Flow Of non-Newtonian Power-law Fluid Research Articles

Transient Friction Analysis of Pressure Waves Propagating in Power-Law Non-Newtonian Fluids

Modulated pressure waves propagating in the drilling fluids inside the drill string are a reliable real-time communication technology that transmit data from downhole to the surface during oil and gas drilling. In the analysis of pressure waves’ propagation characteristics, the modeling of transient friction in non-Newtonian fluids remains a great challenge. This paper establishes a numerical model for transient pipe flow of power-law non-Newtonian fluids by using the weighted residual collocation method. Then, the Newton–Raphson method is applied to solve the nonlinear equations. The numerical method is validated by using the theoretical solution of Newtonian fluids and is proven to converge reliably with larger time steps. Finally, the influencing factors of the wall shear stress are analyzed using this numerical method. For shear-thinning fluids, the friction loss of periodic flow decreases with the increase in flow rate, which is opposite to the variation law of friction with the flow rate for stable pipe flow. Keeping the amplitude of pressure pulsation unchanged, an increase in frequency leads to a decrease in velocity fluctuations; therefore, the friction loss decreases with the increase in frequency.

Power-law fluid annular flows between concentric rotating spheres subject to hydrodynamic slip

ABSTRACT We report analytical solutions to the problem of non-Newtonian power-law fluid flows in the annular space between a pair of concentric spherical surfaces rotating at distinct angular velocities with the inner and outer wall boundaries subject to general asymmetric hydrodynamic slip conditions. Analytical solutions are possible because of assuming constant valued apparent hydrodynamic slip lengths in the linearized kinematic slip conditions, and our solutions can be validated against the limiting results of Newtonian fluids, no-slip conditions or a single rotating sphere reported in previous literature. Comprehensive systematic parametric studies show that (additional to the power-law fluid flow behavior index) the degree of hydrodynamic slip at the inner surface is the dominant factor that determines the limiting values of the viscous torque exerted on the inner sphere as the outer-to-inner radius ratio assumes significantly large values. Nonetheless, the flow behavior index and outer slip length prove to be the crucial key parameters responsible for a variety of torque responses, which can be categorized by a compact analytical expression, as the outer-to-inner radius ratio is increased in the small to moderate regime. We propose a criteria which identifies the proper slip length and outer-to-inner radius ratio combinations for a given power-law flow behavior index such that the hydrodynamic slip wall effects of the outer surface can be minimized or eliminated. A simple method is also presented to characterize and quantify the apparent hydrodynamic slip effects by use of the concentric rotating spheres viscometer.

Wall-modeled large-eddy simulation of turbulent non-Newtonian power-law fluid flows

For high-fidelity predictions of turbulent flows in complex practical engineering problems, the Wall-Modeled (WM) Large-Eddy Simulation (LES) has aroused great interest. In the present study, we prove that the conventional Wall-Stress Models (WSMs) developed for WMLES of Newtonian fluids fail to predict the shear-thinning-induced drag reduction in power-law fluids. Therefore, we propose novel algebraic, integrated, and Ordinary-Differential-Equation (ODE) WSMs, for the first time, for WMLES of power-law Non-Newtonian (NN) fluids and assess their performance against reference Wall-Resolved (WR) LES solutions. In addition, the effects of the key model parameters, including the WSM type, sampling height, sampling cell, and axial grid resolution are explored, and it is revealed that turbulent NN flow predictions have a much higher sensitivity to the choice of WSM, compared to their Newtonian counterparts. It is manifested that, in contrast to WRLES, accurate modeling of the mean apparent and subgrid-scale NN viscosities in the Non-Newtonian ODE (NNODE) model can improve the predictions considerably. Therefore, closures with lower uncertainties on coarse WMLES grids are sought for these terms. Finally, the best performance for the present test cases is obtained via the integrated NN WSM, sampling at the lower edge of the log layer within the third off-the-wall grid cell. Nevertheless, the new NNODE WSM can have an advantage in the presence of non-equilibrium effects in more complex problems.

