Steady Flow Of non-Newtonian Fluid Research Articles

Steady flow of non-Newtonian fluids: Momentum and heat transfer around a rectangular cylinder

This research aims to explore the impact of cross-sectional aspect ratio (AR), power-law index (n), Reynolds number (Re), and Prandtl number (Pr) on convective heat transfer rates using the Nusselt number (Nu) and coefficient of drag (CD) as a key metric. Numerical simulations employ the ANSYS FLUENT solver with the finite volume method. The SIMPLE scheme couples pressure and velocity, and the QUICK differencing scheme discretizes convective terms. This study varies the aspect ratio by adjusting the length-to-width ratio (b/D) to explore different configurations of AR = 1–5 and Pr = 0.7, 1, and 7, which investigate 5 ≤ Re ≤ 10 and 0.2 ≤ n ≤ 1, respectively. An increase in the Reynolds number is observed to diminish the thermal boundary layer thickness, resulting in an escalation of heat transfer rates. Additionally, the Nusselt number exhibits an upward trend with an increase in the Prandtl number. The investigation reveals a decrease in Nu with an increase in both AR and n. Specifically, higher aspect ratios and power-law indices are associated with reduced heat transfer rates. The AR emerges as a significant factor, influencing the coefficient of drag, with CD values showing an increase as AR rises, particularly at low Re. Moreover, CD is found to increase with an elevation in the n value. This study explores new ground by investigating power-law fluid behavior and heat transfer phenomenon across varied aspect ratios. These insights not only enhance the design of heat transfer systems with non-Newtonian fluids but also pave the way for future research in this less explored domain.

On the steady flow of non-newtonian fluid through multi-stenosed elliptical artery: A theoretical model

The study of blood flow through stenotic arteries is more important as the existence and progression of stenosis may lead to severe damage. The current study aims to analyze and understand the non-Newtonian nature of blood flow through the multi-stenosed artery of an elliptical cross-section. The Carreau fluid model accounts for the non-Newtonian nature of blood. The mathematical equations are transformed to dimensionless form, and assumptions of mild stenosis are employed to reduce the non-linearity of the mathematical model. The perturbation method via polynomial technique is utilized to solve the resulting equations by considering We2 as the perturbation parameter. The results of the velocity and wall shear stress are examined graphically. It is found that stenosis severity substantially impacts flow velocity in the narrower portion of the artery. The stenosis growth strongly affects the flow velocity and wall shear stress in the stenotic region. The non-Newtonian effects are found to dominate along the minor axis. This fact assures that the conduit’s narrower cross-section strengthens the fluid’s non-Newtonian behavior. It is observed that the non-Newtonian fluid has a smaller velocity than the Newtonian fluid. Moreover, non-Newtonian fluid has a different nature along the minor and major axes, but Newtonian fluid has the same behavior.

Influence of Couple Stresses and Thermophoresis on Free Convective Heat and Mass Transfer of Viscoelastic Fluid.

A theoretical study has been developed to investigate the influence of thermophoresis and couple stresses on the steady flow of non-Newtonian fluid with free convective heat and mass transfer over a channel bounded by two permeable plates. The considered non-Newtonian fluid follows a viscoelastic model. The problem is modulated mathematically by a system of non-linear differential equations pertaining to describe the continuity, momentum, energy, and concentration. These equations involve the effects of viscous dissipation and chemical reaction. The numerical solutions of the dimensionless equations are found as a function of the physical parameters of this problem. The numerical formulas of the velocity (u), temperature Φ and concentration Θ as well as skin friction coefficient T*, Nusselt number(Nu) and Sherwood number(Sh) are computed. The physical parameter's effects of the problem on these formulas are described and illustrated graphically through some figures and tables. It is observed that any increase in the thermophoretic parameter T leads to reduce in velocity profiles as well as concentration layers. In contrast, the velocity increases with increasing the couple stresses inverse parameter.

Influence of heat generation on magnetohydrodynamic (MHD) flow using a theory of kinetics for liquids

In the present article, the influence of heat generation on the magnetohydrodynamic (MHD) flow of an Eyring–Powell fluid along a permeable plate has been explored. The influence of heat generation or absorption on a steady flow of non-Newtonian fluid over a surface is investigated. The governing equations obtained from Eyring–Powell fluid model are transubstantiated into ordinary differential equations using suitable transformations. Along with the Runge–Kutta method, we attained a numerical solution of the present problem by explicating the shooting technique. Influences of distinct parameters on temperature and the velocity field profiles are highlighted in graphs and tables. The acceleration in the value of γ, velocity profile shows decreasing behavior, but recovery occurs with an increase in M. The streamlines and three-dimensional results have been shown graphically for a selection of different parameters. Numerical results of the present work have been discussed with the support of tables.

