simulated to investigate the effect of Weg and Ohl numbers on secondary breakup for Newtonian, shear-thinning, and shear-thickening fluids. Ohl varies from 10−3 to 101, and, correspondingly, Weg varies from 101 to 103. The non-Newtonian rheology is modeled as a power-law fluid, and the power-law index n ranged from 0.2–1.8. The present work describes the flow field near the droplet and the effects of non-Newtonian parameters and viscosity on the flow field. The various aspects of droplet dynamics like droplet deformation ratio y, deformation rate ẏ, and coefficient of pressure Cp are studied and compared with the internal flow theory. A generalized relation for critical Weber number Weg,cr is proposed for both Newtonian and non-Newtonian fluids and is shown in a phase diagram plot to map the different regimes of secondary droplet breakup.

Electromagnetohydrodynamic Electroosmotic Flow and Entropy Generation of Third-Grade Fluids in a Parallel Microchannel.

The present paper discusses the electromagnetohydrodynamic (EMHD) electroosmotic flow (EOF) and entropy generation of incompressible third-grade fluids in a parallel microchannel. Numerical solutions of the non-homogeneous partial differential equations of velocity and temperature are obtained by the Chebyshev spectral collocation method. The effects of non-Newtonian parameter Λ, Hartman number Ha and Brinkman number Br on the velocity, temperature, Nusselt number and entropy generation are analyzed in detail and shown graphically. The main results show that both temperature and Nusselt number decrease with the non-Newtonian physical parameter, while the local and total entropy generation rates exhibit an adverse trend, which means that non-Newtonian parameter can provoke the local entropy generation rate. In addition, we also find that the increase of non-Newtonian parameter can lead to the increase of the critical Hartman number Hac.

Fully Developed Flow of Third-Grade Fluid in the Plane Duct with Convection on the Walls

In this paper, an appropriate analysis has been performed to study the incompressible fully developed flow of a non-Newtonian third-grade fluid in a plane duct with convection on the walls. The governing equations, continuity, momentum and energy for this problem are reduced to a nonlinear ordinary form. The momentum nonlinear equation and the resulting energy equation with Robin mixed boundary condition are solved with the collocation method. The effects of non-Newtonian parameter on dimensionless velocity profiles, dimensionless temperature profiles and also effect of Biot number on dimensionless temperature profiles have been shown. Finally, the results show that the collocation method was successfully used for solving nonlinear differential equations with Robin mixed condition.

Group-Theoretic Approach to Boundary Layer Equations of an Oldroy-B Fluid

Boundary layer equations are derived for the first time for an Oldroy-B fluid. The symmetry analysis of the equations is performed using Lie Group theory and the partial differential system is transferred to an ordinary differential system via symmetries. Resulting equations are numerically solved for the case of the stretching sheet problem. Effects of non-Newtonian parameters on the solutions are discussed.

Similarity Solutions for Boundary Layer Equations of a Powel-Eyring Fluid

Boundary layer equations are derived for the first time for the Powel-Eyring fluid model, a non-Newtonian model proposed for pseudoplastic behavior. Using a scaling symmetry of the equations, partial differential system is transferred to an ordinary differential system. Resulting equations are numerically solved using a finite difference algorithm. Effects of non-Newtonian parameters on the solutions are discussed.

Homotopy Perturbation Method for Flow of a Third-grade Fluid Through a Vertical Concentric Annulus

Abstract This paper considers a theoretical study on steady incompressible flow of third grade fluid in helical screw rheometer (HSR) with zero flight angles (a vertical concentric annulus). The developed second order non linear coupled differential equations are solved by homotopy perturbation method. Expressions for torsional and longitudinal velocity components are derived. The effects of non-Newtonian parameter β on the velocity profiles are also presented through graphs. It is observed that the velocity profiles are strongly depending upon the Non-Newtonian parameter β.

Boundary Layer Equations and Lie Group Analysis of a Sisko Fluid

Boundary layer equations are derived for the Sisko fluid. Using Lie group theory, a symmetry analysis of the equations is performed. A partial differential system is transferred to an ordinary differential system via symmetries. Resulting equations are numerically solved. Effects of non‐Newtonian parameters on the solutions are discussed.

Convective heat and mass transfer in a non-Newtonian-flow formation in Couette motion in magnetohydrodynamics with time-varing suction

An analysis is carried out to study the effect of heat and mass transfer on a non-Newtonian-fluid between two infinite parallel walls, one of them moving with a uniform velocity under the action of a transverse magnetic field. The moving wall moves with constant velocity in the direction of fluid flow while the free stream velocity is assumed to follow the exponentially increasing small perturbation law. Time-dependent wall suction is assumed to occur at permeable surface. The governing equations for the flow are transformed into a system of nonlinear ordinary differential equations by perturbation technique and are solved numerically by using the shooting technique with fourth order Runge-Kutta integration scheme. The effect of non-Newtonian parameter, magnetic pressure parameter, Schmidt number, Grashof number and modified Grashof number on velocity, temperature, concentration and the induced magnetic field are discussed. Numerical results are given and illustrated graphically for the considered Problem.

Laguerre spectral approximation of Stokes’ first problem for third-grade fluid

A Laguerre–Galerkin method is proposed and analyzed for Quasilinear parabolic differential equation which arises from Stokes’ first problem for a third-grade fluid on a semi-infinite interval. By reformulating this equation with suitable functional transforms, it is shown that the Laguerre–Galerkin approximations are convergent on a semi-infinite interval with spectral accuracy. An efficient and accurate algorithm based on the Laguerre–Galerkin approximations to the transformed equations is developed and implemented. Effects of non-Newtonian parameters on the flow phenomena are analyzed and documented.

Fourier–Galerkin domain truncation method for Stokes’ first problem with Oldroyd four-constant liquid

Using the Fourier–Galerkin method with domain truncation strategy, Stokes’ first problem for Oldroyd four-constant liquid on a semi-infinite interval is studied. It is shown that the Fourier–Galerkin approximations are convergent on the bounded interval. Moreover, an efficient and accurate algorithm based on the Fourier–Galerkin approximations is developed and implemented in solving the differential equations related to the present problem. Also, the effects of non-Newtonian parameters on the flow characteristics are obtained and analyzed. The method developed here is so general that it can be used to study the mathematical models that involve the flow of viscous fluids with shear rate-dependent properties: For example, models dealing with polymer processing, tribology & lubrication, and food processing.

On Stokes' problem for the flow of a third-grade fluid induced bya variable shear stress

The flow of an incompressible third-grade fluid over an infinite wall is considered. The flow is due to a variable shear stress. Both the series and the numerical solutions of the nonlinear partial-differential equation resulting from the momentum equation are obtained. Effects of non-Newtonian parameters on the flow phenomena are analyzed. It is found that with an increase in second-grade parameter and third-grade parameter, the velocity decreases and thus, the boundary-layer thickness increases.PACS No.: 47.15.cb

On Similarity Solutions for Three Dimensional Flow of Second Order Fluids

The existence of similarity solutions for the steady three-dimensional boundary layer flow of a viscoelastic fluid has been investigated. It has been shown that similarity solutions exist for two mainstream flow patterns which correspond to the flow near a stagnation point. The non-linear boundary value problem governing one of these stagnation point flows has been solved numerically combined with a perturbation approach. It is found that the effects of non-Newtonian parameters are to increase the velocity in the boundary layer. Some relevant particular cases have also been discussed.