Quadratic convection in a power-law fluid with activation energy and suction/injection effects

Current research demonstrates the effects of activation energy and quadratic convection on the non-Newtonian power-law fluid flow through an inclined permeable plate. In addition, the fluid’s heat transfer is carefully investigated while taking convective boundary conditions and thermal radiation into account. Also, mass transfer between the flow and the inclined plate was investigated for binary chemical reactions. By appropriate transformations, governing fluid flow equations are changed into the dimensionless form. Numerical solution of this system of equations is obtained by both the local non-similarity method and the successive linearisation method. The effect of emerging parameters on the flow and physical quantities are examined with Biot number ( B i ), activation energy coefficient ( E ), the chemical reaction parameter ( M ), quadratic convection parameters ( α 1 , α 2 ), inclination angle ( Ω ), the suction/injection parameter ( f w ) and the radiation parameter ( R d ). Further, the rate of mass and heat transfer are compared for all the instances of linear and quadratic convective flows. Power-law fluids concentration is increased with activation energy, while it diminishes with chemical reaction. The thickness of thermal boundary layer is considerably enhanced by both Biot number and radiation parameters. The thermal and solutal rates are increasing functions of quadratic convection parameters.

Momentum and heat transfer characteristics of a rotating elliptical cylinder in vortex shedding flow of power-law fluids

A numerical analysis is carried out to comprehend the fluid flow and heat transfer phenomena of non-Newtonian power-law fluid flow around a rotating elliptic cylinder. The investigations are accomplished for parameters, namely, the aspect ratio of the cylinder, e=0.1; the rotational speed of the cylinder, 0.5≤α≤2.0; the Reynolds number, Re=100; the power-law index, 0.4≤n≤1.6; and the Prandtl number, 1≤Pr≤100. A detailed vorticity and isotherm patterns are presented to demonstrate the vortex shedding and heat transfer phenomenon around the cylinder. The results clearly show the strong dependency of fluid behaviors and rotational speed on flow and heat transfer phenomena. At a low rotational speed (α≤1.0), the standard vortex-shedding patterns appear. The behavior of the fluid mainly affects the size and strength of the vortices. At a higher rotational speed (α > 1.0), a hovering vortex (HV) appears for Newtonian and shear-thinning fluids. The shear-thinning tendency of the fluid encourages the formation of HV; however, the HV is not observed for shear-thickening fluids. Due to the rotational motion of the cylinder, the surface Nusselt number varies in a periodic manner with time/orientation. As expected, the Prandtl number (Pr) and shear-thinning (n<1.0) behavior of the fluid encourage the heat transfer from the cylinder. The rotational motion of the cylinder also favors the heat transfer phenomena. Finally, a correlation is presented for the time average surface Nusselt number (Nuavg) as a function of the Prandtl number (Pr), fluid behavior (n), and rotational speed (α).

Non-Newtonian power-law fluids with variable magnetic field and slip conditions

The purpose of this paper is to study the effect of heat transfer and flow of non-Newtonian power-law fluids towards a stretching sheet in the appearance of transverse magnetic field with slip boundary conditions. Suitable similarity transformations are used to change the non-linear partial differential equations to ordinary differential equations. For the numerical solution Maple software by applying built-in command dsolve with numeric is utilized. It is noticed from the obtained results that an increase in the magnetic parameter results in a decrease in the dimensionless velocity profile and in the stream function while the temperature profile increases for the Newtonian, dilatant, and pseudo-plastic fluids. Increasing the velocity slip parameter, a reducing behavior can be seen in the stream function and in the velocity profile while temperature profile is enhancing. Moreover, with increasing thermal slip, a decrease occurs in the dimensionless temperature. The variations in the velocity and temperature profiles under dimensionless parameters are significant for n = 0.8 (pseudo-plastic fluid) rather than for n = 1 (Newtonian fluid) and n = 1.02 (dilatant fluid).