Non-isothermal Steady Flow of Non-Newtonian Fluid in an Axisymmetric Channel

Non-isothermal steady-state flow of a viscoplastic fluid in an axisymmetric channel is studied with account for viscous dissipation at a specified constant flow rate. The rheology of the medium is described by the Herschel-Bulkley law with a temperature dependence of yield stress and consistency defined by exponential law. On the solid wall, the no-slip boundary condition and the assigned temperature are used. The mathematical statement of the problem includes the dimensionless motion and energy equations and boundary conditions. The problem is solved numerically using a finite-difference approach. The difference equations are solved by sweep method. When applying a shock-capturing method for calculating the flow, the rheological model is regularized in order to eliminate stress singularity in the regions of zero shear rates. The steady-state distributions of velocity, temperature, viscosity, and dissipative function are obtained. A limiting value of pressure drop defining the existence domain of a steady solution is proved to exist. Two problem solutions are obtained at a specified pressure drop, which are referred to as high- and low-temperature flow regimes. As a result of computations, different flow structures with unyielded regions occurring near symmetry line and in the dead zone next to a solid wall are revealed.

Secondary flow behavior of electrolytic viscous fluids with Bird-Carreau model in curved microchannels

A curved channel is indispensable for the lab-on-chips system because it provides a convenient scheme for increasing the channel length per unit chip area in the direction of net flow. A secondary Dean flow in curved rectangular microchannels is examined by applying a finite volume scheme with a semi-implicit method for pressure-linked equations revised (SIMPLER) algorithm for the steady flow of non-Newtonian fluids with dilute concentrations in electrolyte solution. The proposed framework is based on a theoretical model coupled with the Cauchy momentum equation of Bird-Carreau fluid, electrostatic interaction, and net charge conservation. The shear thinning effect on the secondary flow at the turn is analyzed with respect to the parameters of interest including zero-shear viscosity and power-law index. The simulation results for the realistic microchannel indicate that the streamwise axial velocity tends to shift toward the inner wall and this is caused by a stronger spanwise pressure gradient, resulting from a sufficiently low Dean number. In the case of the non-Newtonian fluid, the axial velocity becomes a blunt profile by spreading to each side of the wall, and its flow skewness directed asymmetrically to the inner wall is higher than that in the case of the Newtonian fluid. The attaining trend of higher flow skewness is changed by the competing effect of shear thinning and is well matched with the behavior of the secondary flow.

On steady flow of non-Newtonian fluids with frictional boundary conditions in reflexive Orlicz spaces

A stationary viscous incompressible non-Newtonian fluid flow problem is studied with a non-polynomial growth of the extra (viscous) part of the Cauchy stress tensor together with a multivalued nonmonotone frictional boundary condition described by the Clarke subdifferential. We provide an abstract result on existence of solution to a subdifferential operator inclusion and a hemivariational inequality in the reflexive Orlicz–Sobolev space setting modeling the flow phenomenon. We establish the existence result, and under additional conditions, also uniqueness of a weak solution in the Orlicz–Sobolev space to the flow problem.

Steady flow of non-Newtonian fluids — monotonicity methods in generalized Orlicz spaces

Our purpose is to show the existence of weak solutions to steady flow of non-Newtonian incompressible fluids with nonstandard growth conditions of the Cauchy stress tensor. We are motivated by the fluids of strongly inhomogeneous behavior and characterized by rapid shear thickening. Since L p framework is not sufficient to capture the described model, we describe the growth conditions with the help of a general x -dependent convex function and formulate our problem in generalized Orlicz spaces.