A numerical study of two-dimensional laminar flow of power-law fluids around three circular cylinders in side-by-side arrangement

PurposeThis study aims at investigating two-dimensional laminar flow of power-law fluids around three unconfined side-by-side cylinders.Design/methodology/approachThe numerical study is performed by solving the governing (continuity and momentum) equations using a finite volume-based code ANSYS Fluent. The numerical results have been presented for different combinations of the governing dimensionless parameters (dimensionless spacing, 1.2 = L = 4; Reynolds number, 0.1 = Re = 100; power-law index, 0.2 = n = 1.8). The dependence of the kinematic and macroscopic characteristics of the flow such as streamline patterns, distribution of the surface pressure coefficient, total drag coefficient with its components (pressure and friction) and total lift coefficient on these dimensionless parameters has been discussed in detail.FindingsIt is found that the separation of the flow and the apparition of the wake region accelerate as the dimensionless spacing decreases, the number of the cylinder increases and/or the fluid behavior moves from shear-thinning to Newtonian then to shear-thickening behavior. In addition, the distribution of the pressure coefficient on the surface of the cylinders presents a complex dependence on the fluid behavior index and Reynolds number when the dimensionless spacing between two adjacent cylinders is varied. At low Reynolds numbers, the drag coefficient of shear-thinning fluids is stronger than that of Newtonian fluids; this tendency decreases progressively with increasing of Re until a critical value; beyond the critical Re, the opposite trend is observed. The lift coefficient of the middle cylinder is null, whereas, the exterior cylinders experience opposite lift coefficients, which show a complex dependence on the dimensionless spacing, the Reynolds number and the power-law index.Originality/valueThe flow over bluff bodies is a practical engineering problem. In the literature, it can be seen that the previous studies on non-Newtonian fluids are limited to the flow over one or two cylinders (effect of an odd number of cylinders on each other). Besides that, the available results concerning the flow of Newtonian fluids over three cylinders are limited to the high Reynolds numbers region only. However, this work treats the flow of non-Newtonian power-law fluids past three circular cylinders in side-by-side arrangements under a wide range of Re. The outcome of the present study demonstrates that the augmentation of the geometry complexity to three cylinders (effect of pair surrounding cylinders on the surrounded ones in what concerns Von Karman Street phenomenon) causes a drastic change in the flow patterns and in the macroscopic characteristics. The present results may be used to predict the flow behavior around multiple side-by-side cylinders.

Use of Random Vortex Method in Simulating Non-Newtonian Fluid Flow in a T-junction for Various Reynolds Numbers and Power-law Indexes

Past studies show that until now the Random Vortex Method (RVM) has only been used to solve the flow of Newtonian fluids. In this paper, by presenting a new approach, the RVM is developed for the first time with the aim of simulating the flow of non-Newtonian fluids. For this purpose, a numerical simulation of two-dimensional flow of non-Newtonian power-law fluid in a T-junction is presented. The simulation is conducted for Re = 50-200 at the inlet of the channel and different power-law indexes (n = 0.2-1.4). The RVM solves the Navier–Stokes equations as a function of time and determines the velocity at any point of the channel directly and without determining a mesh on the geometry. Potential velocity, an initial condition for the flow analysis by the RVM, is obtained using the Schwarz–Christoffel conformal mapping. The effect of two parameters of power-law index and Reynolds number on the recirculation zone has been investigated. Acceptable agreement among the results of the present study and the existing numerical and experimental results shows the capability of the proposed method, according to which the RVM can be considered a powerful promising method in simulating the non-Newtonian fluids in laminar and turbulent flow regimes.

A third-order two-step numerical scheme for heat and mass transfer of chemically reactive radiative MHD power-law fluid

A two-stage third-order numerical scheme is proposed for solving ordinary differential equations. The scheme is explicit and implicit type in two stages. First, the stability region of the scheme is found when it is applied to the linear equation. Further, the stability conditions of the scheme are found using a linearized homogenous set of differential equations. This set of equations is obtained by applying transformations on the governing equations of heat and mass transfer of incompressible, laminar, steady, two-dimensional, and non-Newtonian power-law fluid flows over a stretching sheet with effects of thermal radiations and chemical reaction. The proposed scheme with an iterative method is employed in two different forms called linearized and non-linearized. But it is found that the non-linearized approach performs better than the linearized one when residuals are compared through plots. Additionally, the proposed scheme is compared to the second-order central finite difference method for second-order non-linear differential equations and the Keller-Box/trapezoidal method for a linear differential equation. It is determined that the proposed scheme is more effective and computationally less expensive than the standard/classical finite difference methods. Moreover, the impact of magnetic parameter, radiation parameter, modified Prandtl and Schmidt numbers for power-law fluid, and chemical reaction rate parameter on velocity, temperature, and concentration profiles are displayed through graphs and discussed. The power-law fluid’s heat and mass transfer simulations are also carried out with varying flow behavior index, sheet velocity, and mass diffusivity. We hoped that this effort would serve as a guide for investigators tasked with resolving unresolved issues in the field of enclosures used in industry and engineering.

Analysis of the transient flow of non-Newtonian power-law fluids in homogeneous reservoirs with the elastic outer boundary

Analysis of the transient flow of non-Newtonian power-law fluids in homogeneous reservoirs with the elastic outer boundary

Flow and heat transfer characteristics of non-Newtonian fluid over an oscillating flat plate

The primary purpose of the present study is to investigate the unsteady flow and heat transfer characteristics of non-Newtonian power-law fluid over an oscillating flat plate. The power-law fluid model is employed to distinguish the non-Newtonian fluid behavior, which has wide applications in nature and technology, such as crude oil exploitation, polymer processing and some bio applications. In this work, the governing equations are set up using the non-Newtonian fluid model. The radial basis function collocation method (RBFCM) and the finite element method (FEM) are used to solve the coupled equations. The numerical results of the fluid velocity and fluid temperature fields are analyzed in detail. For authentication of the proposed schemes, the results are compared with earlier research works. To further verify the validity of the FEM and the RBFCM results, the flow behavior of crude oil was studied and the obtained results were found to be consistent with each other using both methods. Our results provide further guidance for evaluation aspects dealing with crude oil in a pipe, which are basic tools in oil and gas explorations.

Critical parameters for non-Newtonian shear-thickening power-law fluids flow across a channel confined circular cylinder

In this work, the critical parameters for an incompressible flow of non-Newtonian shear-thickening power-law fluids across a channel confined circular cylinder have been investigated numerically. The governing equations have been solved by using the finite volume method for the wide range of power-law (1≤n≤1.8) fluids and for two values of wall blockage ratio (β=2 and 4). The present methodology has extensively been validated with numerical and experimental results available for limited conditions. Transitional insights of channel confined cylinder, in particular, critical parameters indicating the transitions from creeping to separating flows (i.e., onset of steady symmetric wake formation), and from steady symmetric wake to unsteady asymmetric wake formation (i.e., onset of vortex formation) are investigated and presented in terms of the critical Reynolds numbers (Rec and Rec). The relative impacts of unconfined and confined flows on these critical parameters have also been explored. In general, both onsets of the flow separation and wake asymmetry delayed with an increasing values of the power-law index (n) and the wall confinement (λ). The dependence of critical Re on n for the confined (finite β) flow are, however, completely opposite to that for unconfined (β=∞) flow, i.e., critical Re decreased with increasing n. The influence of power-law index on the onset of vortex is quite stronger to that on the onset of wake formation. For instance, Rec for β=(2,4,∞) altered from (12.5, 7.25, 6.25) to (30.5, 9.25, 0.75) and the corresponding changes with Rec are noted from (84.5, 70.25, 46.5) to (449.5, 179.5, 33.5) as n varied from 1 to 1.8, respectively. The Stokes paradox (i.e., no creeping flow even as Re→0) apparent with unconfined flow of power-law fluids is irrelevant in confined flows, under otherwise identical conditions. Finally, the predictive correlations for critical Re as a function of dimensionless parameters (n and β) are presented for their easy use in engineering analysis.