Non-Newtonian flow at lowest order, the role of the Reiner–Rivlin stress

In 1963 Giesekus [H. Giesekus, Die simultane Translations- und Rotationsbewegung einer Kugel in einer elastikoviskosen Flüssigkeit, Rheol. Acta 3 (1962) 59–71] showed that a Stokes velocity field also satisfies the equilibrium equation for the flow of a restricted form of the second order fluid. The same result was found by Tanner [R.I. Tanner, Plane creeping flows of incompressible second order fluids, Phys. Fluids 9 (1966) 1246–1247] in 1966 in the context of plane flow for which the restrictions on the second order fluid are not relevant. Tanner [R.I. Tanner, Some extended Giesekus-type theorems for non-Newtonian fluids, Rheol. Acta 28 (1989) 449–452] later showed that the velocity field for the inertialess, plane flow of the generalized Newtonian fluid is also the velocity field for the flow of a special form of the Criminale–Ericksen–Filbey (CEF) stress system [W.O. Criminale Jr., J.L. Ericksen, G.L. Filbey Jr., Steady flow of non-Newtonian fluids, Arch. Rat. Mech. 1 (1958) 410–417]. In this paper it will be shown that the results of Giesekus and Tanner are special cases of a more general theorem in which the velocity field, in any dimension, of the equilibrium Reiner–Rivlin problem also satisfies the corresponding problem for the materially steady stress system (a generalization of the CEF system) provided the coefficients of the Reiner–Rivlin stress [M. Reiner, A mathematical theory of dilatancy, Am. J. Math. 67 (1945) 350–362; R.S. Rivlin, The hydrodynamics of non-Newtonian fluids, Proc. R. Soc. Lond. 193 (1948) 260–281] are derivable from a strain-rate potential. As with the Giesekus–Tanner theorems the new theorem holds generally for velocity boundary conditions, but in some cases, such as the free jet, stress boundary conditions can be imposed.

Steady flow of non-Newtonian fluids through rectangular ducts

The present paper contains a numerical study for the secondary flow of a Reiner-Rivlin non-Newtonian fluid in laminar flow through ducts of square and rectangular cross section. Finite difference methods are developed to obtain the primary flow, the secondary flow, and the friction factor. The influence of the second normal stress coefficient, the Reynolds number, and the aspect ratio on the magnitude of the secondary flow are considered. In general, the effect of the secondary flow on the primary flow rate and friction factor is found to be negligible.

Numerical study on the flow of a non-Newtonian fluid through an axisymmetric stenosis.

The laminar steady flow of non-Newtonian fluid (biviscosity fluid) through an axisymmetric stenosis is calculated using the finite element methods. The flow pattern, the separation and reattachment points, and the distributions of pressure and shear stress at the wall are obtained. Then, the axial force acting on the stenosis is evaluated. It is suggested by the authors that this force can become one of the causes of post-stenotic dilatation. Calculated results show that the non-Newtonian property of blood weakens the distortion of flow pattern, pressure and shear stress at the wall associated with the stenosis and that the non-Newtonian property of blood decreases the axial force acting on the stenosis.

Flow of micropolar fluid through a tube with stenosis.

A mathematical model for the steady flow of non-Newtonian fluid through a stenotic region is presented. The results indicate that the general shape and size of the stenosis together with rheological properties of blood are important in understanding the flow characteristics and the presence of flow separation.

Steady Flow of Non-Newtonian Fluids in a Square Duct

Steady Flow of Non-Newtonian Fluids in a Square Duct

Steady shear flow of non-Newtonian fluids

In recent years, considerable effort has been expended in attempting to gain an understanding of the behavior of non-Newtonian fluids in shear. MARKOVITZ [1] recently attempted to collect and organize experimental data and to compare it with predictions of existing theories. One difficulty is that conclusions which can be drawn from different types of experiments seem to disagree. Theoretical work on the steady flow of non-Newtonian fluids has brought to light a new phenomenon. According to the linear theory of viscous fluids, it is always possible for a fluid flowing through a cylindrical tube, to which it adheres, to undergo steady rectilinear motion, each particle moving with constant speed in a straight line parallel to the generators of the cylinder. Analyses made by ERICKSEN [2] and by GREEN • RIVLm [31 show that, for many ideal fluids described by the REINER [41 -RIVLIN [5] theory, this simple type of motion is possible only for very special shapes of tubes and that, in general, it is replaced by a flow consisting of such a rectilinear motion combined with a secondary flow in cross-sectional planes. Using the more general theory of fluids proposed by RIVLIN & ERICKSEN [61, LANGLOIS [7] has obtained solutions involving secondary flows in tubes and other types of "boundary geometries. As has been discussed by RIVLIN [8], similar secondary flows have been observed in the mean flow of fluids through non-circular tubes when the motion is turbulent. To our knowledge, it is not known whether secondary flows occur in the steady flow of any real fluid through tubes. Our analysis indicates that, if the conclusions which ROBERTS [9] drew from his experiments ai-e correct, the fluids which he observed should be capable of undergoing rectilinear motionthrough tubes of any shape. MARKOVITZ [11 draws self-consistent conclusions from other experimental data which contradict some of ROBERTS' conclusions. Calculations made in accordance with these conclusions suggest that secondary flows are to be expected in some shapes of tubes. We offer a partial proof that if secondary flows do not occur in elliptical tubes, they will not occur in tubes of any other shape.

Steady flow of non-Newtonian fluids through tubes

Steady flow of non-Newtonian fluids through tubes