Non-Newtonian power-law fluid flow over obstacles embedded inside a cavity

In this study, the flow of non-Newtonian fluid inside the lid-driven cavity with obstacle(s) is examined. The behavior of the fluid is described by the Ostwald-de Waele or power-law model. The lattice Boltzmann method (LBM) with a multiple-relaxation-time (MRT) collision model is employed to simulate complex fluid flows around the circular and square obstacles embedded inside a cavity. The stability of the present MRT-LBM algorithm in terms of so-called, cell-Reynolds number is investigated. The physics of flow structure and examinations of streamlines and vorticity contours are carried out for power-law as well as Newtonian fluids. For a single obstacle, the effects of various parameters such as Reynolds number (with respect to lid-dimension), obstacle size, power-law index, and shape of the obstacle on the flow characteristics and vortex formation are investigated. Furthermore, the effect of two square obstacles arranged in side-by-side and tandem manners inside the cavity is analyzed. Finally, the complex fluid flow over the multiple square obstacles embedded inside the cavity as a porous block for two blockage ratios is examined.

Flow and heat transfer characteristics of non-Newtonian fluid over an oscillating flat plate

The primary purpose of the present study is to investigate the unsteady flow and heat transfer characteristics of non-Newtonian power-law fluid over an oscillating flat plate. The power-law fluid model is employed to characterize the non-Newtonian fluid behavior, which has wide applications in nature and technology, such as crude oil exploitation, polymer processing and some bio applications. In this study, the coupled governing equations are set up using the non-Newtonian fluid model. The radial basis function collocation method (RBFCM) and the finite element method (FEM) are used to solve the coupled equations. The simulation results on the fluid velocity and temperature distribution are analyzed in detail. For authentication of the proposed schemes, the numerical results are compared with earlier research works. To further verify the validity of the FEM and the RBFCM results, the flow behavior of crude oil was studied and the obtained results were found to be consistent with each other using both methods. Our results provide further guidance for evaluation aspects dealing with crude oil in a pipe, which are basic tools in oil and gas explorations.

Time-dependent power-law nanofluid with entropy generation

This work studies the time-dependent convective flow of non-Newtonian power-law fluid by vertical plate. Fluid flow is studied in the presence of thermal radiation. The Buongiorno model is employed to describe the features of nanofluid. Entropy generation and Bejan number are calculated. The flow, temperature and concentration are given by the system of partial differential equations (PDE’s). The system of PDE’s is transformed into dimensionless form by transformation and then solve implementing finite difference technique. Special emphasis is given to the outcomes of Prandtl number, Reynolds number, Eckert number, radiation parameter, thermophoresis, Brownian parameter, and Schmidt number. Velocity, temperature, concentration, skin friction, Sherwood and Nusselt numbers are graphically analyzed. Graphical results show that velocity of fluid enhanced for high Grashof number while shows opposite behavior for Reynold number. For the high estimation of the thermophoresis parameter and Brownian motion parameter temperature and concentration increase. For the higher value of the radiation parameter, the irreversibility of fluid particles increases while the Bejan number decreases.

Finite difference method for solving a physical problem in fluid flow

Interaction between nonuniform heat source/sink, magnetic field and thermal radiation with heat flux through the flow of non-Newtonian power-law fluid due to a linearly stretching sheet was studied numerically using an implicit finite difference method (FDM). The heat flux is assumed to depend on both the thermal conductivity and the thermal radiation. Besides, the effects of all governing parameters, such as the magnetic parameter, thermal conductivity parameter, the power-law index parameter, Prandtl number, the space-dependent heat source/sink parameter, the temperature-dependent heat source/sink parameter, and the radiation parameter, on the profiles of velocities and temperature are studied and discussed. In particular, thermal radiation was found to play a key role in the heat transfer characteristics and in the formation of thermal boundary layer. Generally, our numerical results reveal that both the velocity and temperature distributions are marginally influenced by both the magnetic parameter and power-law index. A good agreement is observed between our results via finite difference method and the previously published numerical results for some special case.

Stability of hydromagnetic boundary layer flow of non-Newtonian power-law fluid flow over a moving wedge

We consider the two-dimensional laminar boundary-layer flow of power-law fluid over a moving wedge in which the uniform magnetic field is applied normally to the flow. The motion of the mainstream and wedge is approximated in terms of the power of the distance from leading boundary-layer edge which helps to reduce the governing partial differential equations to an ordinary differential equation. No analytic solution is feasible due to high nonlinearity; therefore, the numerical simulations are sought by Chebyshev collocation and shooting techniques. These techniques provide a means to assess physical insights into the hydrodynamics of complex flows and particularly the Chebyshev collocation method enables the construction of efficient tools suitable for nonlinear problems. This method often leads to a matrix-based analysis and an iterative technique needs to be employed to solve the problem. The various results on the physical parameters show that the shear-thinning and shear-thickening solutions are demarcated by the Newtonian fluid. It is also noticed that the system yielded a non-unique solution structure for a given set of parameters. However, the non-uniqueness of the solutions disappears for increasing the magnetic field. To assess the nature of the non-unique solutions, it is important to perform the linear stability using large-time asymptotics. This analysis gives as to which of these solutions is practically feasible and models the flow. Eigensolution-based analysis reveals that the first solution is always stable while the other one leading to unstable mode. The results further show that an increase in the magnetic field stabilizes the fluid flow over the moving wedge and promotes the unique solution to the problem. Further, the obtained numerical results are compared by examining the large λ asymptotics. It is observed that there is a qualitative comparison between solutions. The hydrodynamics behind the magnetic field and non-Newtonian fluid are discussed in detail.

Hydrodynamic flow of non-Newtonian power-law fluid past a moving wedge or a stretching sheet: a unified computational approach

A unified mathematical equation that combines two different boundary-layer flows of viscous and incompressible Ostwald-de Waele fluid is derived and studied. The motion of the mainstream and the wedge is approximated in the power-law manner, i.e, in terms of the power of the distance from the leading boundary-layer edge. It is also considered that the wedge can move in the same and opposite direction to that of the mainstream. The governing partial differential equations are transformed into the nonlinear ordinary differential equation using a new set of similarity variables. This transformed equation subjected to the boundary conditions describing the flow is then solved using the Chebyshev collocation method. Further, these numerical results are then validated by determining the flow behaviour at far-field by performing asymptotics. The velocity ratio parameter effectively captures and distinguishes two boundary-layer flows. The boundary layer thickness for shear-thinning fluid is thinner compared to corresponding parameters for shear-thickening fluids and is markedly separated by the Newtonian fluid. Further, the boundary-layer flow of the non-Newtonian fluid predicts an infinite viscosity for shear-thinning fluid quite away from the surface. The hydrodynamics of the obtained results is explained thoroughly.

New Integral Solutions for Magnetohydrodynamic Free Convection of Power-Law Fluids Over a Horizontal Plate

An integral analysis has been performed to theoretically investigate the magnetohydrodynamic natural convection flow of non-Newtonian power-law fluids over a semi-infinite horizontal plate with constant surface heat flux. The governing boundary layer equations are transformed into a set of coupled ordinary differential equations using stretching transformation. The resultant equations are solved analytically using the integral method. A set of new infinite polynomial series are introduced for presenting the velocity and pressure profiles, providing more accurate results compared with traditional solutions. Implicit expressions for the Nusselt number and friction coefficient are presented for wide ranges of the generalized Prandtl number (Pr*), the non-Newtonian power-law viscosity index (n), and the generalized Hartmann number (Ha*).

Flow and heat transfer of MHD non-Newtonian power-law fluids due to rotating disk

In flows over rotating disk, substantial additional flow phenomena arise due to the rotational forces or due to the nature of the three-dimensional boundary layer flows. The resulting flow characteristics can be very complex and almost every rotating system reveals novel and unexpected flow characteristics over a sufficiently wide range of variables which affect the hydrodynamic phenomena. This paper focuses on the flow and heat transfer in non-Newtonian power law fluids due to a rotating disk in the presence of magnetic field. The number of independent variables in the highly non-linear partial differential equations was reduced by suitable similarity transformations. The coupled non-linear ordinary differential equations were solved numerically using the finite difference collocation method of MATLAB bvp4c. The effects of the magnetic parameter and Prandtl number on the flow fields and heat transfer rate were investigated for the cases of shear thinning and shear thickening power law fluids. The heat transfer rate reduces as the magnetic field strength increases but increases as the Prandtl number increases for both types of shear thickening and shear thinning fluids. The effects are more significant in the case for shear thinning fluids.